Together with the general session's talks, the conference will host a number of special minisymposia.

Below are confirmed Minisymposia.

When submitting an abstract please select an option whether you wish to have it in a general session or in a specific minisymposium. You will be able to apply through your personal registration platform after the deadline for submitting proposals is closed.

Organizers

Ivanov Alexander A. (Imperial College London, UK), .

Elena Konstantinova (Sobolev Institute of Mathematics, Siberian Branch of Russian Academy of Science, Russia), e_konsta@math.nsc.ru

Description

G2-series are about strong and beautiful mathematics, especially those involving group actions on combinatorial objects. The main goal of G2G2-Minisymposia is to bring together researchers from different mathematical fields to exchange knowledge and results in a broad range of topics relevant to graph theory and group theory with connections to algebraic combinatorics,finite geometries, designs, computational discrete algebra, vertex operator algebras, topological graph theory, network analysis, and their applications in physics, chemistry, biology.

G2G2-Minisymposia is associated with G2G2-Summer School which will be held in Rogla, 29 June - 4 July, as an internal satellite event of 8ECM.

**Research area:** Combinatorics - 05E, 05A, 05B, 05C, 20B, 20C, 20E, 20F, 68R, 68W

Organizers

Aleksander Cwiszewski (Nicolaus Copernicus University, Poland), aleks@mat.umk.pl

Gennaro Infante (Universita della Calabria, Italy), gennaro.infante@unical.it

Paola Rubbioni (University of Perugia, Italy, Department of Mathematics and Computer Sciences), paola.rubbioni@unipg.it

Description

The minisymposium is devoted to recent advances in topological methods in differential equations. The topological approach has been intensively used in the last years to study differential models arising from the life sciences.

The session will be focused on existence, bifurcation, multiplicity, localization, stability and approximation of solutions to elliptic or parabolic differential equations studied by means of topological degree, fixed point index, Conley-type indices, fixed point and critical point theories as well as dynamical systems. Particular attention will be given to real world applications.

Organizer

Marco Buratti (Università di Perugia, Italy), buratti@dmi.unipg.it

Description

"Combinatorial Designs" is a rich branch of Combinatorics, essentially assembling all the discrete structures having some special "balance properties". Among them, we have, in particular, classic t-designs, graph decompositions, and objects arising from finite geometries.

The main mathematical motivation of the precursors of this theory, among which we may include even Euler (the thirty-six officers problem), probably was the intrinsic beauty of these balanced structures and their connection with other branches of mathematics as Group Theory, Finite Fields, and Number Theory.

Design Theory finally became a very active subject of research since when it exploded with the study of “statistical experimental designs” by R.C. Bose and R.A. Fisher in the 1930s.

Nowadays it can be doubtlessly stated that it is widely investigated in view of its important applications in many other fields such as communications, cryptography, and networking.

We hope that this minisymposium will facilitate a rich exchange of ideas between design theorists of all ages from all over the world.

Organizer

Gershon Wolansky (Technion, Israel Inst. of Technology, Israel), gershonw@technion.ac.il

Description

The theory of optimal transport started with the work of Gaspard Monge in the 19th century. While Monge was motivated by geometry, the theory was revived during the second world war by Leonid Kantorovich, whose motivation was economics. Later, the pioneering work of Yann Brenier explored the connection between optimal transport, functional analysis and convexity theory. Since then, the field is growing exponentially.

Today, optimal transport theory has revealed various connections between many fields in mathematical analysis, including PDE, functional analysis, convexity, geometry and found numerous applications in applied science, including kinetic theory, fluid dynamics, computer science, machine learning, optics, shape optimization, and economics. As such, it attracted many theoretical and applied mathematicians in the last decades.

The objectives of this minisymposium are directed to the application of methods of optimal transport to applied sciences as well as numerical algorithms for computations of optimal transport plans and evolution equations using Wasserstein calculus. In particular, applications to economics, game theory, optics, irrigation and fluid dynamics are welcome, but we do not limit any other possible subject related to optimal transport.

Organizer

Wil Schilders (Eindhoven University of Technology, The Netherlands), w.h.a.schilders@tue.nl

Co-Organizer

Christophe Prud'homme (University of Strasbourg, France ), christophe.prudhomme@agence-maths-entreprises.fr

Description

Knowledge has become the main wealth of nations, companies and people. Investing in research, innovation and education is now the key-leverage for competitiveness and prosperity in Europe. At the heart and foundation of this challenge, mathematics plays a crucial role as it provides a logically coherent framework to industry and a universal language for the analysis, simulation, optimisation, and control of industrial processes. Mathematics is an essential factor in the industrial creation of value and a driving force for innovations, but often, its contributions are invisible in the final industrial products. The use of mathematical techniques gives a competitive advantage to industry by suggesting innovative interdisciplinary approaches.

The goal of EU-MATHS-IN is to explore ways of stimulating and intensifying the collaboration between mathematics and industry. European scientific and industrial communities, in close interaction with policymakers, have developed medium to long-term views and analyses of common issues, questions and “good practices” between mathematics and industry in order to envisage strategies for a stronger interaction of mathematicians with large and medium-sized companies. In this mini-symposium, we will first provide a general introduction to EU-MATHS-IN, its structure and its activities, followed by a number of success stories of mathematics for industrial challenges, addressing different areas in mathematics as well as different industrial sectors.

Organizer

Sarka Necasova (Institute of Mathematics, Academy of Sciences, Czech Republic ), matus@math.cas.cz

Co-Organizers

Anja Schlömerkemper (University of Würzburg, Germany), anja.schloemerkemper@mathematik.uni-wuerzburg.de

Justin Webster ( Univ. Maryland, Baltimore USA ), websterj@umbc.edu

Description

The interaction of fluids or viscoelastic materials and solids shows complex behaviour on an experimental level. The interaction can affect for instance a spoon in a glass of honey or the blood flow in vessels. Existence, uniqueness and regularity of solutions to related mathematical models are needed to prove the relevancy of the model and to justify accompanying numerical simulations.

Mathematically, the interactions of fluids or viscoelastic materials with solids lead to a nonlinear coupling of the velocity of the fluid or viscoelastic material and the evolution of the solid. Various methods have been developed in the context of the Navier-Stokes equations and elasticity theory to overcome or handle concentration and oscillation effects caused by the nonlinear couplings, this includes weak-compactness methods like the div-curl lemma or the notion of dissipative measure valued solutions.

The scope of this minisymposium is to bring together experts of different scientific backgrounds and seniority who work on systems of partial differential equations that contain, e.g., the Navier-Stokes equations or the Cahn-Hilliard equations, models of fluid-structure interaction and simulations of the problems. We will discuss the latest achievements as well as new directions of future research.

Organizer

Victor A. Kovtunenko (University of Graz, Austria), victor.kovtunenko@uni-graz.at

Co-Organizers

Hiromichi Itou (Tokyo University of Science, Department of Mathematics, Japan), h-itou@rs.tus.ac.jp

Alexandr M. Khludnev (Novosibirsk State University, Department of Mathematics and Mechanics, and Lavrentyev Institute of Hydrodynamics SB RAS, Russia), khlud@hydro.nsc.ru

Evgeny M. Rudoy (Novosibirsk State University, Department of Mathematics and Mechanics, and Lavrentyev Institute of Hydrodynamics SB RAS, Russia), rem@hydro.nsc.ru

Description

Mathematical methods based on the variational approach are successfully used in a broad range of applications, especially those fields that are oriented on partial differential equations (PDEs).

Our problem area addresses a class of nonlinear variational problems described by all kinds of dynamic and static PDEs, inverse and ill-posed problems, nonsmooth and nonconvex optimization, and optimal control including shape and topology optimization. Within these directions, we focus but are not limited to singular and unilaterally constrained problems arising in mechanics, which are governed by complex systems of generalized variational equations and inequalities.

While standard mathematical tools are not applicable here, we aim at a non-standard well-posedness analysis, asymptotic and approximation techniques including homogenization, which are successful within the primal as well as the dual variational formalism.

In a broad scope, the minisymposium objectives are directed toward advances that are attained in the mathematical theory of nonsmooth variational problems, its numerical computation and application to engineering sciences.

**Research area:** Calculus of variations and optimal control; optimization - 35-xx, 49-xx, 74-xx

Organizer

Sanda Lefteriu (IMT Lille Douai, France), sanda.lefteriu@imt-lille-douai.fr

Co-Organizer

Ion Victor Gosea (Max Planck Institute, Magdeburg, Germany), gosea@mpi-magdeburg.mpg.de

Description

Dynamical systems typically consist of a collection of differential (or difference) equations that describe the dynamics of a time-dependent process. One common approach to model dynamical systems in practical applications is by employing information from the frequency domain. In doing so, the main tool used to describe the behavior of the system is the transfer function, namely the ratio between the Laplace transform of the response and the Laplace transform of the excitation. For linear time-invariant systems, this quantity is a rational function of a possibly high degree.

For creating a deterministic mathematical model of dynamical systems for subsequent quantitative and qualitative analysis and simulation, the starting point may be data consisting of measurements of the response to known excitations. In the context of data-driven modeling from frequency-domain measurements, the goal is to employ rational approximation to obtain a lower-order model of the system (complexity reduction). For special classes of infinite-dimensional or nonlinear systems, rational approximation is still a very powerful tool.

This mini-symposium brings together European researchers from several countries under the unifying umbrella of modeling dynamical systems by rational approximation and model reduction. These researchers are from applied and industrial mathematics, and the application-driven aspect is very important as the main motivation is to address real-world problems.

Organizer

Egbert Rijke (University of Ljubljana, Slovenia), e.m.rijke@gmail.com

Description

Homotopy Type Theory is a new area of mathematics that emerged with the discovery of the univalence axiom, and the homotopy interpretation of dependent type theory. The basic objects in the language of homotopy type theory are types and terms. Types are interpreted as spaces, and terms are their points. In a major recent development, it has been shown that homotopy type theory is the internal language of higher toposes. Thus, the scope of the subject is immensely broad: any theorem proven in homotopy type theory holds for all higher toposes.

In this mini symposium, the subject is approached from all directions: from higher category theory and semantics to the formalization of mathematics using the univalence axiom.

Organizer

Lisa Maria Kreusser (University of Cambridge, UK), lmk48@cam.ac.uk

Co-Organizer

Jan Haskovec (KAUST, Saudi Arabia), haskovec.jan@gmail.com

Description

In recent years, PDE models have been used to model a variety of applications in the life and social sciences. These models are typically derived from microscopic approaches like individual or lattice based models, discrete network structures, or based on fundamental physical laws. Since these models usually exhibit an underlying energy structure, they are also of great interest for mathematical research. Despite many recent advances, important questions such as the derivation of the mean-field equations and the development of efficient numerical methods are still open.

The main objective of this minisymposium is to bring together experts in PDE modelling, focusing on applications in pedestrian dynamics, collective phenomena in crowds, cell movement and biological network formation. The presentations will include both analytical and computation advances. More specifically, they will range from gradient flow theory on the micro- and macroscopic level, dynamics on discrete networks, derivation of the corresponding mean-field limits to efficient numerical methods. The speakers will report recent progress in their fields, exchange ideas and highlight novel mathematical problems.

Organizer

Elena Resmerita (Alpen-Adria Universität Klagenfurt, Austria), elena.resmerita@aau.at

Co-Organizer

Carola Schönlieb ( Cambridge University, UK), cbs31@cam.ac.uk

Description

The aim of this minisymposium is to offer a short overview of several active areas of pure and applied mathematics, underlying, once again, that the beauty and the success of the mathematical research are essentially based on combining all kinds of ideas from various fields. The minisymposium has been organized by the European Women in Mathematics association (EWM) and the speakers have been proposed by the EMS/EWM joint scientific committee.

Organizer

Deryk Osthus (University of Birmingham, UK), d.osthus@bham.ac.uk

Description

A central theme in Extremal Combinatorics is to study how various parameters influence the existence of certain substructures or patterns. A classical type of questions concerns density conditions which force the existence of a given subgraph. In recent times, the subject has become much broader, and current questions include e.g. degree conditions forcing a triangle decomposition, questions involving rainbow colourings and colourings of locally sparse graphs, as well as Ramsey theory.

Taking an asymptotic perspective has been particularly fruitful. In particular, this enables the use of probabilistic methods, which have had an enormous impact on the area. A recent approach inspired by the asymptotic viewpoints is that of graph limits, which has developed into a rich theory of its own and helped solve a number of classical open problems in Extremal Combinatorics. A related theme has been to consider classical extremal questions from a probabilistic viewpoint, i.e. to obtain probabilistic analogues of classical extremal results e.g. on Hamilton cycles.

The minisymposium will bring together researchers working on the above topics and their interface. The area is developing rapidly and there are rich connections and applications to other related areas such as statistical physics, algebra, probability, design theory, latin squares, discrete geometry and the analysis of algorithms.

Organizer

Stefaan Vaes (KU Leuven, Department of Mathematics, Belgium), stefaan.vaes@gmail.com

Co-Organizer

Stuart White (University of Glasgow, School of Mathematics and Statistics, UK), stuart.white@maths.ox.ac.uk

Description

Operator algebras form a flourishing field of mathematics with strong ties to functional analysis, harmonic analysis, topology, (non-commutative) geometry, group theory and dynamical systems.

Operator algebras come in two flavors: topological and continuous aspects are captured by C*-algebras, while measurable and ergodic phenomena appear in von Neumann algebras. In both areas, important progress was made in the past years, especially in the classification of simple nuclear C*-algebras and in the structure and classification theory of non-amenable von Neumann algebras, often given by groups and measurable dynamics.

A key feature of these developments is a continuous interaction between the traditionally quite distinct C*-algebra and von Neumann algebra approaches. Boundary actions of groups and other methods from geometric group theory play an increasingly important role in studying von Neumann algebras, while the highly developed theory of injectivity and hyperfiniteness for von Neumann algebras is crucial for the ongoing classification theory for nuclear C*-algebras.

The aim of this mini-symposium is to bring together researchers working in a diverse range of topics in operator algebras, so as to exchange a wide variety of ideas and methods, fostering a cross-pollination between these different fields of mathematics.

Organizer

Luboš Pick (Charles University, Prague, Czech Republic), pick@karlin.mff.cuni.cz

Description

The MS will focus on several aspects of contemporary research of a variety of inequalities of functional and geometric nature and their applications. We have seen a significant development in this area recently, but important challenging problems remain open nevertheless.

Main topics will include:

- Sobolev-type inequalities with optimal function spaces and sharp constants and their applications in partial differential equations and mathematical physics, new methods such as mass transportation or flow techniques.
- Nonstandard function spaces, e.g. various generalizations to Lebesgue spaces which proved to be crucial in applications.
- Geometric analysis of Sobolev mappings, fine regularity properties of Jacobians and mappings of finite distortion and their applications in theory of nonlinear elasticity.
- Logarithmic Sobolev inequalities, Moser-type estimates, existence of minimizers.
- Theory of entropy numbers and their relation to noncompactness of Sobolev maps.
- Inequalities involving integral operators and their applications in harmonic analysis

The MS is aimed at gathering leading experts working in the above mentioned areas as well as young researchers, postdocs and Ph.D. students. It will be an excellent occasion for an updated overview on the state of the art, and, hopefully, a point of departure for fruitful future collaborations among participants.

Organizer

Sandra Carillo (University of Rome ``La Sapienza'', Italy), sandra.carillo@uniroma1.it

Co-Organizers

Galina Filipuk (University of Warsaw, Faculty of Mathematics, Informatics and Mechanics), filipuk@mimuw.edu.pl

Federico Zullo (Università di Brescia, DICATAM, Italy), federico.zullo@unibs.it

Description

The Minisymphosium is devoted to recent results concerning applicative problems modelled via differential equations. Contemporary challenges raised by current advances in engineering, applied science and industry involve finite and infinite dimensional dynamical systems. Indeed, new materials, such as materials with memory, materials with fractal boundaries and functionally graded materials are more ad more used in different environments and technology areas. Viscoelastic, magneto-viscoelastic and thermo-viscoelastic bodies are only a few examples of materials that are deserving of growing interest both under the theoretical as well as the applicative point of view.

The Minisymphosium aims to bring together researchers who are all investigating differential problems under different viewpoints to possibly, encourage their interaction to find new results and perspectives via the contamination among their different methodological approaches. Advances in theoretical problems concerning differential equations along with results of current interest in applications are welcome.

Organizer

Laura Sacerdote (University of Torino, Italy), laura.sacerdote@unito.it

Description

The study of First Passage Times (FPT) dates back to the beginning of last century but many related problems are still open. A set of new versions of the FPT Problem has appeared during the last 20 years and nowadays the research includes Markov processes as well as processes with memory. Beside the “Direct Problem”, questions arise in the class of inverse problems: the search of the boundary corresponding to the first exit of a fixed process having the distribution of the FPTs or the search of the process itself.

Analytical solutions of the direct problem exist only in a limited number of cases and alternative tools are the subject of modern investigations. Beside the introduction of implicit formulae for specific processes, new tools include numerical or exact simulation techniques. Applications to reliability theory, neurosciences, engineering, economy and psychology suggest new questions and often there are not mathematical results ready for answering.

Aim of the mini-symposium is bringing together researchers active on FPT Problems, allowing the interaction between different expertise in direct or inverse problems as well as on different types of stochastic processes and applications. The presence of mathematicians working on the theoretical problem with those approaching the study through simulations or numerical techniques will encourage new collaborations. Furthermore, mathematicians motivated by applications will suggest new mathematical problems.

Organizer

Martin Jesenko (Albert-Ludwigs-Universität Freiburg, Germany), martin.jesenko@mathematik.uni-freiburg.de

Description

Especially in applied mathematics, it is common to formulate problems in terms of energy, i.e. as an integral functional. By variational methods its global or local extrema are studied, as they yield global or local solutions of the problem. The most fundamental tool is the direct method in the calculus of variations. Relevant questions are among other existence of minimizers, relaxation of the problem if minimizers do not exist, regularity and effective approximation of the problem (e.g. homogenization, dimension reduction). One relies on the methods from general functional analysis and topology, and employs Gamma-convergence, geometric measure theory, convex analysis etc.

The aim of this minisymposium is to bring together experts in this field and to discuss any problems where variational methods can be a useful tool. Typically the settings arise from material science, but also from optimization, image processing, minimal surfaces, to name just a few. Any theoretical progress in this field will also be of interest and can bring audience new ideas and perspectives for possible applications.

Organizer

Mario Bukal (University of Zagreb, Croatia), mario.bukal@fer.hr

Description

Nonlinear evolution equations of order four and six in spatial derivatives arise in various contexts of mathematical physics. The most prominent examples are the Cahn-Hillard equation describing spinodal decomposition, followed by the fourth-order thin-film equations describing dynamics of the thickness of thin viscous fluid films. Other examples include fourth-order equations in semiconductor modelling, statistical description of interface fluctuations in spin systems, Bose-Einstein condensates, image processing etc, while sixth-order thin-film equations appear as reduced models in fluid-structure interaction problems.

The understanding of the dynamics of higher-order evolution equations, possibly extended by stable or unstable lower-order terms, is of high relevance in industrial applications, for instance in an emerging area of so-called lab-on-a-chip technologies. This minisymposium will bring together renowned experts in the area of mathematical physics, partial differential equations and numerical analysis with aim of stipulating the interplay between the three main aspects of higher-order equations: modelling, analysis and numerics.

Key challenges like positivity, stability of solutions, speed of propagation, construction of structure preserving numerical schemes and justification of higher-order equations as approximate models will be explored.

Organizer

Paul Feehan (Rutgers University, USA), feehan@math.rutgers.edu

Co-Organizers

Raphael Zentner (University of Regensburg, Germany), raphael.zentner@mathematik.uni-regensburg.de

Natasa Sesum (Rutgers University, USA), sesum@math.rutgers.edu

Description

Geometric analysis has had an enormous impact on our understanding of the topology of low-dimensional manifolds and on the structures that such manifolds may carry. Early examples include Uhlenbeck's compactness and generic metrics theorems and Donaldson's study of the moduli space of Yang-Mills instantons with its spectacular application to the topology of smooth 4-manifolds, Yau's proof of the Calabi conjecture, Aubin, Schoen, and Trudinger's solution to the Yamabe problem, and Perelman's proof on the geometrization conjecture for 3-manifolds.

Meanwhile, there are other flavours of gauge theory inspired by Donaldson's methods such as Seiberg-Witten gauge theory, instanton Floer homology, Heegaard-Floer homology due to Ozsvath and Szabo, and monopole Floer homology due to Kronheimer and Mrowka. There is an active area of research in low-dimensional topology that involves applications of these techniques and that is the main focus of the mini-symposium proposed by Owens and Strle. There is an intense demand for further development of these geometric analytical tools and our proposed mini-symposium will focus on those tools and their applications.

Organizer

Frédérique Robin (INRIA Rennes-Bretagne Atlantique, France ), frederique.robin@inria.fr

Co-Organizers

Emmanuelle Anceaume (IRISA), emmanuelle.anceaume@irisa.fr

Bruno Sericola (INRIA), bruno.sericola@inria.fr

Description

Blockchain is an innovative technology that has the potential to transform many areas such as finance, logistics, and connected object management. It provides a means for exchanging or storing information secured by cryptography, without the need of a centralized trusted authority.

The lack of a global trusted third party is bypassed by relying on a publicly readable and writeable blockchain, a data structure in which all transactions are gradually added through the creation of cryptographically linked blocks.

Initially introduced in 2008, the Bitcoin cryptocurrency system offers to its users the possibility to transfer funds (in Bitcoins) securely without a banking authority. Since then, new blockchain models have been introduced: the blockchain technology is still in the development phase and an open field of research. To ensure the viability of candidate improvement solutions, mathematical models and analyses tackling different blockchain aspects (consensus, forks, block creation or block spreading time, etc.), have been proposed during the last decades.

This mini-symposium aims at bringing together researchers active on blockchain analysis, and allowing the interaction between different expertises: Markov chain, game theory, fluid limits as well as on different types of stochastic processes. It also aims at gather mathematicians analyzing blockchains through a theoretical approach to those applying numerical techniques, and thus it will encourage new collaborations.

Organizer

Marc Hellmuth (University of Greifswald, Germany), mhellmuth@mailbox.org

Co-Organizer

Peter F. Stadler (University of Leipzig), studla@bioinf.uni-leipzig.de

Description

Despite the success of mathematics in modeling the dynamics of evolution almost a century ago that has lead to the development of population genetics, much of the life sciences lacks a comprehensive mathematical formalization. It has become clear that the conceptual toolkit of physics does not adequately describe many of the biological phenomena that often seemed unquantifiable, unpredictable and messy. With the advent of molecular biology, and in particular, genomics in the last decades, however, a plethora of accurate data have become available and stimulated the development of new branches of theoretical and mathematical biology.

Biology thus has been considered to be the "new physics" as source of ideas for mathematics. In contrast to the physical sciences, most of formal structures emerging from the life sciences are inherently discrete and combinatorial in nature, centered around genomic sequences, evolutionary trees, or genetic networks.

The aim of this mini-symposium is to bring together researchers working in a diverse range of topics in Discrete Biomathematics which may include but is not limited to Phylogenomics and Evolution, Population Genetics, RNA +Combinatorics, Computational Biology, Evolutionary Game Theory, or Algebraic Aspects in Biology.

Organizer

Franc Forstnerič (University of Ljubljana, Slovenia), franc.forstneric@fmf.uni-lj.si

Co-Organizer

Bernhard Lamel (University of Vienna ), bernhard.lamel@univie.ac.at

Description

Complex analysis and geometry is a very active field with strong connections to numerous areas of mathematics and wider. It studies complex manifolds and holomorphic mappings between them, behaviour of holomorphic objects on smooth submanifolds in complex spaces, the complex Neumann problem, dichotomy between rigidity and flexibility of complex manifolds, approximation and interpolation problems, dynamics of holomorphic maps, among others. Its origins go back to seminal works of some of the most eminent mathematicians such as for example Riemann, Weierstrass, Poincaré, Cartan, Oka, Grauert, Grothendieck, Hörmander, and Kodaira. Today the subject is the focus of a tremendous amount of worldwide activity and has branched off in new directions such as the use of precise quantitative methods, study of degenerate Cauchy-Riemann structures, Gromov hyperbolicity of natural metrics on complex domains, holomorphic evolution equations in several variables, Oka manifolds, study of exotic complex structures, holomorphic directed systems, connections to the theory of minimal surfaces, etc.

This minisymposium will bring together top international experts and some of the most promising young mathematicians in the field. It is expected that the lectures of invited speakers will address several major recent advances, in particular, the Ohsawa-Takegoshi L^2-theory with precise estimates, solution to the strong openness conjecture for plurisubharmonic functions, advances in Cauchy-Riemann geometry, new constructions in complex dynamics, and recent advances in Oka theory. It is becoming increasingly evident that a deeper level of synergies will be needed for further progress, and we hope that the minisymposium will contribute to this goal.

Organizer

Barbara Boldin (University of Primorska, Slovenia), barbara.boldin@upr.si

Description

The interface between mathematics and biology has long been a rich area of research, with the two disciplines deriving mutual benefit from each other. Mathematics provides a wide range of modelling tools that enable us to gain insight into various biological phenomena. On the other hand, interesting and challenging mathematical problems continue to arise from different areas of biology.

The mini-symposium is devoted to recent advances in mathematical biology with some of today’s leading experts in the field exploring a range of topics, e.g., the use of stochastic differential equations to study individual growth, renewal equations as models of hierarchical competition, the use of singular perturbation theory in epidemic models and the problem of inferring the network structure in the brain.

Organizer

Nicolas Van Goethem (Faculdade de Ciências da Universidade de Lisboa, Portugal), vangoeth@fc.ul.pt

Co-Organizers

Filipe Oliveira ( ISEG-University of Lisbon), foliveira@iseg.ulisboa.pt

Riccardo Scala (Università degli Studi di Napoli), riccardo.scala@unipv.it

Description

It is always a challenge to devise modern mathematical tools in continuum mechanics. A topic of interest is the modelling of nucleation and propagation of brittle or cohesive fractures. If the crack is seen as a field singularity, one focuses on their fine analysis in appropriate functional spaces. Otherwise the crack is an interface, and phase field approaches are considered. Another type of singularity are dislocations for which specific functional spaces must be studied and developed. In either case, the lack of regularity of the problem is such that variational approaches are considered to get well-posedness. Moreover, the fine analysis of the singular sets leads to difficult problem addressed by methods of Geometric measure theory. Therefore, in this mini-symposium a holistic approach to continuum mechanics is sought where a problem in mechanics is studied by modern mathematical methods requiring advanced tools in functional analysis, geometry and measure theory.

Another topic is mathematical modelling and PDEs, i.e., the study of differential equations arising in the modelling of real world processes such as elasto-plasticity and wave propagation in continuous media. Elliptic, parabolic, hyperbolic and dispersive systems are considered, possibly with fractional operators, together with asymptotic analysis, homogenization, $\Gamma$-convergence and optimal control.

The scope of this event is to promote collaboration between young and leading European researchers in the field.

Organizer

Luigi Grasselli (University of Modena and Reggio Emilia, Italy), luigi.grasselli@unimore.it

Co-Organizers

Bruno Benedett (University of Miami, USA), bruno@math.miami.edu

Maria Rita Casali ( University of Modena and Reggio Emilia, Italy), mariarita.casali@unimore.it

Antonio Felix Costa (UNED Madrid, Spain), acosta@mat.uned.es

Description

Combinatorial and geometric topology are useful tools to tackle problems in various branches of mathematics, physics, and engineering. Graph and knot theory is connected to biological structures and to string theory. Colored graphs have proved to be an interesting approach to n-dimensional quantum gravity, via random tensor models. Topological insight is becoming crucial in data science, by providing new computational tools for the understanding of complex systems. Meanwhile, computational topology plays a key role in shape theory and pattern recognition.

The goal of the mini-symposium is to showcase present developments in the study of low-dimensional manifolds, focusing on geometric structures, combinatorial methods, and topological tools, with an eye on applications.

The talks will touch upon the themes below:

- geometric topology: PL-manifolds, knot theory, triangulations and shellings, Riemann surfaces.
- combinatorial topology: graph theory, maps on surfaces, matroids, colored triangulations, complexes.
- interplay of computational topology and algebra.
- applications: random tensor models and colored graphs, DNA structures, data analysis and persistent homology.

Organizer

Mihael Perman (University of Primorska, Slovenia), mihael.perman@fmf.uni-lj.si

Co-Organizers

Bor Harej (PRS Prime Re Solutions AG), bor.harej@prs-zug.com

Claudia Klüppelberg (TU München), cklu@tum.de

Thomas Mikosch (University of Copenhagen), mikosch@math.ku.dk

Ermanno Pitacco ( University of Trieste), ermanno.pitacco@deams.units.it

Tomaž Košir ( University of Ljubljana), tomaz.kosir@fmf.uni-lj.si

Description

Risk modeling is an essential tool for the insurance industry. Recent changes in regulation on European level, the global reach of the European insurance industry and changing financial markets along with strong competition have created new challenges for the industry and for mathematicians. A liberal regulatory regime allows insurance companies to develop compehensive risk management systems through internal models. Such models are complex and involve advanced mathematical methods. The integration of statistical data processing, development of actuarial models and management decisions is a challenging problem.

The availability of big data and advanced methods of machine learning is a new frontier for the insurance industry. Applications range from detecting fraudulent practices, segmentation of customers, advanced pricing models to assisted financial decisions. Fundamental mathematical questions of reliability and replicability of such applications must be addressed not only in insurance but in all applications of machine learning.

The speakers will discuss modeling challenges and more fundamental questions of machine learning applications. There has been a rising trend in weather related claims stretching the capacity of (re)insurance to its limits. Complex mathematical models to adjust for trends and assist with pricing in non-life insurance is yet another challenge for mathematical modelling. Some new advances in this respect will be presented.

Organizer

Stefano Pozza (Charles University, Czech Republic), pozza@karlin.mff.cuni.cz

Co-Organizer

Davide Palitta (Max Planck Institute for Dynamics of Complex Technical Systems), palitta@mpi-magdeburg.mpg.de

Description

Numerical linear algebra and matrix computation studies have been at the core of numerical analysis since the early 50s. Indeed, in almost every branch of numerical analysis, from the numerical solution of PDEs to the analysis of complex networks, one ends up facing some kind of matrix problem. This has motivated, and it continues to motivate, the formidable work of our community. Thanks to these enormous efforts, many efficient, accurate, and trustworthy algorithms have been developed, serving as an essential foundation any applied mathematician can rely on. Moreover, new, arduous real-world applications pop up every day presenting unexplored mathematical directions that require continuous improvement in matrix computation techniques.

Nowadays, in many applications such as data analysis and data assimilation, we are witnessing a tremendous increment in the size and complexity of problems. Classical techniques are not able to properly handle such problems, and the development of effective multilinear algebra tools is crucial. The research of many mathematicians is devoted to this timely challenge and important contributions in, e.g., tensor approximation has been achieved in recent years.

The minisymposium aims to bring together experts working in different areas of matrix computations and numerical (multi)linear algebra, to spread their work, and to establish new collaborations among different fields of mathematics.

Organizer

Aleksey Kostenko (University of Ljubljana, Slovenia), aleksey.kostenko@fmf.uni-lj.si

Co-Organizer

Pavel Exner (Czech Technical University, Prague, Czech Republic), exner@ujf.cas.cz

Description

The mini-symposium is aimed to cover a wide variety of problems relating to graphs and having a strong analytic flavour (e.g., analogs of differential equations, spectral theory, geometric analysis etc.). Problems of this kind continue to attract enormous attention and find numerous applications in many branches of mathematics (number theory, group theory, probability, tropical geometry), physics (quantum mechanics, nanophysics and nanotechnology, material sciences), chemistry and computer sciences.

The aim of this mini-symposium is to bring together leading international experts and young promising researchers developing different aspects of analysis on graphs, groups and fractals. This mini-symposium is also a natural extension of the satellite conference 'Contemporary Analysis and its Applications', 1-5 July, Portorož (http://www.caia2020.com/).

Organizer

Cristina Dalfó (Universitat de Lleida, Spain), cristina.dalfo@matematica.udl.cat

Co-Organizer

Francesco Belardo (University of Naples Federico II, Italy), francesco.belardo2@unina.it

Description

A graph (or digraph) can be represented by means of a matrix, as the adjacency or the Laplacian matrix. The spectral invariants of the graph matrices are often connected to the combinatorial or structural properties of the graph. The spectral techniques are particularly useful in investigating graphs with high symmetry or regularity, such as the Cayley graphs, the lifts of voltage digraphs, the distance-regular graphs, and the weakly distance-regular digraphs, which are used to model real networks.

The current directions of research include:

- To obtain the complete spectrum of the lift of a graph from the spectrum of its base graph.
- How the partitions of an integer number give the regular partitions of a graph.
- The spectra of mixed graphs.
- The spectra of signed/gain graphs.
- To distinguish/detect cospectral graphs.
- New properties on the largest eigenvalue of a graph.
- Graphs with extremal eigenvalues.
- Generalizations of the adjacency matrix.
- New bounds on the energy of a graph.
- Weight-regular partitions of graphs.
- Generalized distance matrices.

The scope of this minisymposium is to put together researchers of Spectral Graph Theory that uses spectral techniques with other methods. For example, some researches are applying spectral techniques with methods from Group Theory, Representation Theory, Block Designs, and Orthogonal polynomials, etc. Working with some of these different subareas can allow finding new results on Spectral Graph Theory.

Organizer

María del Mar González Nogueras (Universidad Autónoma de Madrid, Spain), mariamar.gonzalezn@uam.es

Co-Organizers

Luz Roncal (BCAM Basc Centre for Applied Mathematics), lroncal@bcamath.org

Juan Luis Vazquez (Universidad Autónoma de Madrid and Real Academia de Ciencias), juanluis.vazquez@uam.es

Description

Fractional operators are well understood from the point of view of Functional Analysis, and they arise naturally in other areas such as Potential Theory, Harmonic Analysis and Probability.

In the last few years there has been an increasing interest in the study of nonlinear partial differential equations involving fractional operators. Such problems appear in applications like Fluid Dynamics, Strange Kinetics, Anomalous Transport and Financial Mathematics, among many others. It can be said that he trigger for the study of nonlocal PDEs was the celebrated work by Luis Caffarelli and Luis Silvestre and their study of the extension problem, which was already present in several instances of Stochastic Processes with the Bessel operator, Representation Theory or Scattering Theory.

The aim of this mini-symposium is to bring together international experts in different aspects of nonlocal PDEs, fractional operators and probability and explore the connections among different areas where nonlocal objects play an essential role.

Organizer

Katja Berčič (FAU Erlangen-Nürnberg, Germany), katja.bercic@fau.de

Co-Organizers

Thierry Bouche (Université Grenoble Alpes), thierry.bouche@univ-grenoble-alpes.fr

Patrick Ion (IMKT & University of Michigan), pion@umich.edu

Olaf Teschke (zbMATH), olaf.teschke@fiz-karlsruhe.de

Description

The International Mathematical Union has endorsed building a World Digital Mathematical Library repeatedly since 2006. While initial efforts focused on digitizing articles, the goals became more ambitious over the years. The creation of a Global Digital Mathematics Library (GDML) should be positively affected by the widely supported Open Science movement.

Research on capturing the semantics of mathematics in a machine, and using it for search, is already showing some practical results. The work on mechanizable formulations provided by mathematical logic has enabled checking large proofs with automated and machine-aided reasoning. The resulting libraries are valuable and need to be collected, preserved and made available. The same is true for outputs from simulations or computations that computers carry beyond individual human capacities. There is now a study of mathematical research data, whose collections have a much significant internal structure. All of these tools and resources form, together with mathematical software, a mathematician's virtual research environment.

MiDAS will discuss possibilities for digital representation of, improving access to and preservation of mathematical knowledge. Addressing relevant social, technological and financial issues aids the International Mathematical Knowledge Trust to build a GDML. MiDAS will consider many ways of using the digital environment to benefit mathematics and welcomes further examples to help guide progress.

Organizer

Nicolas Trotignon (CNRS, France), nicolas.trotignon@ens-lyon.fr

Co-Organizers

Martin Milanič (Univerza na Primorskem, Slovenija), martin.milanic@upr.si

Daniel Paulusma (Durham University, UK), daniel.paulusma@durham.ac.uk

Sandi Klavžar (University of Ljubljana, Slovenija), sandi.klavzar@fmf.uni-lj.si

Description

We will present recent progress in algorithmic graph theory, which lies at the intersection of Mathematics and Computer Science and has many practical applications. These applications motivate the development of algorithms for computing, exactly or approximately, various graph invariants, such as the chromatic, clique, independence and domination number of a graph. Despite a number of recent breakthroughs, many deep and challenging research questions remain. These include questions on conditions for the existence of a function bounding one graph invariant in terms of another one, and on complexity gaps and other algorithmic aspects of graph problems restricted to special graph classes.

To address such questions, we need to develop new tools combining structural knowledge on graph decompositions, width parameters, containment relations, intersection representations, extremal graph theory, Ramsey theory etc. with algorithmic techniques from both parameterized and classical complexity theory. For this purpose we will bring together leading researchers from both Discrete Mathematics and Theoretical Computer Science with complementary research expertise.

The talks in our minisymposium will cover a large variety of trending topics in algorithmic graph theory, highlighting relevant open problems and possible techniques for solving them. As such, our minisymposium will provide participants an ideal opportunity to develop new research collaborations with one another.

Organizer

Laura Paladino (University of Calabria, Italy), laura.paladino@unical.it

Co-Organizer

Jung Kyu Canc (Hochschule Luzern − Technik and Architektur, Switzerland), jungkyu.canci@hslu.ch

Description

The aim of this minisymposium is to give an overview of some of the most recent results in number theory and give an opportunity to international experts to meet and exchange ideas.

This session will focus especially on all aspects of algebraic number theory and arithmetic geometry, but also topics in analytic number theory will be of interest.

Organizer

Márton Naszódi (Eotvos University, Budapest And Alfred Renyi Inst. of Mathematics, Budapest, Hungary), mnaszodi@gmail.com

Co-Organizer

Konrad Swanepoel (London School of Economics and Political Science), K.Swanepoel@lse.ac.uk

Description

Discrete geometry is a lively and rapidly growing field at the crossroads of geometry, analysis and combinatorics, and with strong connections to computer science. It investigates properties of configurations of geometric objects and covers a broad range of topics that includes the theory of packing and covering, intersection patterns of convex bodies, the combinatorial and metric theory of polytopes, geometric algorithms, and the geometry of numbers.

The purpose of this Minisymposium is to bring together researchers from geometry, geometric functional analysis and combinatorics that share a common interest in discrete geometry. We highlight two topics.

Banach asked whether a normed space is necessarily a Hilbert space if for some fixed n, all n-dimensional subspaces are isometrically isomorphic. Gromov confirmed this for even n, and in a very recent breakthrough, Bor, Hernández-Lamoneda, Jiménez-Desantiago and Montejano for all n congruent 1 mod 4 (with one exception). Thus a quarter of the cases are still open.

Approximation of convex bodies by polytopes. The general question is to find a convex polytope of low complexity (eg. few vertices) close to a given body. Recent work by various researchers provide good bounds in the case of fine approximation, while rough approximation remains poorly understood. The problem is naturally attractive from a theoretical point of view, and at the same time, is the subject of intensive research in computer science.

Organizer

Sara Daneri (Gran Sasso Science Institute, Italy), sara.daneri@gssi.it

Co-Organizer

Matteo Novaga (University of Pisa, Italy), matteo.novaga@unipi.i

Description

The minisymposium aims at bringing together both senior and younger experts working from different perspectives on models involving local/nonlocal interactions. In particular, the invited speakers have been working on: variational models for spontaneous pattern formation in materials or liquid suspensions, where periodic patterns are expected to result from the competition between local attractive/nonlocal repulsive terms; gradient flow-type evolutionary models for aggregation-diffusion; discrete to continuum models for crystallization. Such models arise in several applications to statistical mechanics, material science, crowd dynamics and biology.

Even though experiments and simulations suggest in most cases the existence of a given geometric structure for the equilibrium states, to prove it from an analytically rigorous point of view is in most cases an open challenging problem. Questions in the field which have been addressed by the potential speakers include then: shape, regularity and stability of equilibrium states, existence of solutions to the evolutionary models with convergence to equilibrium states.

One of the peculiar features of this minisymposium is that it would bring together scientists working on similar problems but with different perspectives and techniques. Therefore the aim of the meeting would be to stimulate interaction between different areas to develop new strategies and connections.

Organizer

Claudiu C. Remsing (Rhodes University, South Africa), c.c.remsing@ru.ac.za

Co-Organizer

Zlatko Erjavec (University of Zagreb, Croatia), zlatko.erjavec@foi.hr

Description

In recent decades, the "old"--once dominant--subject of geometry, has enjoyed a spectacular and dramatic resurgence. Nowadays, the "new" differential geometry constitutes a vibrant area of mainstream mathematics with strong links to other mathematical subjects, as well as to other scientific domains (like e.g., nonlinear control systems and various areas of modern physics).

In the last decade or so, interesting new developments in (a) the differential geometry of curves and surfaces in specific spaces, as well as in (b) the geometry of homogeneous spaces and related topics (like, e.g., Cartan geometries and locally homogeneous G-structures) have taken place. Thus a few promising new directions of research, as well as some specific problems, have been identified and are currently subject of research activity.

This mini-symposium aims at bringing together international experts in a range of topics in differential geometry (classical, local, and global); connections between these areas, as well as connections with other areas of modern mathematics, and beyond, will be explored.

Organizer

Gerald Teschl (University of Vienna, Austria), gerald.teschl@univie.ac.at

Co-Organizer

Aleksey Kostenko (University of Ljubljana, Slovenia), aleksey.kostenko@fmf.uni-lj.si

Description

The mini-symposium is aimed to cover a wide variety of problems relating to spectral theory of ordinary and partial differential operators.

The aim of this mini-symposium is to bring together leading international experts in the field as well as young promising researchers. This mini-symposium is also a natural extension of the satellite conference 'Contemporary Analysis and its Applications', 1-5 July, Portorož (http://www.caia2020.com/).

Organizer

Oliver Dragičević (University of Ljubljana, Slovenia), oliver.dragicevic@fmf.uni-lj.si

Description

The event's purpose is to present recent exciting ideas and developments in one of classical areas of mathematical analysis, namely, the interplay between harmonic analysis and partial differential equations. The minisymposium is designed to encompass a diverse range of research topics and facilitate exchange of different mathematical ways of thinking. The targeted audience are researchers with interest in the subject matter, in a broad sense. Graduate students or researchers from other areas with overlapping interests are equally welcome.

The minisymposium will in part be a continuation of the 8ECM satellite conference "Contemporary Analysis and Its Applications", taking place at the same venue immediately preceding the 8ECM itself. The conference webpage is:

www.caia2020.com

Thus participants of either of these two events are encouraged to attend the other, as well.

Organizer

Juan J. Moreno-Balcázar (University of Almería, Department of Mathematics, Spain), balcazar@ual.es

Co-Organizers

Galina Filipuk (University of Warsaw, Poland), filipuk@mimuw.edu.pl

Francisco Marcellán (University Carlos III of Madrid, Spain), pacomarc@ing.uc3m.es

Description

Since the classical text written by Szegő in 1939, which set the foundations for the theory for orthogonal polynomials on the real line and on the unit circle, great advances both in the general theory and in the interaction with other areas of mathematics take place. Among them, we highlight here the links with numerical analysis (via classical Gaussian integration and their extensions as well as spectral methods for boundary value problems), approximation theory, spectral theory of differential operators, or potential theory in the complex plane.

In the last few years, a very fruitful area of research for the mathematical community working in orthogonal polynomials is related to the theory of random matrices, determinantal random processes and integrable systems. Structural properties of polynomials in the framework of standard L2 orthogonality with respect to a Borel measure (or a weight function) have been deeply studied for other patterns of orthogonality like multiple orthogonal polynomials, orthogonal polynomials in several variables or Sobolev orthogonal polynomials.

The aim of this mini-symposium is to bring together international experts in different aspects of the theory of orthogonal polynomials, from analytic to numerical aspects with a special emphasis on their applications, and give the community more visibility in an international meeting that has a larger scope than the regular conferences on the topic.

**Research area:** Special functions - 33C45, 33C47, 33D45, 33C50

Organizer

Yuliya Mishura (Taras Shevchenko National University of Kyiv, Ukraine), myus@univ.kiev.ua

Co-Organizers

Mark Podolskij (Aarhus University, Denmark), mpodolskij@math.au.dk

Nikolaj Leonenko (Cardiff University, Wales), leonenkon@cardiff.ac.uk

Giulia Di Nunno (University of Oslo, Norway), giulian@math.uio.no

Description

The phenomena of roughness and long-range dependence are being actively investigated by various research groups throughout the world. The reason of such profound interest to these phenomena is their ubiquity in different areas, such as natural sciences (including fluid mechanics, physics, biology, chemistry, neuroscience and so on), economics and social studies (financial mathematics, insurance), as well as technology and engineering (electronics, cellular communications).

Along with practical importance, this topic is of great interest from mathematical point of view and it attracts specialists from stochastics and theory of random processes, number theory, geometry, theory of differential equations etc.

The minisymposium aims at bringing together the leading specialists in the field of roughness and long-range dependence that can be modeled by the tools of fractional and multifractional stochastic processes, fractional calculus and fractional stochastic analysis; fractional equations and fractional dynamics. The topics that will be addressed at the minisymposium include but are not limited to tempered fractional multi-stable and multi-fractional motions, Levy moving averages, fractional point processes with long-range dependence, persistence probabilities for fractional processes, stochastic calculus for Volterra type dynamics, spectral asymptotics of fractional processes and its applications, fractional financial markets.

Organizer

Joanna Ellis-Monaghan (Saint Michael's College, USA), jellismonaghan@gmail.com

Co-Organizer

Mark Ellingham (Vanderbilt University, USA), mark.ellingham@vanderbilt.edu

Description

Graphs, embeddings of graphs in surfaces (also known as ribbon graphs), matroids, and knots all have various associated polynomials, such as the Tutte, Bollob{\'a}s-Riordan, Martin, Jones, and Kauffman polynomials. The many polynomials in this field are interrelated, and their relationships reflect a rich web of connections among graphs, embeddings, and knots, which moreover often generalize to other structures such as delta-matroids. Furthermore, the interconnections among graphs, surfaces, knots, and polynomials encompass a wide range of combinatorial concepts such as colorings, flows, cycle double covers, and eulerian circuits, and beyond with applications in physics and biology. Various forms of duality, such as Chmutov's partial duality for ribbon graphs, play an important role in these connections.

This minisymposium will highlight recent developments on all of the topics mentioned above. There is a long history in this area of results in one field leading to breakthroughs in another when techniques are transferred, so this minisymposium particularly aims to promote such cross-fertilization of ideas.

Organizer

Amalija Žakelj (University of Primorska, Faculty of Education, Slovenia), amalija.zakelj@pef.upr.si

Description

Considering the current research findings of national and international studies in the field of teaching and learning mathematics, technological advancement, and ICT development, the minisymposium Mathematics in Education will focus on the recent trends and open issues in the area of mathematics teaching methodology from preschool education to university-level instruction.

The main topics of interest cover contemporary approaches to learning and teaching mathematics, including the recent results of the international study on the integration of computational/algorithmic thinking into school mathematics, the role and significance of deductive and inductive approaches in learning and teaching mathematics, approaches to teaching algebra in primary education, discovery-oriented learning, mathematics comprehension strategies, visual and other presentations of mathematical concepts, the importance and role of textbooks in the learning process and other topics.

One of the main aims of the minisymposium is also to bring together leading international researchers in mathematics teaching methodology and other related areas. The discussion will revolve around the challenges and open issues on different aspects of future mathematics education at both pre-university and university level, especially focusing on developing competences which will support and prepare individuals to meet the undefined challenges of the future.

Organizer

Francesca Da Lio (ETH, Zurich, Switzerland), fdalio@math.ethz.ch

Co-Organizer

Annamaria Montanari (Department of Mathematics, University of Bologna, Italy), annamaria.montanari@unibo.it

Description

Partial differential equations (PDEs) are one of the most fundamental tools for describing continuum phenomena in the sciences and engineering.

They also have play an important role in the development of other branches of mathematics, including harmonic analysis, geometric analysis, probability, optimization and control theory. The phenomena described by PDEs are as complex as the world around us; the mathematical techniques needed to study PDEs are very diverse.

In particular, the methods that have been introduced to study PDEs differ to each other if the PDE is linear or nonlinear, uniformly elliptic or degenerate elliptic, scalar or vector-valued.

The mini-symposium aims to bring together young mathematicians working in partial differential equations with applications in sub-Riemannian geometry and in some geometrical variational problems allowing the interaction between different expertise.

The main themes include, but are not strictly limited to, the regularity theory for solutions of sub-elliptic second order partial differential equations, regularity issues in Carnot-Carathéodory geometry, curvature prescribed equations, Liouville-type properties for solutions to fully nonlinea elliptic PDEs, calculus of variations of surfaces, regularity of elliptic and parabolic systems.

Organizer

Stanislawa Kanas (University of Rzeszow, Poland), skanas@ur.edu.pl

Description

The topic of the Minisymposium “Current Topics in Complex Analysis” concentrates mainly on conformal, quasiconformal and harmonic mappings as well as complex dynamical systems. Important mathematicians associated with complex analysis include names of Euler, Gauss, Riemann, Cauchy, Weiestrass, Julia, Ahlfors, Grötzsch, Lavrentiev and many more in the 20th century. In recent years, their theories have taken on new life and entered a period of renewed activity and development in Geometric Function Theory.

The principal aim of the Minisymposium “Current Topics in Complex Analysis” is to bring together leading experts in the mentioned fields, with an eye toward setting the agenda for future investigations, especially as relates to applications in allied areas of Mathematical Analysis. A collateral aim is to provide participants with current updates in the subjects covered by the minisymposium.

Organizer

Simone Dovetta (CNR- Centro IMATI, Italy), simone.dovetta@imati.cnr.it

Co-Organizer

Lorenzo Tentarelli ( Università degli Studi di Napoli Federico II, Italy), lorenzo.tentarelli@unina.it

Description

Since its first appearance in physical chemistry in 1953, the analysis of dynamics on networks has been proposed to model almost one-dimensional ramified structures. Despite being more than sixty years old, it is within the last two decades that the theory of evolution on networks became popular, mainly driven by ubiquity of networks in applications, from quantum mechanics to fluid dynamics, from nonlinear optics to traffic regulation. To date, a wide variety of equations is being investigated from different communities all over the world. Significant results have been achieved for instance in the study of Schr\"odinger and Dirac equations, in the theory of conservation laws and traffic flows and in the description of complex systems of interacting agents through mean field games theory. A broad range of methods is used, such as spectral analysis, operator theory, existence and uniqueness methods in PDEs, calculus of variations.

The minisymposium aims at gathering international experts in the field alongside with promising young mathematicians working on PDEs on networks. A primary goal is to bring together people coming from different communities, so to allow exchange of ideas and diffusion of open problems. We hope that the minisymposium will foster a crossover between groups useful to fuel the future growth of the overall theory.

Organizer

Christian Budde (North-West University, South Africa), christian.budde@nwu.ac.za

Co-Organizer

David Seifert (Newcastle University), david.seifert@ncl.ac.uk

Description

The theory of operator semigroups on Banach spaces has a rich history going back to the first half of the 20th century. It is a theory characterised by a beautiful mix of techniques and ideas coming from many different areas of mathematics, including functional analysis, harmonic analysis and complex analysis. Operator semigroups moreover provide the main theoretical framework for the study of various types of evolution equation arising in physics, biology and elsewhere.

The past decade has seen a number of exciting developments in the theory of operator semigroups featuring, on the one hand, striking applications to problems arising within mathematics and outside and, on the other hand, deep theoretical contributions, for instance to our understanding of the qualitative and quantitative asymptotic behaviour of operator semigroups. One particularly notable area of progress has been the study of energy decay for damped waves.

This mini-symposium aims to bring together a number of leading researchers in the field of operator semigroups. There will be speakers from various different mathematical backgrounds, and the hope is to generate a fruitful exchange of ideas which will help to prepare the ground for many further years of exciting work on the theory and applications of operator semigroups.

Organizers

Lajos Molnár (University of Szeged, Hungary), molnarl@math.u-szeged.hu

Bojan Kuzma (University of Primorska, Slovenia), bojan.kuzma@famnit.upr.si

Description

Preserver problems represent a quite broad mathematical field stretching over diverse areas that include linear and abstract algebra, functional analysis, geometry and certain parts of discrete mathematics. A preserver is a transformation between mathematical structures that leaves a certain quantity/operation/relation/subset etc. invariant. The usual goal is to describe or characterize those transformations. Typical examples include isomorphisms of groups (i.e. maps which respect group operations), isometries of metric spaces (i.e. maps preserving distances), invertibility preserving maps on (operator or other) algebras, maps which are monotone with respect to a specific order, symmetries of graphs, etc.

The study of preserver problems goes back to Ferdinand Georg Frobenius who, motivated by the need of deeper understanding of a group determinant, described the structure of linear maps on matrix algebras which preserve the determinant. Since then a lot of work has been done concerning linear preservers on (general or more specific) algebras or linear spaces, and also concerning general (non-linear) preservers on domains like structures of bounded linear operators or continuous functions. Interestingly, in recent research, linearity and continuity (when the domain is endowed with a topology), are often deduced rather than imposed on preservers.

The purpose of this mini-symposium is to bring together mathematicians who are working on or interested in such questions. We plan to have talks on preserver problems related to linear or abstract algebra, functional analysis, geometry, mathematical physics and operator theory. We encourage everybody interested in this topic to participate in the meeting.

Organizer

Sergey Grigorian (University of Texas Rio Grande Valley, USA), sergey.grigorian@utrgv.edu

Co-Organizers

Mahir Bilen Can (Tulane University), mcan@tulane.edu

Sema Salur (University of Rochester), salur@math.rochester.edu

Description

The subject of geometric structures on Riemannian manifolds is a very important, and intensely studied, subject in Differential Geometry. In particular, geometric structures such as contact geometry, symplectic geometry, calibrated geometry, and special holonomy geometries, are all defined by differential forms, and turn out to be very closely related to one another. Ever since the foundational work of Harvey and Lawson in 1982, the relationship between calibrated geometry and special holonomy has been of fundamental importance in Differential Geometry, as any $G$-invariant $p$-form on $\mathbb{R}^{n}$ induces a calibration on a connected Riemannian manifold $( M^{n}, g)$ with holonomy $G \subset O(n)$. Moreover, recent directions in research shows that there are manifolds that lie at the intersection of contact geometry and special holonomy, in particular, $G_{2}$ and $Spin(7)$ holonomy manifolds, and that many ideas from both contact geometry and symplectic geometry have analogues to manifolds with special holonomy. Many of these objects have complexifications which are amenable to algebraic geometric techniques. In turn, real algebraic analogues provide a new frontier for research.

The cross-pollination of ideas from different areas of geometry takes roots in papers such as those of Fernandez and Gray from the 1960's wherein manifolds with special holonomy are treated as analogues of K\"ahler manifolds. Moreover, because of the introduction in recent years of such powerful tools in symplectic and contact geometries such as Floer homology theories and its relatives, it is more important than ever to understand the connections between these fields as this will yield deeper results about manifolds with special holonomy and calibrated geometries than have been possible up to this point.

Our goal is to bring together a group of both junior and senior mathematicians who are experts in these different geometric structures in order to create a venue where they can interact and exchange ideas and developments, and to further the understanding of the relationships between these geometries, as well as the implications in gauge theory, (real) algebraic geometry, geometric PDE's, and mathematical physics.

Organizer

John Shawe-Taylor (University College London, Knowledge 4 All Foundation, UK), jst@cs.ucl.ac.uk

Co-Organizers

Benjamin Guedj (University College London, UK), benjamin.guedj@inria.fr

Marc Deisenroth (University College London, UK), m.deisenroth@ucl.ac.uk

Maria Florina Balcan (Carnegie Mellon University, USA), ninamf@cs.cmu.edu

Avrim Blum (TTIC, USA), avrim@ttic.edu

Description

Artificial Intelligence aims to understand and reproduce intelligent behaviour and decision making in computing systems. There has been a burgeoning interest in the topic following high profile successes such as the AlphaGo system that was able to defeat leading human players in the game of Go, widely regarded as a yardstick of human intelligence. This development did not come from nowhere, but rather built on developments in machine learning, reinforcement learning, statistical learning, in many cases supported by various mathematical and statistical foundations.

This minisymposium aims to bring together mathematical work that explores the underpinnings of all aspects of artificial intelligence, including (but not limited to) statistical learning theory, empirical process theory, stochastic control, Bayesian inference, decision theory, data compression, information theory, natural language processing, deep learning, model reduction, combinatorial search, network analysis, etc.

Organizer

Krzysztof Szajowski (Wrocław University of Science and Technology, Poland), krzysztof.szajowski@pwr.edu.pl

Co-Organizer

Vladimir V. Mazakov (KRC RAS, Petrozavodsk, Russia), vmazalov@krc.karelia.ru

Description

The theme of the mini-symposium is devoted to game-theoretic modeling in a wide range of fields. Different optimality or rationality principles are presented. The problems of stable cooperation and myopic behavior in multi-agent systems will be investigated. Among others, we will consider the optimal location and allocation of the resource on the plane and related with them optimal routing in networking.

A new formulation for differential games will be suggested. It is supposed that the players leave the game at random time instants $T_i$ with known probability distribution $F_i$ which can be different for different players. The example of differential games with environment context is represented. The Nash equilibrium is calculated under some circumstances.

Further research on an optimal stopping problem for point processes will be presented. The illustrated examples are extensions of various online auctions and the research on the "debugging problem". The typical process of software testing consists of checking subroutines. In the beginning, many kinds of bugs are searching. The consecutive stopping times are moments when the expert stops general testing of modules and he starts checking the most important, dangerous types of error. Similarly in proofreading the natural is to look at typographic and grammar errors at the same time. Next, we are looking for language mistakes.

Details of other models will be subject to contributed papers.

Organizer

Grzegorz Graff (Gdansk University of Technolgy, Poland), grzegorz.graff@pg.edu.pl

Co-Organizer

Prof. Piotr Oprocha (AGH University, Kraków, Poland), oprocha@agh.edu.pl

Description

The application of various types of topological methods in dynamical systems is a relatively new and promising area of research, which has been developing rapidly during the last two decades. The minisymposium will be focused on (but not limited to) topological invariants and they use to study dynamical systems. The session will cover the following topics: Lefschetz and Nielsen numbers, zeta-type functions, fixed point index and fixed point indices of iterations, Conley index, measures of complexity, entropy, as well as their applications (in dynamics, periodic point theory, differential equations, physics, etc).

Organizer

Karin Cvetko-Vah (University of Ljubljana, Slovenia), karin.cvetko@fmf.uni-lj.si

Co-Organizers

Michael Kinyon (Denver University, USA), karin.cvetko@fmf.uni-lj.si

Joao Pita Costa (Institute Jozef Stefan, Slovenia), joao.pitacosta@ijs.si

Description

Universal algebra and category theory are meeting points for a range of algebraic theories that come together in finding solutions. Recently, noncommutative generalizations of lattices and related structures have seen an upsurge in interest, with new ideas and applications emerging, from quasilattices to noncommutative frames and noncommutative topoi. Much of this activity derives in some way from the initiation, thirty years ago, by Jonathan Leech, of a research program into structures based on Pascual Jordan's notion of a noncommutative lattice.

This second workshop on noncommutative structures aims to present the breadth of contemporary research in the area. It will bring together top researchers in the field, and provide space for fruitful interaction between the participants. The attendee does not need a specific background knowledge to access the discussions held, other than basic knowledge from order structures and possibly semigroup theory.

Organizer

Carlo Marinelli (University College London, UK), cm788bz@gmail.com

Description

The main themes of the minisymposium are the theory and applications of stochastic evolution equations. Such equations arise in many fields within mathematics as well as in physics, life sciences, and finance, to mention just a few, and have been intensively studied in the last years.

The session will include contributions on the well-posedness of stochastic evolution equations in various settings (e.g., in the functional analytic, random field, and variational approach, as well as in the recently developed frameworks of rough paths and regularity structures), on the asymptotic behavior of the solutions, and on control problems. Both abstract and specific models will be discussed.

The mini-symposium will be an opportunity for interaction and exchange of ideas among international experts and early-career mathematicians working in this field.

Organizer

Primož Potočnik (University of Ljubljana, Faculty of Mathematics and Physics), primoz.potocnik@fmf.uni-lj.si

Co-Organizer

Primož Šparl (University of Ljubljana, University of Primorska, Slovenia), primoz.sparl@pef.uni-lj.si

Description

Investigation of symmetry of a discrete structure (such as an abstract polytope or a graph) can be approached either by purely combinatorial means (think, for example, of the classical treatment of the Platonic solids by ancient Greeks), or by considering the automorphism group and the action thereof on different parts of the structure (such as vertices or edges of a graph).

This research area, therefore, lies at the intersection of discrete mathematics (combinatorics) and algebra (mainly group theory) thus drawing to it researchers from both of these mathematical disciplines.

Objects whose automorphism group acts transitively on the parts that constitute them are particularly interesting, both from the combinatorial as well as algebraic point of view. Families of such objects include vertex-transitive, edge-transitive and arc-transitive graphs, regular maps, and regular abstract polytopes. Investigation of these combinatorial objects is an active and quickly growing research area.

The proposed minisymposium will serve as an opportunity to reflect on recent advances and open challenges in this area, as well as to discuss and propose new avenues of research.

Organizers

Sašo Strle (University of Ljubljana, Slovenia), saso.strle@fmf.uni-lj.si

Brendan Owens (University of Glasgow, School of Mathematics and Statistics, UK), brendan.owens@glasgow.ac.uk

Description

Low-dimensional topology is the study of manifolds of dimension 4 or lower, such as our physical universe and spacetime. This subject had its origins in Europe with the work of such luminaries as Poincaré, Heegaard, Seifert and Möbius. Dramatic developments in the later 20th century came from the work of, in particular, Donaldson, Freedman, Gromov, Ozsváth, Szabó, and Witten. Today the subject is the focus of a tremendous amount of worldwide activity and has been enjoying a resurgence across Europe in the last two decades. Modern methods in low-dimensional topology draw on and are deeply connected with many other subjects including physics, differential geometry, combinatorics and representation theory.

This mini-symposium will bring together international experts in the subject including some of the most promising early career mathematicians working in the field. A range of topics and their connections to each other and other areas of mathematics will be explored. These will include symplectic and contact topology, Heegaard Floer homology, Seiberg-Witten theory and monopole Floer homology, and knot theory including Khovanov homology.

**Research area:** 57 Manifolds and cell complexes

Organizer

Francesca Bucci (Università degli Studi di Firenze, Italy ), francesca.bucci@unifi.it

Co-Organizer

Barbara Kaltenbacher (Alpen-Adria-Universität Klagenfurt, Austria), barbara.kaltenbacher@aau.at

Description

Partial differential equations (PDEs) are a powerful tool for modeling real world phenomena ranging from physics to engineering, biology and also economic sciences.

Consequently, their mathematical analysis is a highly active area reaching out into both pure and applied mathematics. Often, quantities in the PDE model such as coefficients, geometric characteristics, initial or boundary conditions, can be used to steer the PDEs solution to a certain desired state. On the other hand, in many applications, some of these quantities are unknown and need to be determined from additional observations derived from the PDE solution.

This leads to control and inverse problems, respectively. Both tasks heavily rely on the quantitative and qualitative knowledge on the PDE; including e.g. the regularity or the asymptotic behaviour of the corresponding solutions. There are even much closer synergies between optimal control and inverse problems in view of the analogies between controllability and observability as well as uniqueness via duality. From a computational point of view, regularization methods for inverse problems often take a variational form, with regularization incorporated via penalty terms or via constraints on the searched quantity which – in the language of optimal control – usually takes the place of the control.

In spite of these strong common interests, the communities of control and inverse problems for PDEs are still largely separated (with a few exceptions), in the absence of a regular forum for the dissemination of the ongoing research, along with the exchange on topical questions, methods, techniques and open problems.

The aim of this Minisymposium is therefore to foster discussion, encourage cooperation, stimulate networking among individuals (or research groups) from different communities, countries and generations. It is our aim to involve both seniors and juniors pursuing research work within the aforesaid contexts, as well as more generally in the area of mathematical analysis of composite PDE systems describing diverse physical interactions.

Organizer

Rita Fioresi (University of Bologna, Italy), rita.fioresi@unibo.it

Co-Organizers

Ugo Bruzzo ( Sissa, Italy), bruzzo@sissa.it

Fabio Gavarini (Universita' di Roma, Tor Vergata, Italy), gavarini@mat.uniroma2.it

Norbert Poncin (University of Luxembourg, Luxembourg), norbert.poncin@uni.lu

Description

Supergeometry, noncommutative geometry and quantum groups are three theories that extend usual geometry and Lie theory to include some form of noncommutative or ``quantum’’ behavior. These theories have been a very active area of research over the last 40 years. After the pioneering work by Berezin on supergeometry, later on further developed by Leites, Manin and Deligne, and others, Witten with his work on supermoduli spaces of SUSY curves, has paved the road towards deeper results and applications.

The original motivation of the theory of Quantum Groups was to find a version of geometric group theory which was well adapted to fit into a quantum mechanical description of the microscopic worlds. Then, it developed to be an independent and active field of mathematics. After the seminal works by Drinfel'd and Jimbo, later developed by Manin and others, currently there is more focus on specific topics. In this workshop, in particular, we want to cover the theory of homogeneous quantum spaces and their (universal) differential calculus and categorification theory.

Main topics of the workshop:

- Supermoduli spaces
- Super Lie groups and Lie superalgebras
- Quantum Groups and quantum algebras
- Non commutative geometry
- Supergeometric and quantum methods in physics

The aim of this mini-symposium is to bring together researchers working in the field of supersymmetry and quantum theory, to foster the exchange of ideas between these fields, which also have a rich interaction with other areas in mathematics.

Organizer

Luca Heltai (International School for Advanced Studies, Italy), luca.heltai@sissa.it

Co-Organizer

Wenyu Lei (International School for Advanced Studies ), wenyu.lei@sissa.it

Description

Singular source terms are widely used in partial differential equations to model complex physical phenomena happening at lower dimensional scales, such as immersed interfaces or fibers, fluid-structure interaction problems, dislocations phenomena, as well as doping or defects in electronic devices. From the computational point of view, one challenging problem is to deal with the discretization of singular source terms whose support may be moving or may not be aligned with the discretisation of the physical domain. To resolve the issue, many techniques have been developed in the last three decades, including variational formulations, regularization of the Dirac measure, adaptive methods, cut cell and extended finite element methods, and others.

This mini-symposium aims at gathering researchers in related areas. The discussion will focus on recent advances on the theory of PDEs involving singular source terms, their approximation techniques, and the corresponding numerical analysis.

Organizer

Nicola Zamponi (Charles University of Prague, Czech Republic), zamponi@karlin.mff.cuni.cz

Co-Organizers

Esther S. Daus (Vienna University of Technology, Austria), esther.daus@tuwien.ac.at

Josipa Pina Milišić (University of Zagreb, Croatia), pina.milisic@fer.hr

Description

The problem of describing the transport of chemical mixtures in porous media is very important in many industrial applications, like for example oil engineering, waste-water treatment, nuclear waste repository management, or carbon dioxide sequestration.

The aim of this minisymposium is to connect experts in the field of multiphase flow modeling in porous media with those involved in cross-diffusion systems and entropy methods.

Cross diffusion is the phenomenon in which a gradient in the concentration of one species affects the diffusion flux of another species, which happens as well in many physical applications. From the mathematical viewpoint, these cross-diffusion systems are strongly coupled nonlinear parabolic equations. Because of their strong coupling, many tools from the theory of partial differential equations, like maximum principles and regularity theory, cannot be applied to such systems. In recent years, entropy methods have been successfully extended to cross-diffusion systems, which allowed us to reveal in some cases their formal gradient-flow structure and to develop a global existence analysis.

In the framework of this minisymposium, we would like to discuss possible extensions of entropy methods to cross-diffusion systems in porous media with drift and reaction terms, the thermodynamical background of the proposed models and the construction of efficient numerical approximations which preserve physical properties of the solutions.

Organizer

Francesco Polizzi (Università della Calabria, Italy), polizzi@mat.unical.it

Co-Organizer

Matteo Penegini (Università degli Studi di Genova, Italy), penegini@dima.unige.it

Description

Algebraic Surfaces are a classical and central topic in Algebraic Geometry, having deep and often surprising connections to other broad subjects like Differential Geometry, Symplectic Geometry, Complex Geometry, Commutative Algebra and Number Theory.

Many old problems in the field have recently been solved, like the Severi Conjecture (Pardini), the classification of fake projective planes (Prasad and Yeung), the construction of simply connected numerically Campedelli surfaces (Lee and Park), the density of Chern slopes of simply connected surfaces of general type in the interval [2, 3] (Roulleau and Urzúa). However, many open questions and challenging problems still remain ahead of us.

The Special Session on “Arithmetic and Geometry of Algebraic Surfaces” will bring together several experts, with particular emphasis on young scientists, in order to discuss the latest developments in this important area of research.

A wide range of topics will be explored: K3 surfaces, Abelian surfaces, elliptic surfaces, surfaces of general type, Hodge structures, automorphism groups and moduli spaces. Particular emphasis will be given to the interactions and the connections between the arithmetic and the geometric point of view.

This minisymposium will facilitate a rich exchange of ideas between people working on different aspects of the theory of Algebraic Surfaces; furthermore, it will be an opportunity for PhD students and postdocs to learn results and techniques in such an exciting and rapidly-changing subject.

Organizer

Miroslav Bulíček (Charles University, Faculty of Mathematics and Physics, Czech Republic), mbul8060@karlin.mff.cuni.cz

Co-Organizer

Dalibor Pražák ( Charles University), prazak@karlin.mff.cuni.cz

Description

Modern continuum thermodynamics provides a framework for mathematical modelling of behaviour of fluids, gases and solids at time and length scales accessible to direct human experience. It is indispensable in modelling of various important natural phenomena and also phenomena met in engineering practice. Most of the processes that are of interest in this field are, in the language of thermodynamics, strongly non-equilibrium processes or entropy producing processes. Concerning the mathematical point of view, one needs to deal with complicated dynamics of infinite dimensional dynamical systems.

The far-from-equilibrium processes give birth to dissipative structures (known also as self-sustaining processes, coherent structures or convectons) which can be understood as large scale structures that dominate the behaviour of the system. Such structures have been identified in many experiments and, to a limited extent, in simulations based on numerical solution of the corresponding system of partial differential equations. A solid mathematical theory that would allow one to study the dissipative structures is however largely non-existing. The aim of the symposia is to present a variety of available new tools and methods that could help us to understand far-from-equilibrium processes and that would serve as a rigorous mathematical background, in particular, the methods that would allow one to identify the conditions for the formation of the structures, and tools for identification of the structures as low dimensional subsystems in infinite dimensional dynamical systems.

Organizer

Saeid Alikhani (Yazd University, Iran), alikhani206@gmail.com

Description

The minisymposia will study polynomials canonically associated to graphs and their zeros. Example of some graph polynomials include the chromatic polynomial, the reliability polynomial, the Tutte polynomial, the independent polynomial, the matching polynomial, the domination polynomial and the total domination polynomial. From the point of view of statistical physics, these polynomials are nothing other than the partition functions of standard statistical-mechanical models (e.g. the Ising model, the Potts model, the lattice gas, the monomer-dimer model) living on the graph. Combinatorialists study the real and complex zeros of such polynomials to ascertain how they are related to the combinatorial properties of the underlying graph (planarity, chromatic number, maximum degree, connectivity, etc.).

The minisymposia will bring together some of the principal researchers in this field to review recent advances and to brainstorm concerning the many unsolved problems. It will also feature tutorial seminars describing the main results and proof techniques, such as deletion/contraction, the multivariate approach, cluster expansion, and transfer matrices. The topics will be of interest to combinatorial mathematicians, mathematical physicists, theoretical physicists and computer scientists.

Organizer

Yan-Quan Feng (Beijing Jiaotong University, China), yqfeng@bjtu.edu.cn

Co-Organizer

Rong-Xia Hao (Beijing Jiaotong University, China), rxhao@bjtu.edu.cn

Description

The interconnection networks are usually represented by an undirected graph, in which vertices represent processors and edges represent links between processors. To achieve high performance, mathematicians and computer scientists recommend graphs with high levels of symmetry as models for interconnection networks, because of the many advantages that they exhibit. The study of graph symmetries is closely related to the fields of group theory, as well as graph theory, and the symmetry of a given graph is measured principally from a group-theoretic viewpoint. This forms an important interdisciplinary subject of group theory, graph theory and network theory, and nowadays, it is becoming a very important and rapidly growing area of study.

The goal of this proposed minisymposium would be to provide an excellent forum for leading experts in the interdisciplinary area of groups, graphs and networks to share recent developments and techniques among themselves, to develop further collaborations, and to provide an opportunity for younger, up-and-coming researchers to meet and learn from established authorities in the subject area.

Topics of this proposed minisymposium would include (but not be limited to) the following: automorphisms of graphs; interactions with permutation groups; Cayely and bi-Cayley networks; algorithm of graphs; matching cover; faulty tolerance and reliability analysis of networks; cycles and factors in graphs; network design problems from communication.

Organizer

Aleksandra Puchalska (University of Warsaw, Poland), apuchalska@mimuw.edu.pl

Co-Organizer

Delio Mugnolo ( University of Hagen, Germany), delio.mugnolo@fernuni-hagen.de

Description

Graphs are used to model physical processes - be they of diffusive, elastic or quantum mechanical nature, to name a few - taking place on network-like structures. The analysis of evolutionary problems on graphs has a long tradition; along with a classical approach based on operator semigroups, variational methods have recently received much attention.

Among other lively subjects we mention spectral geometry for the asymptotic analysis of parabolic equations, quadratic form methods for extension theory, and optimal transport.

All these subjects also rate among the manifold mathematical interests of the member of the research project “Mathematical models for interacting dynamics on networks". Chaired by Marjeta Kramar Fijavž (Ljubljana) and funded by the COST-Association between 2019 and 2023 (Grant CA-18232), this program is devoted to both fundamental research and industrial applications: this Minisymposium will also serve as a showcase of the ongoing research projects.

The topics touched upon during our Minisymposium will include continuous, discrete or hybrid models of graphs; large networks and fractals; linear and nonlinear problems; spectral theory along with evolutionary equations.

We are going to gather colleagues who are currently developing different aspects of dynamical systems jointed by an underlying network structure; thus fostering the dialogue between our and neighbouring communities.

Organizer

Paweł Dłotko (Mathematical Institute, Polish Academy of Sciences, Warsaw, Poland), pdlotko@impan.pl

Co-Organizers

Wacław Marzantowicz (Institute of Mathematics, Adam Mickiewicz University, Poznan, Poland), marzan@amu.edu.pl

Petar Pavešić (University of Ljubljana, Slovenia), petar.pavesic@fmf.uni-lj.si

Description

Topological ideas and methods are increasingly becoming part of the standard tool-kit of modern science and technology. Conversely, practical applications give rise to very interesting and challenging topological problems and is giving a strong impetus to the development of completely new areas of topological research.

This session aims to bring together experts developing innovative ideas and methods for applications of topology in science and engineering. We will focus on tools that have a potential to solve problems in physics (including phase transition phenomena and topological hypothesis), data science, machine learning and scientific visualization (geometric and topological invariants of discrete data, etc.), material science (descriptors of porous materials, crystals, etc), algorithms for robot motion planning and more.

The session will be open to scientists from other disciplines with the aim to trigger new discussions and collaborations.

Organizer

Karl-Theodor Sturm (University of Bonn, Hausdorff Center for Mathematics), sturm@uni-bonn.de

Co-Organizer

Eva Kopfer (University of Bonn, Germany), eva.kopfer@iam.uni-bonn.de

Description

The last fifteen years have seen a tremendous progress in the understanding of the structure of metric measure spaces in general and in particular of those carrying some synthetic lower bound on the Ricci curvature. In the Lagrangian approach, such bounds are formulated in terms of semi-convexity of the Boltzmann entropy w.r.t. optimal transport; in the Eulerian approach, they are formulated in terms of the Gamma_2-operator associated with the Sobolev spaces built on the respective spaces. The interplay of analysis, geometry, and probability in recent years led to many deep insights and gave rise to numerous powerful new developments with important applications in various areas of mathematics. In the meantime, most of the results originally known for Ricci-limit spaces in the sense of Cheeger-Colding have been generalized to length spaces with such synthetic lower Ricci bounds. Current challenges aim at a better understanding of boundaries, of distribution-valued Ricci bounds, and an optimal transport formulation of the full Einstein equations of general relativity. For discrete spaces, important homogenization results have been obtained in recent years.

The aim of this mini-symposium is to bring together leading international experts and young promising researchers developing different aspects of Metric Measure Spaces with Synthetic Ricci Bounds, of Geometric Analysis on Singular Spaces with particular focus on heat flow and gradient flows, and of Optimal Transport. We will discuss the latest achievements as well as new directions of future research.