These are confirmed Satellite Conferences that will be held under the 8th European Congress of Mathematics.

## Internal Satellite

Optimization in Insurance | Portorož, Slovenia |

**23 June 2021 **

**Congress Centre Bernardin, Portorož, Slovenia**

This internal satellite conference is held during the 8th European Congress of Mathematics - 8ECM.

The scope of the conference Optimization in insurance is to present concrete optimization problems in insurance, from gathering and storing data to risk control. The lecturers come mostly from industry and will present concrete examples they have encountered in their professional work. The contributions are of particular interest to risk managers and actuaries working in the insurance industry. The lectures are aimed at ideas on how to make companies more competitive.

Participants are invited to contribute with a poster presentation.

This satellite conference is **open free of charge** to all **registered participants of the 8ECM** with their 8ECM accreditation badge.

If you would like to participate in this satellite conference only, please visit https://conferences.famnit.upr.si/event/20/registrations/15/ for more information.

The Satellite conference is co-organized by the Slovenian Insurance Association.

## External Satellites

# Graphs and Groups, Geometries and GAP (G2G2-Summer School)

##### External Satellite Conference

https://conferences.famnit.upr.si/event/13/

##### Research area:

Combinatorics

##### Short overview:

G2G2-Summer School is associated with G2G2-Minisymposia of 8ECM. It belongs to the G2-series that are about strong and beautiful mathematics, especially those involving group actions on combinatorial objects.

The main goal of G2G2-Summer School is to bring together experts and students to exchange ideas and to enrich their mathematical horizon.

We organize two short courses and four colloquium talks to let participants see order and simplicity from possibly new perspectives and share insights with experts.

Students will have a chance to present their 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, and biology. The scientific program of the G2G2-Summer School consists of the following two courses each of which is presented by eight lectures.

• Mini course 1 (Lecturer: Atsushi Matsuo, The University of Tokyo, Japan): Representations of vertex operator algebras

• Mini course 2 (Lecturer: Leonard H. Soicher, Queen Mary University of London, UK): Graphs, groups and geometries in GAP

There will be daily solving problems sessions on the mini courses to help students in understanding the courses. There will be at least 12 short contributed talks given by students.

##### Date:

**27 June 2021 - 3 July 2021**

##### Location:

Rogla, Slovenia

##### Organizers:

Elena Konstantinova (Sobolev Institute of Mathematics, Siberian Branch of Russian Academy of Science, Russia)

Contact: e_konsta@math.nsc.ru

Alexander A. Ivanov (Imperial College London, UK)

# Combinatorics around the q-Onsager algebra

##### External Satellite Conference

https://conferences.famnit.upr.si/event/15/

##### Research area:

Combinatorics

##### Short overview:

At the conference we will be celebrating the 65th birthday of Paul Terwilliger. As such, the general theme of this conference will be the mathematical topics that Paul has worked on over the years (which all have relationships to the q-Onsager algebra). These topics include the following:

• Topics in algebraic graph theory, such as distance-regular graphs, association schemes, the subconstituent algebra, and the Q-polynomial property;

• Topics in linear algebra, such as Leonard pairs, tridiagonal pairs, billiard arrays, lowering-raising triples, and a linear algebraic approach to the orthogonal polynomials of the Askey scheme;

• Topics in Lie theory, such as the tetrahedron algebra and the Onsager algebra;

• Topics in algebras and their representations, such as the equitable presentation of U_q(sl_2), the q-tetrahedron algebra, the mathematical physics of the q-Onsager algebra, and the universal Askey-Wilson algebra.

One of the invited speakers for this satellite conference is a Fields medalist Sir Vaughan F.R. Jones.

##### Date:

**28 June 2021 - 3 July 2021**

##### Location:

Kranjska gora, Slovenia

##### Organizers:

Štefko Miklavič (University of Primorska, Andrej Marušič Institute, Slovenia)

Contact: stefko.miklavic@upr.si

Mark Maclean (Mathematics department, Seattle University, USA)

Contact: macleanm@seattleu.edu

# Combinatorial Designs and Codes

##### External Satellite Conference

https://cdc2020-math.uniri.hr/

Research area:

Combinatorics

##### Short overview:

The goal of the conference is to bring together researchers interested in combinatorial designs, algebraic combinatorics, finite geometry, graphs, and their applications to communication and cryptography, especially to codes (error-correcting codes, quantum codes, network codes, etc.) .

The main topics of the conference are:

- construction of combinatorial designs and strongly regular graphs, including constructions from finite groups and codes;

- construction of linear codes from graphs and combinatorial designs;

- network codes related to combinatorial structures;

- hadamard matrices;

- association schemes;

- codes, designs and graphs related to finite geometries;

- q-analogues of designs and other combinatorial structures.

The talks presented at the conference will also cover other related topics suggested by the participants. The conference will give an opportunity to research faculty and young researchers in discrete mathematics to learn about the latest developments and explore different visions for their future work. The talks will cover both the theoretical and applied aspects of discrete mathematics, and the latter will be particularly beneficial for faculty and young researchers, by giving them the opportunity to learn more about contemporary applications of combinatorics to communications and information security.

##### Date:

**11 - 16 July 2021**

##### Location:

Rijeka, Croatia

##### Organizer:

Dean Crnković, University of Rijeka, Croatia

Contact: deanc@math.uniri.hr

##### Coorganizer:

Sanja Rukavina, University of Rijeka, Croatia

Contact: sanjar@math.uniri.hr

# Integrable systems in geometry and mathematical physics. In memoriam of Boris Dubrovin (1950-2019)

https://indico.sissa.it/event/41/

##### External Satellite Conference

##### Research area:

Dynamical systems and ergodic theory

##### Short overview:

The notion of integrable systems in classical mechanics dates back to Joseph Liouville (1809-1882) and has an illustrious and long history. The modern resurgence of activity was spurred by the analysis of soliton solutions of nonlinear wave equations like the Korteweg-deVries and Kadomtsev-Petviashvili equations. This renewed interest brought along the invention and development of far reaching techniques of solution, including the inverse scattering method and the Sato-Segal-Wilson theory of infinite Grassmannians.

The notion of integrable systems has since expanded considerably and often refers to a wide range of techniques. The development of techniques and new classes of integrable models has both cross-fertilized and received input from distant areas of mathematics and physics. In string-theory it famously and surprisingly appeared in the conjecture of Witten, later proved by Kontsevich, and with a different techniques by Okounkov, that the generating function of certain geometric invariants of the moduli space of pointed stable Riemann surfaces is a so--called Tau-function of the KdV hierarchy. This connection can be exploited in effective ways to actually compute these intersection numbers by means of explicit formulas that stem precisely from their connection with the KdV hierarchy as recently shown by Dubrovin et al.

In more general terms, the appearance of integrable systems from the structure of the intersection theory of the moduli space of curves has become an active and rich research topic in both algebraic geometry and symplectic topology, after the work of Givental, Eliashberg, Dubrovin, Shadrin, Buryak, Rossi and others.

Integrable system techniques and ideas weave into many other outstanding areas of mathematics. One example occurs in the study of Yang-Mills equations, where Hitchin introduced the notion of Higgs bundles and associated to them a class of integrable systems.

Another significant example is represented by the theory of Random Matrices in the last twenty years, where much of the modern development occurred with the realization of the connection with orthogonal or biorthogonal polynomials and their intimate link with the Toda and KP hierarchies. This connection allowed also several outstanding developments thanks to the introduction of the Riemann--Hilbert approach and the nonlinear steepest descent method.

Along these lines the study of several determinantal random point fields (of which the eigenvalues of random matrices are a particular instance) led to the resurgence of the theory of Fredholm determinants and their unexpected connections with Painlevé equations, as exemplified by the case of the Tracy-Widom distribution.

Painlevé equations appear also in asymptotic analysis of small dispersion limits of integrable nonlinear wave equations including the KdV, Nonlinear Schrödinger, KP equations; for example in the study of leading edge asymptotics the dispersionless limit of KdV (second member of the first Painlevé hierarchy) and in the semiclassical limit of NLS (tritronquée solution of Painlevé I).

The latter case suggested a conjecture (Dubrovin-Grava-Klein) about the location of the poles of the tritronquée solution (later proved by O. Costin). Another open conjecture relates to the so-called universality property of these type of behaviour. Like the universality of scaling limit near the edge of the spectrum for random matrices, the appearance of Painlevé transcendents in semiclassical limits of nonlinear waves is conjectured to survive also perturbations that break the integrable nature of the equation.

Geometry of finite-dimensional invariant submanifolds of systems of integrable PDEs was the starting point for creating the theory of Frobenius manifolds that proved to be instrumental for understanding of deep relationship between the theory of Gromov-Witten invariants, topology of the Deligne--Mumford moduli spaces of algebraic curves and singularity theory on one side and the theory of integrable systems on the other. On this basis the theory of integrable systems of topological type has been built.

Integrable systems have also appeared in other unexpected corners of mathematics; for example the notion of Cluster Algebras was born as a generalization of the Plücker relations which underlie the ring of regular functions on the Grassmannian; in this respect the point of contact was first the pentagram map of R. Schwartz, but there are now several other instances where the two notions come together, like in the study of line solitons and the positive Grassmannian of Kodama and Williams.

The conference aims at bringing together leading mathematicians that have contributed and are contributing to the success and dissemination of methods and ideas originating from integrable systems in all areas of mathematics and physics.

The conference is dedicated in memoriam of Boris Dubrovin, whose activity in the past forty years has been a driving force and a reference beacon for many researchers in Mathematical Physics.

##### Date:

**28 June 2021 - 2 July 2021**

##### Location:

SISSA, Trieste, Italy

##### Organizer:

Marco Bertola, SISSA (Italy) and Concordia University (Canada)

Contact: marco.Bertola@sissa.it

Coorganizers:

Tamara Grava, SISSA, Trieste, Italy and University of Bristol, UK

Davide Guzzetti, SISSA, Trieste, Italy

Paolo Rossi, Universitá di Padova, Italy

# Contemporary Analysis and Its Applications

##### External Satellite Conference

https://www.caia-conference.eu/

##### Research area:

Analysis and Partial Differential Equations

##### Short overview:

Mathematical analysis goes back at least to the pioneering works of Newton and Leibniz and has since then experienced immense developments. The contributions by Bernoulli, Fourier, Hilbert and many other prominent mathematicians have laid the foundations for the development of both mathematical analysis and its close companion, mathematical physics. Modern daily life could not be imagined without major achievements in those areas. Today analysis has split into many closely related subfields. While hardly anyone can claim expertise in all of them, they bear one common general approach: dividing objects into smaller parts and looking at them at that level. In this context it is desirable to foster collaboration between analysts of various specializations, which is the guiding idea of the present conference.

The main focus of our conference is on (real) analysis and its numerous applications (the core topics include harmonic analysis and nonlinear PDEs, analysis on graphs, groups and manifolds, spectral theory and completely integrable systems).

Our goal is to provide an update on recent results, a discussion forum for future research goals and a starting point for new collaborations in the stimulating atmosphere of the ECM.

##### Date:

**16 - 20 June 2021**

Location:

Online

Portorož, Slovenia

##### Organizer:

Oliver Dragičević, University of Ljubljana, Slovenia

Contact: caia.conf@gmail.com

# 9th Linear Algebra Workshop

## - Cancelled

##### External Satellite Conference

http://www.law05.si/law20/index.php

##### Research area:

Linear and multilinear algebra; matrix theory

##### Short overview:

The Ninth Linear Algebra Workshop (LAW’20) will continue the tradition of the previous meetings. Its main theme will be the interplay between operator theory and linear algebra on one side and algebra with a variety of algebraic and geometric structures on the other.

Linear algebra is an interesting branch of mathematics that has gained in popularity lately. Since many problems from various branches of mathematics and applications are easily stated in the language of linear algebra, it is attracting people of a great variation of backgrounds, although their motivation to work in the area may differ a lot. It is our intention to bring together people whose motivation for linear algebra comes primarily from problems in operator theory, algebra and statistics, with applications, but are willing to learn (or are already familiar with) deeper concepts from either field that may help solve them. These concepts might come from the theory of groups and semigroups, from the theory of associative algebras and Lie algebras and include tools coming from algebraic geometry.

We believe that we should include the time to think about the problems, not only to listen to each other's formal talks. So, the workshop will be organized in a less formal way. After a few hours of morning talks as a motivation for our discussions later, we will split into smaller groups in the afternoon to concentrate on our problems.

The participants are welcome to suggest their own topics of interest for a working group. All topics of linear algebra that are within the broad scope outlined above are welcome.

##### Date:

29 June – 4 July 2020 **Cancelled**

##### Location:

Portorož, Slovenia

##### Organizers:

Matjaž Omladič (Institute of Mathematics, Physics and Mechanics, Slovenia)

Contact: matjaz@omladic.net

##### Coorganizers:

Damjana Kokol Bukovšek (University of Ljubljana, Slovenia)

Heydar Radjavi (University of Waterloo, Canada)

Tomaž Košir (University of Ljubljana, Slovenia)

Bojan Kuzma (University of Primorska, Slovenia)

Blaž Mojškerc (University of Ljubljana, Slovenia)

# Advanced Variational Methods for Solid Mechanics

## Cancelled

##### External Satellite Conference

##### Research area:

Calculus of variations and optimal control; optimization

##### Short overview:

Many challenging problems in solid mechanics require the use of advanced mathematical techniques. In particular, these are needed to model different kinds of inelastic behaviours. Another interesting field of application concerns the interplay between microscopic and macroscopic properties of solids, which can guide the design of novel materials starting from their nano-structure.

The goal of this conference is to bring together researchers interested in the applications of the calculus of variations to these problems. The main focus will be on the following topics: dislocations, plastic deformations, damage, fracture, and other defects. Both equilibrium and dynamic problems will be addressed.

Homogenisation techniques, which allow to deal with different space and time scales, and to describe the effective behaviour of materials, will also be covered in the conference. In particular, the recent advances in stochastic homogenisation will be presented.

Computational issues are very important in these fields, and the complexity of the phenomena requires advanced techniques based on the most recent developments of the mathematical modelling of these problems. Several invited speakers are well known experts in computational mechanics.

##### Date:

29 June – 2 July 2020** - Cancelled**

##### Location:

University of Udine, Udine, italy

##### Organizer:

Gianni Dal Maso (SISSA, Trieste, Italy)

Contact: dalmaso@sissa.it

##### Coorganizer:

Rodica Toader, University of Udine, Italy

Contact: toader@uniud.it

# Complex Analysis, Geometry, and Dynamics - Ljubljana 2021

## Reschedulled to 2022

##### External Satellite Conference

##### Research area:

Several complex variables and analytic spaces

##### Short overview:

The main goal is to bring together leading researchers worldwide in complex analysis, geometry, and dynamics, with the aim of enhanced future collaboration. These fields are strongly interrelated, and in order to be able to solve deep challenging problems, it is becoming necessary to pursue synergies among them to a bigger degree than in the past.

Topics:

- Holomorphic approximation theory

- L^2 techniques, plurisubharmonic functions, pluripotential theory

- Holomorphic dynamics in higher dimensions (wandering domains, Fatou components, attracting basins, Loewner chains)

- Holomorphic directed systems (contact systems, applications to minimal surfaces)

- Flexibility in complex geometry (manifolds with many symmetries)

- Rigidity in complex geometry

There have been major recent advances in all these fields (development of modern Oka theory, advances in Ohsawa-Takegoshi L^2 theory with precise estimates, solutions to the strong openness conjecture for plurisubharmonic functions, constructions of wandering domains and topologically nontrivial attracting basins, a unified theory of Lowner chains in higher dimensions, recent applications of complex analysis to holomorphic directed systems and minimal surfaces, advances in holomorphic flexibility and rigidity theory. It is becoming increasingly evident that a deeper level of synergies will be needed for further progress.

##### Date:

**14 June – 18 June 2021 ****- Reschedulled to 2022**

##### Location:

Ljubljana, Slovenia

##### Organizer:

Franc Forstnerič, University of Ljubljana, Slovenia

Contact: franc.forstneric@fmf.uni-lj.si

##### Coorganizers:

John Erik Fornaess, NTNU Trondheim

Xiaojun Huang, Rutgers University

Xiangju Zhou, University of Chinese Academy of Sciences

# RAMSES: Reduced order models; Approximation theory; Machine learning; Surrogates, Emulators and Simulators

##### External Satellite Conference

##### https://indico.sissa.it/event/43/

##### Research area:

Numerical analysis

##### Short overview:

The workshop deals with recent algorithmic and mathematical advances and the development of new research directions for Mathematical Model Approximations via RAMSES in the setting of parametrized partial differential equations with sparse and noisy data in high-dimensional parameter spaces. The workshop will impact the scientific, engineering, social, financial, economic, and environmental communities.

The workshop focuses on four promising approaches for near-future improvements in the way model approximation in the partial differential equation setting is carried out. The central objective of the workshop is to gather together both senior and junior researchers

- to exchange the latest knowledge and results each of these participants brings to the table;
- to provide guidelines for the most promising approaches for near-future research;
- to provide junior researchers with new problems that they can incorporate into their research plans.

A novelty of the workshop is the interaction of the mathematical community with application researchers who will be carefully chosen from among those that themselves have made algorithmic advances in approximations of PDEs and who are known to interact effectively and synergistically with mathematicians.

The focus on junior participants is perhaps the most important novelty of our workshop, as opposed to other approximation/data-science/machine learning meetings whose focus is primarily on senior participants with a much smaller percentage of junior participants being involved. The poster blitz and related poster session will give them visibility and allow for interactions with experts.

A very important feature of our workshop is that at the end of the second and third day a discussion session will take place. At these sessions, participants will review the talks of the day and discuss, in the context of the theme of the day, what are the most important and promising research directions that should be pursued in the future. The discussions will be facilitated by a panel of selected speakers, non-speaking experts and funding agency personnel. The outcome of these sessions will not only be of benefit to workshop participants, especially the junior ones, but will be a central aspect of our dissemination activities (e.g. submission of an article to SIAM News, publication of discussion notes on workshop’s webpage).

Expected outcome and impact of workshop

- The exchange, among participants in each focus topic of the workshop, of recent and even unpublished progress and results;
- The construction of guidelines for the most promising directions of near-future research;
- Synergistic exchanges between the mathematics and data science communities and establishment of new collaborations between them;
- Exposure of a sizeable group of junior researchers already active in the field to new problem areas and new directions for their research.

The workshop is also approved as PROESOF Trieste 2020 event. We apply to be also an external satellite event for 8ECM.

Participants

There will be approximately 120/150 participants: 20 invited senior and junior speakers. 30 junior poster presenters (graduate students or early postdocs). 5 miscellaneous participants (non-speaking organizers, funding agency personnel, etc.).

Confirmed senior speakers: P. Bochev (SNL), R. DeVore (Texas A&M), W. Dahmen (U SC), J. Hesthaven (EPFL), G.E. Karniadakis (Brown U), D. Oliver (CalTech), A. Quaini (U Houston), C. Schönlieb (U Cambridge), R. Smith (NC State), E. Ullman (TU Munich), C. Webster (ORNL), K. Willcox (UT Austin).

Note on diversity

The organizers are committed to include a diverse set of participants in the workshop. So far, 4 out of 12 confirmed speakers are women who have made significant contributions to at least one of the themes of the workshop. We emphasize that these women are not tokens; they genuinely deserve to be invited because of their accomplishments. We will also aggressively seek junior women and other underrepresented groups to participate as poster presenters.

Broader Impact and dissemination plans

The impact of the workshop will extend well beyond that on its participants. A complete and up to date web site will be created to report on what was presented at the workshop. All presentations and contact details will be made available on a web site as soon as the workshop is over and remain available on a semi-permanent basis. In addition, the outcome of the discussion sessions will be used to prepare a report summarizing what transpired at the workshop and what conclusions were drawn about future directions. A volume of special proceedings is also planned.

##### Date:

**7 - 10 June 2021**

##### Location:

SISSA Trieste, Italy

##### Organizer:

Gianlugi Rozza, SISSA Trieste

Contact: gianluigi.rozza@sissa.it

##### Coorganizers:

Dr. Marta D'Elia, Sandia NL, USA

Prof. Max Gunzburger, Florida State, USA

# Complex Geometry

## - Cancelled

http://icms.bg/complex-geometry/

##### External Satellite Conference

##### Research area:

Geometry

##### Short overview:

Complex Geometry is a leading subject in modern mathematics. In recent years, major advances were made in several areas. We will briefly mention a few directions:

- Birational Geometry
- Homological Mirror Symmetry
- Derived Algebraic Geometry
- Enumerative Geometry
- Symplectic Geometry
- Hodge theory
- Geometric Langlands.

The conference Complex Geometry, Sofia, July 15 - 18, 2020 will be an in-augural conference for the new International Center for Mathematical Sciences in Sofia (ICMS - Sofia).

We propose 6 stipends for young participants and 6 stipends for female participants.

- The total budget will be $ 50.000 coming from Simons Foundations and ICMS - Sofia.
- 6 stipends for young participants $ 1.000 each - altogether $ 6.000 mainly from Eastern Europe.
- 6 stipends for female participants $ 1.000 each - altogether $ 6.000.
- 25 stipends for other participants $ 1.000 each - altogether $ 25.000.
- administrative, organizational expenses $ 3.000.

In addition, we plan a conference on Homological Mirror Symmetry, to be held in Albena, Bulgaria, July 19 - 22, 2020.

Inaugural conference of ICMS - Sofia

Conference on Homological Mirror Symmetry

##### Date:

15 – 18 July 2020 **- Cancelled**

##### Location:

ICMS - Institute of Mathematics and Informatics, Bulgarian Academy of Sciences,

Sofia, Bulgaria

##### Organizer:

Ludmil Katzarkov, University of Vienna

Contact: lkatzarkov@gmail.com

##### Coorganizers:

Blagovest Sendov

Oleg Mushkarov

Johann Davidov

Velichka Milousheva (vmil@math.bas.bg)

Aleksander Petkov

# Rings and Polynomials

http://integer-valued.org/rings2021/

##### External Satellite Conference

##### Research area:

Commutative algebra

##### Short overview:

The scope of the conference "Rings and Polynomials" includes algebraic, number theoretic and topological aspects of rings, algebras and polynomials. The main focus lies on bringing together all these different aspects of ring theory. Therefore we do not restrict ourselves to commutative rings, but are also interested in non-commutative set-ups, e.g. in factorization theory of non-commutative rings. Beside talks to well-known concepts such as multiplicative ideal theory, Zariski-Riemann spaces of valuation domains, factorization theory in rings and semigroups, Dedekind, Prüfer, and Krull domains, there will be two special session on integer-valued polynomials and topological methods in ring theory in memory of Paul-Jean Cahen.

##### Date:

**19 - 24 July 2021**

##### Location:

University of Technology Graz, Austria

##### Organizer:

Sophie Frisch, Technical University of Graz, Austria

Contact: frisch@blah.math.tugraz.at

# Analysis and Numerics of Design, Control and Inverse Problems

##### External Satellite Conference

##### Research area:

Partial differential equations

##### Short overview:

The workshop was selected by INdAM (Istituto Nazionale di Alta Matematica “F. Severi”, Roma, Italy) as one of the INdAM workshop for the year 2020. As the title of the workshop suggests, it will cover several topics in Applied Mathematics, including Control of PDEs, Shape Optimization, Inverse Problems and Numerical Analysis and Scientific Computing. In many applications of mathematics one is confronted with the problem of steering a given system to a prescribed configuration, and often to do so in an optimal way. Sometimes this requires the optimal design of the shape of a body. All these issues can be addressed with a common body of techniques, ranging from functional analysis to partial differential equations, always in strict contact with numerical analysis for necessary implementation. Surprisingly enough, some of these techniques can be used to recover information on parameters from measurements of the solution. These are so-called inverse problems which play an important role in climate science and bio mathematics. The aim of this session is to bring together experts in the above fields to explore the possibility of collaboration. We particularly expect the participation of young researchers, for whom the session is dedicated.

##### Date:

**28 June - 2 July 2021**

##### Location:

Istituto Nazionale di Alta Matematica (INdAM) "F. Severi",

Roma, Città Universitaria - P.le Aldo Moro 5, 00185 - Roma, Italy

##### Organizer:

Giuseppe Floridia, Università Mediterranea di Reggio Calabria, Italy

Contact: floridia.giuseppe@icloud.com

##### Co-organizer:

Enrique Zuazua, Friedrich–Alexander University (FAU), Erlangen–Nürnberg (Germany) & University of Deusto, Bilbao & UAM, Madrid

Contact: enrique.zuazua@fau.de

# International Conference on Topology and its Applications (ICTA2020)

## - Cancelled

##### External Satellite Conference

##### Research area:

General topology

##### Short overview:

The International Conference on Topology and its applications is devoted to all areas of Topology as General Topology, Homotopy and Shape, Topological Dynamics, Digital Topology, Computational Topology, … In the last decade, the methods of intrinsic shape were successfully applied, for detecting how the limit sets in Dynamical systems “look like”. Shape theory is more applicable than homotopy since limit sets usually have complicated local structure. These methods are in fact methods of discretization and are related to methods used in Digital topology and Computational topology.

History of the Conference: The First International Conference on Topology and its Applications ( ICTA 2000) was organized in Ohrid, N.Macedonia, in 2000. Several conferences were organized after this in N. Macedonia, Greece and Turkey. Usually, conferences in Macedonia are organized every fourth year by the Institute of Mathematics, Faculty of Natural Sciences and Mathematics at University of St. Cyril and Methodius, Skopje.

The conference will be organized by Institute of Mathematics , Faculty of Natural Sciences and Mathematics at University of St. Cyril and Methodius, Skopje. The venue of the Conference is Institute of Mathematics, Faculty of Natural Sciences and Mathematics. The Institute of Mathematics, although not far from the city center, is situated on the hill, surrounded by forest and is really far from the urban noise. There are several hotels nearby, the most known is hotel Continental, where is planned the accommodation of most participants. We are expecting about 100 participants.

Registration fee of 100 euros will cover the conference materials and coffee breaks. Supporters of the Conference:

- University of St. Cyril and Methodius
- Ministry of Science and Education of N.Macedonia
- Union of Mathematicians of N.Macedonia

##### Date:

30 June – 3 July 2020 **- Cancelled**

##### Location:

Institute of Mathematics, Faculty of Natural Sciences and Matjematics at University of St. Cyril and Methodius,

Skopje, North Macedonia

##### Organizer:

Nikita Shekutkovski, University of St. Cyril and Methodius, Faculty of Natural Sciences and Mathematics, Institute of Mathematics, Skopje, North Macedonia

Contact: nikita@pmf.ukim.mk

# Equivalences, Numberings, Reducibilities

##### External Satellite Conference

##### Research area:

Logic and Mathematical Aspects of Computer Science

##### Short overview:

A major theme in contemporary mathematics is to classify structures according to various criteria: one may classify countable graphs up to isomorphism, complete metric spaces up to isometry, $n$-square complex matrices up to similarity, etc. If for a certain class one finds nice invariants that identify when two different structures are ``equivalent'', then the study of all structures can be reduced to the study of the equivalence classes labeled by the invariants. As is clear, a classification can be more or less satisfactory depending on the complexity of the equivalence relation that it generates. More generally, equivalence relations appear everywhere in mathematics and logicians put considerable effort in developing reducibilities to measure their complexity.

In descriptive set theory, one often deals with equivalence relations defined on Polish spaces, which are classified in terms of Borel reductions. The theory of Borel equivalence relations is now a central field of modern descriptive set theory, that shows deep connections with topology, group theory, combinatorics, model theory and ergodic theory---to name a few.

In computability theory, the study of the algorithmic complexity of equivalence relations is a broad research program which has multiple roots, being initiated many times with parallel interests and purposes. This partially reflects the historical development of the subject, that was studied, largely independently, in both Soviet Union and the West. Nowadays, this study is quite heterogeneous, consisting of various research directions which, although conceptually close, are often conducted with few interactions.

The goal of this workshop is to enhance the integration between existing ways of evaluating the complexity of equivalence relations. This will allow leading logicians from across the globe to exchange ideas and techniques, possibly individuating new encompassing questions and formulating a common agenda.

The workshop will assemble 12 speakers and it will last for three days. The workshop is hosted by University of Udine but, due to the ongoing restrictions for Covid-19 outbreak, it will be held virtually. Nonetheless, we plan to adopt several strategies (e.g., recordings of the talks, virtual rooms for informal gatherings, digital blackboards) to mitigate the shortcomings of virtual workshops.

The topics of the workshop include but are not limited to:

- numberings, ceers, and computable reducibility
- word problems and other algorithmic problems in algebra
- computable functors and algorithmic reductions for classes of structures
- effective analogues of the theory of Borel equivalence relations

##### Date:

16 - 18 June 2021

##### Location:

Udine, Italy

##### Organizer:

Luca San Mauro (Technische Universität Wien, Austria)

Contact: luca.sanmauro@gmail.com

##### Co-Organizers:

Nikolay Bazhenov (Sobolev Institute of Mathematics, Novosibirsk, Russia),

Contact: bazhenov@math.nsc.ru

Alberto Marcone (Università degli Studi di Udine, Italy),

Contact: alberto.marcone@uniud.it

Manat Mustafa (Nazarbayev University, Nur-Sultan, Kazakhstan),

Contact: manat.mustafa@nu.edu.kz

Sergei Ospichev (Sobolev Institute of Mathematics, Novosibirsk, Russia)

Contact: ospichev@math.nsc.ru