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

To apply with a Satellite Conference proposal, please visit https://www.8ecm.si/calls/call-for-satelite-conferences

Combinatorics

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, 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.

29 June – 4 July 2020

**Rogla, Slovenia**

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

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

**Contact**: e_konsta@math.nsc.ru

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

Combinatorics

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.

13 – 18 July 2020

**Kranjska gora, Slovenia**

**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

Research area:

Combinatorics

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 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.

12 July – 17 July 2020

Rijeka, Croatia

**Dean Crnković**, University of Rijeka, Croatia

Contact: deanc@math.uniri.hr

**Sanja Rukavina**, University of Rijeka, Croatia

Contact: sanjar@math.uniri.hr

Research area:

Dynamical systems and ergodic theory

The notion of integrable system 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 {\it 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) lead to the resurgence of the theory of Fredholm determinants and their unexpected connections with Painlev\'e\ equations, as exemplified by the case of the Tracy-Widom distribution.

Painlev\'e\ equations appear also in asymptotic analysis of small dispersion limits of integrable nonlinear wave equations including the KdV, Nonlinear Schr\"odinger, KP equations; for example in the study of leading edge asymptotics the dispersionless limit of KdV (second member of the first Painlev\'e\ hierarchy) and in the semiclassical limit of NLS (tritronqu\'ee solution of Painlev\'e\ I).

The latter case suggested a conjecture (Dubrovin-Grava-Klein) about the location of the poles of the tritronqu\'ee 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 Painlev\'e\ 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 been also appeared in other unexpected corners of mathematics; for example the notion of Cluster Algebras was born as a generalization of the Pl\"ucker 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 to the 70th anniversary 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.

14 July – 19 July 2020

SISSA, Trieste, Italy

**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

Internal Satellite Conference

Partial differential equations

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.

July 1, 2020 - July 5, 2020

Location:

**Portorož, Slovenia**

Oliver Dragičević, University of Ljubljana, Slovenia

Contact:

oliver.dragicevic@fmf.uni-lj.si

**Aleksey Kostenko**, University of Ljubljana, Slovenia

**Contact**: aleksey.kostenko@fmf.uni-lj.si

**Gerald Teschl**, University of Vienna, Austria

**Contact**: gerald.teschl@univie.ac.at