In this series of talks, we will explore how the field of self-organized criticality is useful to inform the structure of artificial models of life. This is joint work with Kalinin, Tabares and Shkolnikov, and with Cruz, Muñoz and Viafara.

ICMS-Sofia and IMSA-Miami present the next part of the Consortium Distinguished Lecture Series. Prof. Ernesto Lupersio (CINESTAV) will talk on Localization Methods for Orbifolds and Motivic Integration. The series will be on May 26-27, 2022, 19:00 (EEST, Sofia time), via Zoom.

Functional inequalities constitute a very useful toolbox in various fields of Mathematics, like analysis, spectral analysis, mathematical physical, theory of partial differential equations and differential geometry. For each of them, knowing the best constant in the inequality and as much as possible about the extremal, optimizing, functions is very important. In these presentations I will describe how this field has developed very strongly in the last decades and how now we dispose of a good set of strategies to address all the above issues for a large family of inequalities. Also a recent set of important results are devoted to the improved inequalities that can be written for non optimizers, topic which is denoted as “stability” for the inequalities. The methods that one can use and the different results that have been obtained will be discussed via the choice of a set of particular inequalities which enjoy interesting features or that are very useful in particular applications.

The International Center for Mathematical Sciences at the Institute of Mathematics and Informatics (ICMS–Sofia) will commemorate the 90th anniversary of the birth of Prof. Sendov with a special talk by Edward Saff from Vanderbilt University, USA - "Sampling with Minimal Energy: A talk in commemoration of Bl. Sendov's 90th birth date."

These lectures will present a board survey of recent work on new q-series invariants of 3-manifolds labeled by Spin-C structures. While the original motivation for studying these invariants is rooted in topology, they exhibit a number of unexpected properties and connections to other areas of mathematics, e.g. turn out to be characters of logarithmic vertex algebras. The integer coefficients of these q-series invariants can be understood as the answer to a certain enumerative problem, and when q tends to special values these invariants relate to other invariants of 3-manifolds labeled by Spin and Spin-C structures.

We will start these series by reviewing the general framework of geometric Langlands correspondence, and state the main conjectures in the de Rham and Betti settings. We will also recall V. Lafforgue's theorem about the spectral decomposition in the classical Langlands over function fields. We will then proceed to the formulation of "restricted" Langlands correspondence, which unifies the different contexts. We will state the restricted version of the geometric Langlands conjecture, and explain its relation with the classical Langlands conjecture via the operation of categorical trace.

One of the key developments in combinatorics and algebra of recent years has been the discovery of Lefschetz principles beyond Hodge structures, resolving several long-standing conjectures. I will provide an overview of recent developments, and discuss joint work with Johanna Steinmeyer, Stavros Papadakis and Vasiliki Petrotou.

During the course of the last few years a number of startling connections between quantum invariants of knots and 3-manifolds and high-level number theory have emerged. Already the rigidity theorems of 3-dimensional hyperbolic topology, which have been known for many years, had a quite non-trivial arithmetic content, with the volume of every hyperbolic 3-manifold being linked via the dilogarithm to the so-called Bloch group and algebraic K-theory, and another connection comes from the Kashaev invariant, which is linked via his famous conjecture to the hyperbolic volume but also belongs to the so-called Habiro ring, which is a beautiful number-theoretical object that is not yet well known to number theorists.