# About us

The newly established **International Center for Mathematical Sciences – Sofia** is a dynamic research unit for developing and dissemination of cutting edge new directions in Mathematics. It is affiliated with the Institute of Mathematics and Informatics of the Bulgarian Academy of Sciences which is providing the infrastructure for the activities of the Center. The Center is supported by the Ministry of Education and Science of the Republic of Bulgaria. The Activities of the ICMS – Sofia are carried out in collaboration with the Institute of the Mathematical Sciences of the Americas at the University of Miami (IMSA) and Higher School of Economics, National Research University, Moscow (HSE University). The ICMS-Sofia is also working in collaboration with Bulgarian universities and institutes of the Bulgarian Academy of Sciences.

The Center was created following inspirational discussions with many members of the mathematical community in Bulgaria and the Bulgarian mathematical diaspora. In July 2019, ICMS-Sofia initiated its full-scale presence on the European mathematical scene with the full support of Acad. Julian Revalski, President of the Bulgarian Academy of Sciences.

The first director of ICMS-Sofia was Acad. Blagovest Sendov.

# Next event

# First Annual Meeting of Young Bulgarian Mathematicians

This meeting is the inaugural event of a series of annual meetings ICMS initiates. The series, which commemorates the brightest Bulgarian holiday *the Day of Bulgarian Enlightenment and Culture and the Slavоnic Alphabet* May 24, has as its main objective bringing together young Bulgarian mathematicians working all over the world.

We envision two main outcomes:

- enriching relations between young mathematicians working in Bulgaria and the Bulgarian mathematical diaspora;
- enhancing professional development of young Bulgarian mathematicians by presenting new opportunities using the national and European scientific programmes.

Following the conclusion of the scientific part of the event on May 19, we plan to organise a special round table to discuss these opportunities.

We are all elated by this exciting event and we are looking forward to seeing you there. This year the talks will happen via Zoom. We all hope to have an actual onsite live event starting next year.

## Invited speakers

## Invited speakers

**The Almost Schur Lemma in Quaternionic Contact Geometry**

*Abstract:* We consider in this talk the quaternionic contact (qc) version of the almost Schur lemma. Namely, we show that a compact quaternionic contact Einstein manifold of dimension bigger than seven with positive qc-Ricci tensor must be with constant qc scalar curvature. The latter is a consequence of a more general result, namely an integral inequality, that informally states that if the traceless qc Ricci tensor and some traces of the covariant derivatives of the qc torsion tensor are “close” to zero, then the qc scalar curvature is “close” to a constant.

**Rigidity in Dimension 2**

*Abstract:* I will discuss an approach to proving the conjecture that a normal rigid surface is smooth. The approach is based on the notion of deficient conormal singularities introduced by the speaker.

**Hidden Variables in Linear Causal Models**

*Abstract: *Identifying causal relationships between random variables from observational data is an important hard problem in many areas of data science. The presence of hidden variables, though quite realistic, brings up a variety of further problems. Linear structural equation models, which express each random variable as a linear combination of all of its parent variables, have long been used for learning causal structure from observational data.

Surprisingly, when the random variables in a linear structural equation model are non-Gaussian the full causal structure can be learned without interventions, while in the Gaussian case one can only learn the underlying graph up to a Markov equivalence class. In this talk, we first discuss how one can use high-order cumulant information to learn the structure of a linear non- Gaussian structural equation model with hidden variables. While prior work posits that each hidden variable is the common cause of two observed variables, we allow each hidden variable to be the common cause of multiple observed variables. Next, we discuss hidden variable Gaussian causal models and the difficulties that arise with learning those. We show it is hard to even describe the Markov equivalence classes in this case, and we give a semialgebraic description of a large class of these models.

**Counting Irreducible Sparse Polynomials of a Given Degree over a Finite Field**

*Abstract: *A classical result of Gauss states that among all monic polynomials of degree d over a finite field, approximately 1/d are irreducible. Extending previous results in the literature, we prove that under a mild assumption, the proportion of irreducible polynomials does not change even if only the last two coefficients are allowed to vary. Our approach is geometric. The talk will be nontechnical and accessible to a broad audience.

**Optimal Control for the Evolution of Deterministic Multi-agent Systems**

*Abstract: *We investigate an optimal control problem with a large number of agents (possibly infinitely many). Although the dynamical system (a controlled ordinary differential equation) is of the same type for every agent, each agent may have a different control. So, the multi-agent dynamical system has two levels: a microscopic one, which concerns the control system of each agent, and a macroscopic level, which describes the evolution of the crowd of all agents. The

state variable of the macroscopic system is the set of positions of the agents. We define and study the evolution of such a global dynamical system whose solutions are called solution tubes. We also consider a minimization problem associated with the multi-agent system and we give a new characterization of the corresponding value function as the unique solution of a Hamilton- Jacobi-Bellman equation stated on the space of compact subsets of $R^d$.

The talk is based on joint work with Marc Quincampoix.

**What is the smallest algebraic integer?**

*Abstract: * We survey Lehmer’s problem on the smallest Mahler measure of an integer non-cyclotomic polynomial, synthesizing an introduction to this subject along with the state-of-art results known today. Then we will present the solution of a closely related conjecture of Schinzel and Zassenhaus, and propose some answers towards the question of our title. Time permitting, we discuss also some related recent results on the geometry of integer polynomials.

# News and Announcements

#### Noncommutative Geometry Conference

In 2020 Alexander Efimov, a Research Fellow at the International Laboratory for Mirror Symmetry and Automorphic Forms (HSE University) and a Senior Researcher at the Algebraic Geometry Section of Steklov Mathematical Institute of RAS, has been awarded by the European Mathematical Society’s Prize.

#### Recent Applications of the Theory of O-Minimal Structures to Various Questions in Hodge Theory

The International Center for Mathematical Sciences – Sofia (ICMS-Sofia) invites you to attend the virtual conference **Recent Applications of the Theory of O-Minimal Structures to
Various Questions in Hodge Theory** - November 16 – 20, 2020

#### Irrational Fans in Physics and Mathematics

The International Center for Mathematical Sciences – Sofia (ICMS-Sofia) invites you to attend the virtual conference **Irrational Fans in Physics and Mathematics** - October 19 – 21, 2020

# Inaugural Conference

Because of the complicated situation concerning the spread of COVID-19 and in view of the safety and well-being of all participants,** a final decision was taken to cancel the conference “Complex Geometry”**, Inaugural Conference of the International Center for Mathematical Sciences – Sofia and Satellite conference of the 8th European Congress of Mathematics.

**Stay safe and stay healthy!**

# Activities 2020 - 2021

# Sendov’s conjecture for sufficiently high degree polynomials

Colloquium talk in memory of Acad. Blagovest Sendov by **Terence Tao**, University of California, Los Angeles (UCLA)

Winner of the Fields Medal 2006, the Breakthrough Prize in Mathematics 2014, the Crafoord Prize 2012.

Women in Mathematics in South-Eastern Europe

Lecturers in this webinar are **Ana Irina Nistor**, Department of Mathematics and Informatics, “Gh. Asachi” Technical University of Iasi, Romania; **Betul Bulca**, Department of Mathematics, Uludag University, Burca, Turkey; **Mina Teicher**, Department of Mathematics and Gonda Brain Research Center, Bar-Ilan University, Israel; **Nadezhda Ribarska**, Faculty of Mathematics and Informatics, Sofia University “St. Kliment Ohridski”; **Natasa Krejic**, Faculty of Science, University of Novi Sad, Serbia; **Sanja Atanasova**, Faculty of Electrical Engineering and Information Technologies, “Ss. Cyril and Methodius” University in Skopje, North Macedonia; **Sofia Lambropoulou**, School of Applied Mathematical and Physical Sciences, National Technical University of Athens, Greece; **Velichka Milousheva**, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Bulgaria.

# Hodge Theory and Local Systems

**Prof. Carlos Simpson**, CNRS, Université Côte d’Azur, Nice, will give a series of lectures on Hodge theory and local systems in the period March 3-5, 2020.

Other lecturers will be Prof. Alexander Efimov (Steklov Mathematical Institute of Russian Academy of Sciences), Prof. Ludmil Katzarkov, Prof. Viсtor Przyjalkowski (Steklov Mathematical Institute of Russian Academy of Sciences).