# 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 founder and first director of ICMS-Sofia was Acad. Blagovest Sendov.

# Next Event

## International Center for Mathematical Sciences – Sofia (ICMS-Sofia)

Institute of the Mathematical Sciences of the Americas at the University of Miami (IMSA)

Union of Bulgarian Mathematicians (UBM)

# 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, the Crafoord Prize 2012

Acad. B. Sendov was the founding director of ICMS-Sofia. We celebrate his memory with a talk we hope will make him happy.

**Abstract**: In 1958, Blagovest Sendov made the following conjecture: if a polynomial *f *of degree *n **≥ *2 has all of its zeroes in the unit disk, and *a *is one of these zeroes, then at least one of the critical points of *f *lies within a unit distance of *a*. Despite a large amount of effort by many mathematicians and several partial results (such as the verification of the conjecture for degrees *n **≤ *8), the full conjecture remains unresolved. In this talk, we present a new result that establishes the conjecture whenever the degree *n *is larger than some sufficiently large absolute constant *n*_{0}. A result of this form was previously established in 2014 by Degot assuming that the distinguished zero *a *stayed away from the origin and the unit circle. To handle these latter cases we study the asymptotic limit as *n **→ ∞ *using techniques from potential theory (and in particular the theory of balayage), which has connections to probability theory (and Brownian motion in particular). Applying unique continuation theorems in the asymptotic limit, one can control the asymptotic behavior of both the zeroes and the critical points, which allows us to resolve the case when *a *is near the origin via the argument principle, and when *a *is near the unit circle by careful use of Taylor expansions to gain fine asymptotic control on the polynomial *f*.

The webinar will be held via Zoom. No registration is required. A direct link to the webinar protocol and some technical tips on Zoom are available below.

All times are EET (UTC+2) – Sofia local time.

# 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 move the **conference “Complex Geometry”**, Inaugural Conference of the International Center for Mathematical Sciences – Sofia and Satellite conference of the 8th European Congress of Mathematics, to 2021.

The conference is rescheduled for **July 7 – 10, 2021**. The new dates are correlated with the new dates of the European Congress of Mathematics which is moved to June 20 – 26, 2021.

Please follow the website for the latest information.

Stay safe and stay healthy!

# Activities 2020

# 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).

# Birational Geometry

**Yuri Tschinke**l (Currrant Institute NYU and Simons foundation, USA), **Ivan Cheltsov** (University of Edinburgh, UK) and **Ludmil Katzarkov** (University of Miami, USA; Institute of Mathematics and Informatics at the Bulgarian Academy of Sciences; National Research University Higher School of Economics, Russian Federation) will discuss the recent advances in birational geometry.

Because of the complicated situation concerning the spread of COVID-19, the workshop on Birational Geometry will be postponed. The new dates will be announced later.

Please follow the website for the latest information.

Stay safe and stay healthy!

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.