## New Programme of the ICMS – Theory of Atoms

The International Center for Mathematical Sciences – Sofia (ICMS-Sofia) is happy to announce that based on a strong selection process done by the Recruitment committee, the Advisory Board of ICMS-Sofia approved Prof. Ludmil Katzarkov as a Chair of a new programme - Theory of Atoms.

## Generalized integral points and strong approximation, talk by Boaz Moerman

A seminar talk by Boaz Moerman, Utrecht University

**Abstract:** The Chinese remainder theorem states that given coprime integers p_1, ..., p_n and integers a_1, ..., a_n, we can always find an integer m such that m ~ a_i mod p_i for all i. Similarly given distinct numbers x_1,..., x_n and y_1, ..., y_n we can find a polynomial f such that f(x_i)=y_i. These statements are two instances of strong approximation for the affine line (over the integers Z and the polynomials k[x] over a field k). In this talk we will consider when an analogue of this holds for special subsets of Z and k[x], such as squarefree integers or polynomials without simple roots, and different varieties. We give a precise description for which subsets this holds on a toric variety.

## IMSAC Days in Sofia

The event is set to gather prominent mathematicians and researchers from around the world, fostering an environment of knowledge exchange and collaboration. The event will feature a series of presentations and discussions on cutting-edge developments in mathematical sciences. IMSAC Days in Sofia aims to celebrate the very successful collaboration between the institutes involved in the Institute of the Mathematical Sciences of the Americas Consortium (IMSAC). It will solidify connections and further expand the prosperous cooperation between these esteemed institutions.

## P-adic L-functions and the geometry of the Eigencurve, talk by Mladen Dimitrov

An ICMS seminar talk by Mladen Dimitrov, University of Lille

**Abstract:** An amazing feature of the p-adic L-functions is their ability to live in families, thus their laws are governed by the geometry of p-adic eigenvarieties. In this lecture we will illustrate this philosophy through examples coming from classical modular forms and the Coleman-Mazur eigencurve.

## Rational points and Campana points on toric varieties and their subvarieties, talk by Marta Pieropan

A seminar talk by Marta Pieropan, Utrecht University

**Abstract:** In joint work with Damaris Schindler we develop a new version of the hyperbola method for counting rational points of bounded height that generalizes the work of Blomer and Brüdern for products of projective spaces. The hyperbola method transforms a counting problem into an optimization problem on certain polytopes. For rational points on subvarieties of toric varieties, the polytopes have a geometric meaning that reflects Manin's conjecture, and the same holds for counts of Campana points of bounded height. I will present our results as well as some general heuristics.

## Highlights from the Fourth Annual Meeting of Young Bulgarian Mathematicians

The conference aimed to bring together young Bulgarian mathematicians working in different universities worldwide to foster collaboration and exchange of ideas and to introduce their research to the mathematical community in Bulgaria. This annual event has become a pivotal platform for young researchers to present their achievements and engage with peers and senior mathematicians.