The goal of this workshop is to explain the foundations of the new theory of atoms, introduced recently by L. Katzarkov, M. Kontsevich, T. Pantev and T. Yu. We will discuss recent advances in this field, applications and future directions.

The initiative Women in Mathematics of South-Eastern Europe has been established in 2020 and has proven its worth in the last few years. Тhis is the fifth in a series of conferences of this initiative, the purpose of which is to make women in mathematics more visible, to help them share their ideas and scientific achievements and to communicate with each other not only scientifically but also empathetically and emotionally.

The aim of this mini-workshop is to bring together a multifaceted group of researchers working in potential theory, approximation, special functions, point configurations, lattices, and numerical analysis who have recently made important contributions to energy minimization and polarization problems to report on their work and to collaborate in trying to resolve some of the fundamental questions in the field.

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.