The workshop will bring renowned specialists from different subfields of contemporary probability theory. Along with the invited lectures, anyone interested may apply for a contributed talk.
In this talk, I will first introduce the basic facts and ideas of non-archimedean uniformization and discuss some applications in mirror symmetry if time is permitted.
In my talk, I will overview progress in the area and its connection with other fields: theoretical computer science, number theory, and analysis. In particular, I will discuss a joint work with Zilin Jiang confirming Fejes Toth's long-standing zone conjecture and recent results with Alexey Glazyrin and Roman Karasev on a polynomial plank problem, a far-reaching generalization of Bang's theorem.
In this talk, partly based on joint work with H. Seppanen, I will present a description of the GIT-classes of L-ample line bundles on X and some properties of the respective GIT-quotients. Under mild assumptions, we prove the existence of a quotient whose Cox ring is, up to a finite extension, isomorphic to the ring of L-invariants in the Cox ring of X. This is indeed a special property, as such a quotient inherits, a priori, only information about the ample line bundle with respect to which it is defined.
We employ the Jordan algebras for a succinct description of the dynamical conformal symmetries of integrable models.
The study of codes over the rings (ring-linear codes) attracted great interest after the work of Calderbank, Hammons, Kumar, Sloane, and Sole in the early 1990s. In this seminar, the basic theory of linear codes over finite commutative rings will be presented including the importance of codes over rings, various kinds of rings for ring-linear coding theory, the weight functions on finite rings, MacWilliams equivalence theorem and the connection between these codes and codes over fields via the Gray maps. Moreover, the cyclic codes over finite commutative rings will be considered. Finally, some well-known generalizations of cyclic codes such as negacyclic, quasi-cyclic, polycyclic, multivariable, polynomial and Abelian codes will be introduced.
We investigate lattice packings of Minkowski balls and domains. By results of the proof of Minkowski conjecture about the critical determinant we divide the balls and domains on 3 classes: Minkowski, Davis and Chebyshev-Cohn. The optimal lattice packings of the balls and domains are obtained. The minimum areas of hexagons inscribed in the balls and domains and circumscribed around them are given. These results lead to algebro-geometric structures in the framework of Pontrjagin duality theory.
In recent months, several new results were obtained in Homological Mirror Symmetry. The purpose by now, in this traditional winter conference, is to survey these results and open new directions for development and collaboration.
Andrés Navas is a mathematician specializing in dynamical systems, geometry, and group theory and is a world-renowned expert in ergodic theory. He was a student of Étienne Ghys. For his scientific achievements, he was awarded the MCA prize.
The initiative Women in Mathematics of South-Eastern Europe, aiming at promoting the role of female mathematicians, started in Dec 2020, when the inaugural conference took place. We intend to make these conferences annual. The main goal of these conferences is to celebrate women in Mathematics, to disseminate new results and create new long-term collaborations among scientists in South-Eastern Europe. We hope Women in Mathematics of South-Eastern Europe will attract the attention of young researchers and researchers from less-favoured countries.