ICMS Seminar
The ICMS seminar aims to present and disseminate advances in different fields of the contemporary fundamental and applied mathematics, and to promote new cutting edge directions in Mathematics.
The ICMS seminar aims to present and disseminate advances in different fields of the contemporary fundamental and applied mathematics, and to promote new cutting edge directions in Mathematics. The seminar hosts scientific reports by collaborators and visitors of the ICMS, as well as colloquium-style lectures by invited speakers. The interdisciplinary features of the ICMS are reflected in the variety of topics covered in the seminar, ranging in algebraic and differential geometry, number theory, category theory, combinatorics, representation theory, mathematical physics, algebraic coding theory, etc. The venue is open to a wide audience, and the lectures are followed by time for interaction and discussion.
Seminar issues
Variations of GIT-quotients of flag varieties, ICMS Seminar Talk by Valdemar Tsanov
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.
Jordan algebra conformal toolbox, ICMS Seminar Talk by Todor Popov
We employ the Jordan algebras for a succinct description of the dynamical conformal symmetries of integrable models.
Linear and Cyclic Codes over Rings – ICMS Seminar talk by Maryam Bajalan
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.
On optimal packing of Minkowski balls and applications – ICMS Seminar talk by Nikolaj Glazunov
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.
Introduction to Resolution of Singularities
In these lectures I will introduce the very basic objects that help study resolutions of singularities, from the point of view of valuations. This is the historic strategy pioneered by Zariski and later by Abhyankar. My goal is to present a proof of the resolution of surfaces in characteristic zero, via the local uniformization problem. This approach had lost momentum after Hironaka’s acclaimed breakthrough, but has regained interest in the 90s as new ideas emerged in the works of Spivakovsky and Teissier.
