ICMS Seminar

16 02, 2023

Variations of GIT-quotients of flag varieties, ICMS Seminar Talk by Valdemar Tsanov

2023-02-16T15:39:31+02:00February 16th, 2023|ICMS Seminar, News|

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.

27 01, 2023

Linear and Cyclic Codes over Rings – ICMS Seminar talk by Maryam Bajalan

2023-02-03T13:43:13+02:00January 27th, 2023|ICMS Seminar, News|

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.

27 01, 2023

On optimal packing of Minkowski balls and applications – ICMS Seminar talk by Nikolaj Glazunov

2023-01-27T12:36:28+02:00January 27th, 2023|ICMS Seminar, News|

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.

27 01, 2023

Introduction to Resolution of Singularities

2023-01-27T12:08:30+02:00January 27th, 2023|ICMS Seminar|

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.

19 07, 2022

Vafa-Witten invariants on 4 and 3 dimensional manifolds, by Artan Sheshmani

2022-07-20T09:36:29+03:00July 19th, 2022|ICMS Seminar, News|

I will talk about joint work with Shing-Tung Yau, Sergei Gukov, and earlier joint work with Gholampour and Yau on Mathematical definition of Vafa-Witten invariants on 4 and 3 dimensional manifolds.

11 04, 2022

Introductory Toric Geometry

2022-07-18T13:47:04+03:00April 11th, 2022|ICMS Seminar|

This is the first part, consisting of four lectures, of a mini-course in which the combinatorial geometry related to toric varieties will be introduced. It will be developed to define and express properties of toric varieties and toric morphisms, and to investigate the geometry of the orbits by the torus action, in particular the orbit decomposition. Next, toric divisors, invertible and reflexive sheaves on toric variety, and their groups will be introduced and studied.

16 10, 2021

The congruence property in two-dimensional rational conformal field theory, revisited

2021-10-16T13:43:47+03:00October 16th, 2021|ICMS Seminar|

In a joint work with Frank Calegari and Yunqing Tang, we use methods from transcendental number theory to prove a conjecture that goes back to Atkin and Swinnerton-Dyer, in a special case, and generalized by Mason to the following form: A vector-valued modular form on SL(2,Z) whose components have q-expansions with bounded denominators are exactly the ones for which the underlying representation of SL(2,Z) has a finite image with kernel containing the congruence subgroup of matrices reducing to the identity modulo some positive integer N. In this talk, I will outline the basic ideas of the proof of the conjecture, describe the relation to mathematical physics and the representation theory of vertex algebras, and explain how our result in particular recovers a completely new proof of the so-called "congruence property" in rational conformal field theory.

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