ICMS Seminar

27 06, 2023

Introduction to tensor triangular geometry

2023-06-27T10:49:08+03:00June 27th, 2023|ICMS Seminar, News|

In a series of four talks, I will try to give a brief introduction to the subject and look at examples and applications following the exposition of universality, functoriality and localization, and triangulated categories and localization. The main references on the subject are the tensor triangulated categories and the Balmer spectrum and some examples and applications.

9 05, 2023

Objectivity and Subjectivity in Mathematics

2023-05-09T15:41:59+03:00May 9th, 2023|ICMS Seminar, News|

In the first part of the talk, I shall explore the consequences of distinguishing the foundations of meaning and the foundations of truth in mathematical statements, or imagination and rigor as motors of mathematical development. The foundations of meaning can be sought in our largely unconscious perception of the world, which modern cognitive science is exploring.

9 03, 2023

Non-Archimedean Uniformization and its Application, ICMS seminar talk by Jiachang Xu

2023-03-09T15:39:14+02:00March 9th, 2023|ICMS Seminar, News|

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.

9 03, 2023

Plank Problems: Discrete Geometry and Convexity, ICMS Seminar Talk by Alexander Polyanskiy

2023-03-09T15:40:19+02:00March 9th, 2023|ICMS Seminar, News|

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.

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.

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