ICMS Seminar

17 10, 2023

Density of Hasse failures for diagonal affine cubic surfaces, a talk by Vladimir Mitankin

2024-01-25T15:58:35+02:00October 17th, 2023|ICMS Seminar, News|

In this talk we shall apply the integral version of the Brauer-Manin obstruction to construct the first examples of such failures not explained by local conditions in the setting of affine diagonal ternary cubics. We will then explore in three different natural ways how such failures are distributed across the family of affine diagonal ternary cubics.

9 10, 2023

Tropical structures in sandpile model, talk by Mikhail Shkolnikov, IMI-BAS

2023-10-23T14:25:56+03:00October 9th, 2023|Geometry Seminar, ICMS Seminar, News|

I will tell how tropical curves arise in the scaling limit of the sandpile model in the vicinity of the maximal stable state and explain two major consequences inspired by this fact. The first one is that there is a continuous model for self-organized criticality, the only known model of a kind, defined in the realm of tropical geometry. The second is that the totality of recurrent states in the original sandpile model, the sandpile group, approximates a continuous group, a tropical Abelian variety, which is functorial with respect to inclusions of domains, allowing to compute its scaling limit as a space of circle-valued harmonic functions on the whole lattice.

29 09, 2023

Invariant theory, homogeneous projective varieties, and momentum maps, course by Valdemar Tsanov

2023-10-23T13:30:17+03:00September 29th, 2023|ICMS Seminar, News|

After introducing the basic notions, I will derive some properties of momentum images related to fundamental forms and osculating varieties, as well as a lower bound on the minimal positive degree of a homogeneous invariant, derived using secant varieties. At the end I will present a class of homogeneous projective varieties, characterized by a special property of their secant varieties, where the relations between the above three concepts take a particularly pristine form.

29 09, 2023

Introduction to Projective Structures and Opers, course by Peter Dalakov

2023-10-23T13:27:22+03:00September 29th, 2023|ICMS Seminar, News|

A complex projective structure on a Riemann surface is determined by an atlas, whose transition functions are Moebius (fractional-linear) transformations. There are multiple   descriptions of these structures: as certain flat PGL_2-bundles, as Sturm-Liouville operators, as holomorphic connections on the (first) jet bundle of the dual of a theta-characteristic, etc. This mini-course is an introduction to the fundamentals of projective structures, accessible to students and non-specialists. We will also explore links to some classical geometric objects (such as quadratic differentials and Schwarzian derivatives), as well as some generalisations (G-opers) introduced by Beilinson and Drinfeld.

29 09, 2023

About a generalisation of Sylvester’s law of inertia, talk by Stéphanie Cupit-Foutou

2023-10-05T13:00:01+03:00September 29th, 2023|ICMS Seminar, News|

Sylvester’s law of inertia can be formulated in terms of group actions when considering real linear groups acting on real quadratic forms by base change. After reviewing this celebrated result from this perspective, I will give a generalisation of it in the setting of so-called spherical varieties (a class of complex varieties including flag varieties, toric varieties, symmetric spaces, etc.). This is a joint work with D. Timashev

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.

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