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
Recent developments in the study of Følner functions, talk by Bogdan Stankov
The Følner function of a group is defined on positive integers n as the smallest size of a Følner set, the boundary of which is at most 1/n times the size of the set. Its values are then finite if and only if the group is amenable. It can be thought of as encoding "how amenable a group is". We will give an overview of how our understanding of Følner functions has progressed. We will mostly talk about two major types of development. The first one concerns proving, for a given type of function, the existence of a group that has a Følner function of that type. The other one is connections between the asymptotics of Følner functions and those of the growth function.
de Sitter (dS) Relativity versus Poincaré Relativity, talk by Hamed Pejhan
This presentation introduces a novel holographic correspondence in d-dimensional de Sitter (dS_d) spacetime, connecting bulk dS_d scalar unitary irreducible representations (UIRs) with their counterparts at the dS_d boundary, all while preserving reflection positivity. The proposed approach, with potential applicability to diverse dS_d UIRs, is rooted in the geometry of the complex dS_d spacetime and leverages the inherent properties of the (global) dS_d plane waves, as defined within their designated tube domains.
Density of Hasse failures for diagonal affine cubic surfaces, a talk by Vladimir Mitankin
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.
Tropical structures in sandpile model, talk by Mikhail Shkolnikov, IMI-BAS
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.
Invariant theory, homogeneous projective varieties, and momentum maps, course by Valdemar Tsanov
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.
