News

12 01, 2024

The H-flux on flag manifolds generated by infinitesimal T-duality, talk by Carlos Varea

2024-01-12T13:04:33+02:00January 12th, 2024|ICMS Seminar, News|

A talk by Carlos Varea, (Universidade Tecnológica Federal do Paraná - Campus Cornélio Procópio, Brazil) on January 16, 14:00 Sofia time.

10 01, 2024

Nilpotent algebras, groups and beyond, talk by Yuri Bahturin

2024-01-15T14:38:13+02:00January 10th, 2024|ICMS Seminar, News|

We study various correspondences between finite-dimensional nilpotent algebras and (quasi)groups similar to those given by the circle product in the case of associative algebras or by the Baker-Campbell-Hausdorff formulas in the case of Lie algebras or their generalizations. In the particular case of Malcev's correspondence, we obtain some new results about groups using Lie algebras and vice versa.

4 01, 2024

The Milnor number of a smoothable curve, talk by Antony Rangachev

2024-01-04T12:32:11+02:00January 4th, 2024|ICMS Seminar, News|

In this talk I will derive an algebraic formula for the Milnor number of a smoothable complex analytic curve singularity X by relating it to the Euler characteristic of its smoothing, which in turn I will relate to the multiplicity of the Jacobian ideal of X and and the multiplicity of X at its singular point. If time permits I will discuss generalizations to higher dimensions. This is a report on a joint work with Gaffney and Bengus-Lasnier.

4 01, 2024

Stratified Morse theory and the critical locus of a linear functional, talk by Antony Rangachev

2024-01-04T12:29:00+02:00January 4th, 2024|ICMS Seminar, News|

In this talk I will use stratified Morse theory to relate the number of critical points of a generic linear functional on a complex analytic manifold M to the Euler characteristics of M and a generic hyperplane slice of M.

30 11, 2023

Recent developments in the study of Følner functions, talk by Bogdan Stankov

2023-11-30T12:13:00+02:00November 30th, 2023|ICMS Seminar, News|

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.

24 11, 2023

de Sitter (dS) Relativity versus Poincaré Relativity, talk by Hamed Pejhan

2023-11-24T08:59:48+02:00November 24th, 2023|ICMS Seminar, News|

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.

14 11, 2023

Bubbling symplectic structures on moduli, a talk by Tony Pantev

2023-11-20T17:05:44+02:00November 14th, 2023|Consortium Distinguished Lecture Series, News|

 I will describe a new geometric method for constructing and controlling shifted symplectic structures on the moduli of vector bundles along the fibers of a degenerating family of Calabi-Yau varieties. The method utilizes bubbling modifications of the boundaries of limiting moduli spaces to extend the symplectic structure on the general fiber to a relative symplectic structure defined on the whole family. As a proof of concept we show that this produces a universal relative symplectic structure on the moduli of Gieseker Higgs bundles along a semistable degeneration of curves. We also check that the construction works globally over the moduli stack of stable curves and show that the Hitchin map has the expected behavior in the limit. This is a joint work with Oren Ben-Bassat and Sourav Das.

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.

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