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

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

## Nilpotent algebras, groups and beyond, talk by Yuri Bahturin

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.

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

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.

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

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.

## 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.