Geometric quantization on symplectic manifolds plays an important role in representation theory and mathematical physics, deeply

relating to symplectic geometry and differential geometry. A crucial problem is to understand the relationship among geometric

quantization associated to different polarizations.  In this talk, we will focus on the  quantum space associated with this mixed polarization on Toric varieties.  

In this talk I will explain a general mechanism, based on derived symplectic geometry,  to glue the local invariants of singularities that appear naturally in Donaldson-Thomas theory.  This mechanism recovers the categorified vanishing cycles sheaves constructed by Brav-Bussi-Dupont-Joyce, and provides a new more evolved gluing of Orlov’s categories of matrix factorisations, answering questions of Kontsevich-Soibelman and Y.Toda. This is a joint work with B. Hennion (Orsay) and J. Holstein (Hamburg).

In this seminar we will talk about results concerning faithful representations of abelian groups as automorphisms of one-rooted trees. In particular, we show the self-similarity of the free abelian group of uncountable rank and of the Baer-Specker group.

Let $G$ be a group and consider the group $\chi(G)$ obtained from the free product $G \ast G$ by forcing each element $g$ in the first free factor to commute with the copy of $g$ in the second free factor. In the last 44 years, this group has been a formidable tool for obtaining finiteness conditions in Group Theory. In this talk, we want to present some important results related to the group $\chi (G)$. Moreover, we want to establish some properties of the exponent of $\chi(G)$ when $G$ has finite exponent. 

In the context of the theory of Gelfand-Tsetlin modules, Drinfeld categories were introduced in 2017 by V. Futorny et al. to prove that every irreducible 1-singular Gelfand-Tsetlin module is isomorphic to a subquotient of the universal 1-singular Gelfand-Tsetlin module. The authors also observed that these categories could be used to generalize the classification of Gelfand-Tsetlin modules for $\mathrm{sl}(n)$, which, at that time, was only known for $\mathrm{sl}(3)$.

In physics, CS/WZNW duality is an equivalence between Chern–Simons gauge theory and WZNW conformal field theory first proposed by Witten in 1989. This statement was formalised by Beauville, Laszlo, and Pauly over the next decade by proving the vector space isomorphism between the geometric quantisation of the moduli space of flat connections, representing the Hilbert space of gauge fields between charges on a surface, with the Tsuchiya–Ueno–Yamada (TUY) space of conformal blocks, representing the conformal vacua between operator insertions corresponding to the charges.

After a brief introduction to non-Euclidean 2D geometry using fleece surfaces (tecido polar), volunteers will put on a VR headset to try their hand at billiards in 3D spherical, Euclidean and hyperbolic spaces, with the rest of the audience following along on the lecture hall’s main screen. Even experienced geometers may find some surprising optical effects, which we’ll explain using the fleece surfaces.

Abstract: In this panoramic talk, we shall provide an overview of Poisson geometry and some recent results obtained by the speaker and collaborators. First, we shall present the key definitions and concepts, and relate them to their foundationalmotivations in relation to both classical and quantum mechanics.

The non-abelian tensor product $G \otimes H$ of groups G and H was
introduced by Brown and Loday, following works of Miller and
Dennis. Ellis showed the finiteness of the
non-abelian tensor product $G \otimes H$ when both $G$ and $H$ are finite. 

I will present some related results concerning the (local) finiteness of the non-abelian tensor product $G \otimes H$.

This is a joint work with Nora\'i Rocco (Universidade de Bras\'ilia) e Irene Nakaoka (Universidade Estadual de Maring\'a). 

Given a flow on a manifold, how to perturb it in order to create a periodic orbit passing through a given region? This question was originally asked by Poincaré and was initially studied in the 60s. However, various facets of it remain largely open. Recently, several advances were made in the context of Hamiltonian and contact flows. I will discuss a connection between this problem and Gromov-Witten invariants, which are "counts" of holomorphic curves. This is based on a joint work with Julian Chaidez.