## Kashiwara crystals and the moduli space of stable rational curves – Leonid Rybnikov (HSE University, Faculty of Mathematics, Moscow)

The category of Kashiwara crystals for a semisimple complex Lie algebra $\mathfrak{g}$ is a combinatorial model of the tensor category of finite-dimensional  $\mathfrak{g}$-modules, where $\mathfrak{g}$-modules are represented by colored oriented…

TBA…

## Verma modules for the Lie superalgebra E(5,10) – Nicoletta Cantarini (Università degli Studi di Bologna, Italy)

In this talk, we will describe the construction of the so-called finite Verma modules for $\mathbb{Z}$-graded Lie superalgebras and study the finite Verma modules over the exceptional linearly compact Lie superalgebra $E(5,10)$. This is done through…

## Approximations of a Nichols algebra from a geometric point of view – Giovanna Carnovale (Università degli Studi di Padova, Italy)

​The talk is based on an ongoing joint project with Francesco  Esposito and Lleonard Rubio y Degrassi. Nichols (shuffle) algebras are a family of graded Hopf algebras (in a braided monoidal category) which includes symmetric algebras, exterior…

## Generalized Schur-Weyl duality for quantum affine symmetric pairs and orientifold KLR algebras – Andrea Appel (Università di Parma, Italy)

​In the work of Kang, Kashiwara, and Kim, the Schur–Weyl duality between quantum affine algebras and affine Hecke algebras is extended to certain Khovanov-Lauda-Rouquier (KLR) algebras, whose defining combinatorial datum is given by the poles of the…

## Elliptic Artin Monoids and Higher Homotopy Groups – Kyoji Saito (RIMS, Japan)

​A half-century ago when simply elliptic singularity was introduced, it was a natural question whether its discriminant complement is a $K(\pi,1)$ space. At that time, Fulvio Lazzeri suggested the possibility of the existence of a…

## Partial and global representations of finite groups – Michele D’Adderio (Université Libre de Bruxelles, Belgium)

​The notions of partial actions and partial representations have been extensively studied in several algebraic contexts in the last 25 years. In this talk, we introduce these concepts and give a short overview of the results known for finite groups.…

## Ricci curvature, graphs and Coxeter groups – Viola Siconolfi (Università di Pisa, Italy)

​I will talk about a notion of curvature for graphs introduced by Schmuckenschläger which is defined as an analogue of Ricci curvature. This quantity can be computed explicitly for various graphs and allows to find bounds on the spectral gap of the…

## Representation theory and configuration spaces – Roberto Pagaria (Università degli Studi di Bologna, Italy)

​We introduce the category of finite sets and we study their representations. Then we apply this tool to the study of cohomology of ordered configuration spaces of points on a manifold. In the case of configurations of points on an elliptic curve,…

## On a quadratic polynomial attached to simple Lie algebras – Paolo Papi (Sapienza Università di Roma)

We will introduce a polynomial $p_{\mathfrak{g}}(k)$ attached to a simple Lie algebra $\mathfrak{g}$. It appears in several different contexts: the minimal quantization of the adjoint representation of Drinfeld’s Yangian $\mathsf{Y}(\mathfrak{g})$;…

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