## P=W via $H_2$ – Anton Mellit (University of Vienna)

By $H_2$ we denote the Lie algebra of polynomial hamiltonian vector fields on the plane. We consider the moduli space of stable twisted Higgs bundles on an algebraic curve of a given coprime rank and degree. De Cataldo, Hausel and Migliorini proved…

## Baxter Q-operators, QQ-systems and the shifted Yangian – Rouven Frassek (Università di Modena e Reggio Emilia)

I plan to discuss the construction of Baxter Q-operators within the framework of the Quantum Inverse Scattering Method. The method follows the standard procedure for the transfer matrix construction of spin chains that was developed by Faddeev and…

## Coherent Sheaves, Quivers and Affine-Yangian Representations – Miroslav Rapcak (CERN)

According to the famous result of Schiffmann and Vasserot, the cohomology of the ADHM moduli space carries the structure of an affine-Yangian module. For the purpose of our talk, it is useful to view this moduli space from a three-dimensional…

## Hyperplane arrangements, monodromy via deformation theory, and stability conditions – Michael Wemyss (University of Glasgow)

The infinite hyperplane arrangements associated to affine Dynkin diagrams (and their associated braid groups) are fundamental throughout mathematics. I will explain a variation on this, which allows us to produce many more arrangements. Whilst these…

## Flag spheres and $\gamma$-positivity – Lorenzo Venturello (Università di Pisa)

The $f$-vector of a simplicial complex is the vector whose entries record the number of faces in each dimension. It is typically convenient to study an integer linear transformation of the $f$-vector, called the $h$-vector, which naturally appears…

## 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…

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