Flag manifolds are topological spaces parametrizing nested subspaces in a fixed vector space. On the complete flag manifold of $\mathbb{C}^n$ and $\mathbb{R}^n$ there is a natural action of the symmetric group on $n$ letters. In this talk I will…
Categoria evento: Seminar on Combinatorics and Lie Theory and Topology
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…
Logarithmic Comparison Theorems for Hyperplane Arrangements, Twisted or Otherwise – Dan Bath (KU Leuven)
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…