Based on recent advances in representations based on topological descriptors, the talk will discuss how to leverage persistent homology for dealing with classification tasks of digital data. Applications to biomedical signal processing will be given…

# Categoria evento: Seminar on Combinatorics and Lie Theory and Topology

## Vertex labeling properties on simplicial complexes – Bruno Benedetti (University of Miami)

Hamiltonian graphs are graphs where one can find a closed walk that touches all vertices exactly once. Equivalently, they are the graphs whose vertices can be labeled from 1 to n so that all of 12, 23, 34, …, n1 feature among the edges. This…

## Introduction to persistent homology – Maria Antonietta Pascali (CNR, Pisa)

The talk will trace the history of persistent homology from its definition to the recent developments, describing the most important properties and theorems of persistent diagrams, with an eye to their applications.…

## Maps enumeration and Symmetric functions – Houcine Ben Dali (Université de Lorraine)

A map is a graph which is drawn on a compact orientable surface. There exist various results relating the generating series of maps to the theory of symmetric functions. In this talk, I present two different approaches which allow to relate the…

## Charge, Atoms and Crystals in Representation Theory – Leonardo Patimo (Albert-Ludwigs-Universität Freiburg)

The dimensions of the weight spaces of irreducible representations of reductive groups can be q-deformed, obtaining the Kostka-Foulkes polynomials, which measure the dimensions of the Brylinski-Kostant filtration and therefore have positive…

## The mod $p$ cohomology of complete unordered flag manifolds in $\mathbb{C}^n$ and $\mathbb{R}^n$ – Lorenzo Guerra (Università di Roma ‘Tor Vergata’)

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…

## 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…