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.…
Categoria evento: Seminar on Combinatorics and Lie Theory and Topology
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 $\mathsf{Y}(\mathfrak{g})$;…
Lefschetz theory beyond positivity – Karim Adiprasito (University of Copenhagen, Denmark)
I will survey and present techniques for Lefschetz theorems beyond the case of Kaehler manifolds, and in particular discuss the Lefschetz theorem for non-projective toric varieties. Click here to see the video of the talk.…
Levi restriction for Coulomb branch algebras and categorical $\mathfrak{g}$-actions for truncated shifted Yangians – Joel Kamnitzer (University of Toronto, Canada)
Given a representation $V$ of a reductive group $G$, Braverman-Finkelberg-Nakajima defined a Poisson variety called the Coulomb branch, using a convolution algebra construction. This variety comes with a natural deformation quantization, called a…
The $K(\pi,1)$ conjecture for affine Artin groups – Giovanni Paolini (Caltech, USA)
Artin groups are a generalization of braid groups, and arise as the fundamental groups of configuration spaces associated with Coxeter groups. A long-standing open problem, called the $K(\pi,1)$ conjecture, states that the higher homotopy groups of…
Moduli spaces of Riemann surfaces: Models, Homology Operations, and Computations – Carl-Friedrich Bödigheimer (University of Bonn)
Il seminario sarà diviso in due parti, di 45 minuti ciascuna. La prima parte, di carattere introduttivo, sarà adatto anche ad un pubblico di non esperti (studenti di magistrale e dottorandi). L’abstract è scaricabile a questo link.…
La teoria di Hodge dell’algebra di Hecke e in teoria delle rappresentazioni – Leonardo Patimo (Max Planck Institute for Mathematics, Bonn)
Le congetture di Kazhdan-Lusztig forniscono una formula esplicita per calcolare il carattere delle rappresentazioni con peso più alto di un’algebra di Lie semisemplice complessa. La dimostrazione originale di queste congetture si basa su risultati…
Enumerative Properties of Gene tree configurations in species trees – Filippo Disanto (Università di Pisa)
New developments concerning the relationships between species trees, representing the branching histories of populations of organisms, and gene trees, which represent the histories of individual genomic regions, have generated new…