Organizer: Francesco Sala
Scientific Committee: Filippo Callegaro, Giovanni Gaiffi, Andrea Maffei, Francesco Sala, Mario Salvetti
Partially supported by: PRIN 2017YRA3LK "Moduli spaces and Lie Theory"
YouTube channel: click here
Scientific Committee: Filippo Callegaro, Giovanni Gaiffi, Andrea Maffei, Francesco Sala, Mario Salvetti
Partially supported by: PRIN 2017YRA3LK "Moduli spaces and Lie Theory"
YouTube channel: click here
Upcoming Talks
Christmas Break
The seminar will be broadcasted online via the Google Meet Platform. To have access, please click here (the link will be active from 2.45 pm).
For those who do not have a UniPi account, the meeting uses a waiting room. Everyone in the waiting room will be admitted by the host. Late arrivals will be admitted as soon as the host is available to do so, as will anyone who loses their connection and rejoins the meeting, but please be patient.
For those who do not have a UniPi account, the meeting uses a waiting room. Everyone in the waiting room will be admitted by the host. Late arrivals will be admitted as soon as the host is available to do so, as will anyone who loses their connection and rejoins the meeting, but please be patient.
Old Talks
December 9, 2020 at 3.00 pm (GMT+1).
Roberto Pagaria
Università di Bologna, Italy 
Title: Representation theory and configuration spaces
Abstract: 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, we obtain some new results on the Betti numbers and their growth. 
November 11, 2020 at 3 pm (GMT+1).
Paolo Papi
Università di Roma Sapienza, Italy 
Title: On a quadratic polynomial attached to simple Lie algebras
Abstract: We will introduce a polynomial \(p_{\mathfrak{g}}(k)\) attached to a simple Lie algebra \(\mathfrak{g}\). It appears in several different contexts:
The results pertain to joint projects with Kac and Moseneder Frajria. 
May 26, 2020 at 4 pm (GMT+2).
Karim Adiprasito
University of Copenhagen, Denmark, and Einstein Institute for Mathematics, Jerusalem, Israel 
Title: Lefschetz theory beyond positivity
Abstract: I will survey and present techniques for Lefschetz theorems beyond the case of Kaehler manifolds, and in particular discuss the Lefschetz theorem for nonprojective toric varieties. Click here to see the video of the talk.

May 18, 2020 at 4 pm (GMT+2).
Joel Kamnitzer
University of Toronto, Canada 
Title: Levi restriction for Coulomb branch algebras and categorical \(\mathfrak{g}\)actions for truncated shifted Yangians
Abstract: Given a representation \(V\) of a reductive group \(G\), BravermanFinkelbergNakajima defined a Poisson variety called the Coulomb branch, using a convolution algebra construction. This variety comes with a natural deformation quantization, called a Coulomb branch algebra. Important cases of these Coulomb branches are (generalized) affine Grassmannian slices, and their quantizations are truncated shifted Yangians. Motivated by the geometric Satake correspondence, we define a categorical \(\mathfrak{g}\)action on modules for these truncated shifted Yangians. Our main tool is the study of how the Coulomb branch algebra changes when we pass from \(G\), \(V\) to \(L\), \(U\), where \(L\) is a Levi in \(G\) and \(U\) is the invariants for a coweight defining \(L\). 
April 28, 2020 at 5 pm (GMT+2).
Giovanni Paolini
Caltech, USA 
Title: The \(K(\pi, 1)\) conjecture for affine Artin groups
Abstract: Artin groups are a generalization of braid groups, and arise as the fundamental groups of configuration spaces associated with Coxeter groups. A longstanding open problem, called the \(K(\pi, 1)\) conjecture, states that the higher homotopy groups of these configuration spaces are trivial. For finite Coxeter groups, this was proved by Deligne in 1972. In the first part of this talk I will introduce Coxeter groups, Artin groups, and the \(K(\pi, 1)\) conjecture (so that only few topological and combinatorial prerequisites are needed). Then I will outline a recent proof of the \(K(\pi, 1)\) conjecture in the affine case, which is a joint work with Mario Salvetti. 