05/12/23  Seminario  16:00  17:00  1201 Dal Passo  Liangjun Weng  Università di Roma "Tor Vergata"  Titolo
Seminario di Equazioni Differenziali
The capillary Minkowski problem
The classical Minkowski problem asks for necessary and sufficient conditions on a nonnegative Borel measure on the unit sphere to be the surface area measure of a convex body. In a smooth setting, it reduces to the study of a MongeAmpere equation on the unit sphere. This problem has been completely solved through the seminal works of Nirenberg, Pogorelov, ChengYau, etc. In this talk, a new Minkowskitype problem will be introduced. The problem asks for the existence of a convex hypersurface with prescribed GaussKronecker curvature and capillary boundary supported on an obstacle, which can be deduced as a MongeAmpere equation with a Robin (or Neumann) boundary value condition on the spherical cap. Then obtain a necessary and sufficient condition for solving this problem.
NB:This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C23000330006

05/12/23  Seminario  14:30  16:00  1101 D'Antoni  Ruadhaí Dervan  University of Glasgow  Stability conditions for varieties
Stability conditions in algebraic geometry are used to construct moduli spaces. Experience from the theory of vector bundles (and coherent sheaves) suggests it is useful to have many stability conditions, so that one can geometrically understand the birational behaviour of resulting moduli spaces by varying the stability condition. Motivated by this, I will describe a mostly conjectural analogous story for projective varieties with an ample line bundle. Here the classical notion of stability is Kstability, which aims to construct higher dimensional analogues of the moduli space of stable curves, and the main point will be to introduce variants of Kstability defined using extra topological choices. The main results will link these new stability conditions with differential geometry, through the solvability of certain geometric PDEs, and I will try to explain how these links come about and what the general picture should be. 
01/12/23  Seminario  16:00  17:00  1201 Dal Passo  Sophie CHEMLA  Université Sorbonne  Paris Cité 
Algebra & Representation Theory Seminar (ARTS)
"Duality properties for induced and coinduced representations in positive characteristic"
N.B.: partially supported by the MIUR Excellence Department Project MatMod@TOV (CUP E83C23000330006) awarded to the Department of Mathematics, University of Rome "Tor Vergata"
Let k be a field of positive characteristic p>2. We explain a duality property concerning the kernel of coinduced representations of Lie k(super)algebras. This property was already proved by M. Duflo for Lie algebras in any characteristic under more restrictive finiteness conditions. It was then generalized to Lie superalgebras in characteristic 0 in previous works.
In characteristic 0, it is known that the induced representation can be realized as the local cohomology with coefficients in some coinduced representation. In positive characteristic, in the case of a restricted Lie algebra, we prove a similar result for the restricted induced representation.

01/12/23  Seminario  14:30  15:30  1201 Dal Passo  Victoria SCHLEIS  University of TübingenBonn 
Algebra & Representation Theory Seminar (ARTS)
"Tropical Quiver Grassmannians"
N.B.: partially supported by the MIUR Excellence Department Project MatMod@TOV (CUP E83C23000330006) awarded to the Department of Mathematics, University of Rome "Tor Vergata"
Grassmannians and flag varieties are important moduli spaces in algebraic geometry. Quiver Grassmannians are generalizations of these spaces arise in representation theory as the moduli spaces of quiver subrepresentations. These represent arrangements of vector subspaces satisfying linear relations provided by a directed graph.
The methods of tropical geometry allow us to study these algebraic objects combinatorially and computationally. We introduce matroidal and tropical analoga of quivers and their Grassmannians obtained in joint work with Alessio Borzì and separate joint work in progress with Giulia Iezzi; and describe them as affine morphisms of valuated matroids and linear maps of tropical linear spaces.

29/11/23  Seminario  16:00  17:00  1201 Dal Passo  Rainer Verch  Uni. Leipzig 
Operator Algebras Seminar
Relative entropy for states on the CAR algebra
In this talk, the relative entropy between states of the CAR algebra will be considered. One of the states (the "reference state") is a KMS state with respect to a 1parametric automorphism group induced by a unitary group on the 1particle Hilbert space, and the other is a multiexcitation state relative to the reference state. In the case that the reference state is quasifree, a compact formula for the relative entropy can be derived. The results are taken from joint work with Stefano Galanda and Albert Much (MPAG 26 (2023) 21; arXiv:2305.02788 [mathph]). Time permitting, results on work in progress (with Harald Grosse and Albert Much) will be mentioned on the relative entropy for coherent states of the RieffelMoyal deformed quantized Klein Gordon field on algebras of wedge regions on Minkowski spacetime.
Note: This talk is part of the activity of the MUR Excellence Department Project MatMod@TOV (CUP E83C23000330006) 
28/11/23  Seminario  16:00  17:00  1201 Dal Passo  Luca Martinazzi  Università di Roma "La Sapienza"  Seminario di Equazioni Differenziali
Critical points of the MoserTrudinger functional on closed surfaces
Given a 2dimensional closed surface, we will show that the MoserTrudinger functional has critical points of arbitrarily high energy. Since the functional is too critical to directly apply to it the known variational methods (in particular the Struwe monotonicity trick), we will approximate it by subcritical ones, which in fact interpolate it to a Liouvilletype functional from conformal geometry. Hence our result will also unify and give common results for these two apparently unrelated problems. This is a joint work with F. De Marchis, A. Malchiodi and PD. Thizy.
NB:This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C23000330006

28/11/23  Seminario  14:30  16:00  1101 D'Antoni  Francesco Polizzi  Università Federido II di Napoli  Double Kodaira fibrations with extraspecial symmetry
Let C be a smooth complex curve of genus 2. We construct double Kodaira fibrations with small signature as (branched) Galois covers of C × C, whose Galois group is extraspecial of order 32.
This is based on joint papers with A. Causin and P. Sabatino. 
24/11/23  Seminario  16:00  17:00  1201 Dal Passo  Frank Neumann  U Pavia  Preludes to the EilenbergMoore and the LeraySerre spectral sequences
The LeraySerre and the EilenbergMoore spectral sequence are fundamental tools in algebraic topology for computing cohomology. We describe the relationship between these two spectral sequences when both of them share the same abutment. There exists a joint trigraded refinement of the LeraySerre and the EilenbergMoore spectral sequence. This refinement involves two more spectral sequences which abut to the initial terms of the LeraySerre and the EilenbergMoore spectral sequence, respectively. We show that one of these always degenerates from its second page on and that the other one satisfies a localtoglobal property: it degenerates for all possible base spaces if and only if it does so when the base space is contractible. When the preludes degenerate early enough, they appear to echo Deligne's decalage machinery, but in general, this is an illusion. We will discuss several principal fibrations to illustrate the possible cases and give applications, in particular, to Lie groups, group extensions, and torus bundles.
This talk is part of the activity of the MIUR Excellence Department Project MatMod@TOV (CUP E83C23000330006). 
24/11/23  Seminario  14:30  15:30  1201 Dal Passo  Roberto Pagaria  U Bologna  Cohomology ring of arrangement complements
The aim of this talk is to provide a uniform and intuitive description of the cohomology ring of arrangement complements. We introduce complex hyperplane arrangements and state the OrlikSolomon theorem (1980). Then, we describe the real case and the GelfandVarchenko ring (1987). We define toric arrangements and present their cohomology ring (De Concini, Procesi (2005) and Callegaro, D'Adderio, Delucchi, Migliorini, and P. (2020)). Finally, we show a new technique to prove the OrlikSolomon and De ConciniProcesi relations from the GelfandVarchenko ring. The technique applied to abelian arrangements provides a presentation of their cohomology. This is work in progress with Evienia Bazzocchi and Maddalena Pismataro.
This talk is part of the activity of the MIUR Excellence Department Project MatMod@TOV (CUP E83C23000330006). 
22/11/23  Seminario  16:00  17:00  1201 Dal Passo  Yuto Moriwaki  Riken (Wako, Japan) 
Operator algebras seminar
Operator product expansion in two dimension conformal field theory
Conformal field theory can be defined using the associativity and the commutativity of the product of quantum fields (operator product expansion). An important difference between conformal field theory and classical commutative associative algebra is "the divergence" arising from the product of quantum fields, a difficulty that appears in quantum field theory in general.
In this talk we will explain that in the twodimensional case this algebra can be controlled by "the representation theory" of a vertex operator algebra and that the convergence of quantum fields is described by the operad structure of the configuration space. 