15/05/24  Seminario  16:00  17:00  1201 Dal Passo  Giulio Codogni  Università di Roma Tor Vergata 
Operator Algebras Seminar
Vertex algebras and Teichmüller modular forms
Vertex algebras are algebraic structures coming from two dimensional conformal field theory. This talk is about their relation with moduli spaces of Riemann surfaces.
I will first review some background material. In particular, I will recall that a vertex algebra is a graded vector space V with additional structures, and these structures force the HilbertPoincaré series of V, conveniently normalized, to be a modular form.
I will then associate to any holomorphic vertex algebra a collection of Teichmüller modular forms (= sections of powers of the lambda class on the moduli space of Riemann surfaces), whose expansion near the boundary gives back some information about the correlation functions of the vertex algebra. This is a generalization of the HilbertPoincaré series of V, it uses moduli spaces of Riemann surfaces of arbitrarily high genus, and it is sometime called partition function of the vertex algebra. I will also explain some partial results towards the reconstruction of the vertex algebra out of these Teichmüller modular forms.
Using the above mentioned construction, we can use vertex algebras to study problems about the moduli space of Riemann surfaces, such as the Schottky problem, the computation of the slope of the effective cone, and the computation of the dimension of the space of sections of powers of the lambda class. On the other hand, this construction allows us to use the geometry of the moduli space of Riemann surfaces to classify vertex algebras; in particular, I will discuss how conjectures and known results about the slope of the effective cone can be used to study the unicity of the moonshine vertex algebras.
This is a work in progress with Sebastiano Carpi.
The Operator Algebra Seminar schedule is here: https://sites.google.com/view/oastorvergata/homepage?authuser=0 
15/05/24  Seminario  14:30  15:30  1201 Dal Passo  Agostino Patella  Humboldt Universität zu Berlin, Institut für Physik & IRIS Adlershof 
Operator Algebras Seminar
Extracting Scattering Amplitudes from Euclidean Correlators
The MS Teams link to the streaming of the seminar in the abstract
Scattering amplitudes can be extracted from timeordered $n$point functions by means of the well known LSZ reduction formula, even in nonperturbative Quantum Field Theories, such as Quantum Chromodynamics (QCD). However, in the context of Lattice QCD, one can access only Euclidean $n$point functions sampled at discrete points and with finite (but systematically improvable) precision and accuracy. This makes the problem of analytically continuing back to Minkowski spacetime illposed. I will present here one particular strategy which allows to extract scattering amplitudes from Euclidean correlators, while avoiding analytic continuation, technically turning an illposed problem into a merely illconditioned one.
Working in the axiomatic framework of the HaagRuelle scattering theory, we show that scattering amplitudes can be approximated arbitrarily well in terms of linear combinations of Euclidean correlators at discrete time separations. The essential feature of the proposed approximants is that one can calculate them, at least in principle, from LatticeQCD data. In this talk, after reviewing the basic ideas behind HaagRuelle scattering theory, I will sketch the derivation of the approximations formulae, and discuss extensively how they can be used in practical numerical calculations. Also, similarities and differences with other methods, e.g. Lüscher's formalism, will be reviewed.
MS Teams link to seminar streaming:
https://teams.microsoft.com/l/meetupjoin/19%3a9d30e9bd907b4500bbe1387b3dcad011%40thread.tacv2/1715274588963?context=%7b%22Tid%22%3a%2224c5be2ad76440c5997582d08ae47d0e%22%2c%22Oid%22%3a%229b393957c38b46ad8d9a31172e44b55f%22%7d

14/05/24  Seminario  16:30  18:00  1201 Dal Passo  Michele Coti Zelati  Imperial College, London  Titolo
Seminario di Equazioni Differenziali
Diffusion and mixing for twodimensional Hamiltonian flows
We consider general twodimensional autonomous velocity fields and prove that their mixing and dissipation features are limited to algebraic rates. As an application, we consider a standard cellular flow on a periodic box, and explore potential consequences for the longtime dynamics in the twodimensional Euler equations.
NB:This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C23000330006

14/05/24  Seminario  14:00  15:30  1101 D'Antoni  Valeria Bertini  Università di Genova  Geometry Seminar Deformation families of IHS varieties: classification problem and new examples
A fruitful way to produce examples of IHS varieties is to consider terminalizations of symplectic quotients of symplectic varieties. In a work in collaboration with A. Grossi, M. Mauri and E. Mazzon we classify all terminalizations of quotients of Hilbert schemes of K3 surfaces and generalized Kummer varieties by the action of symplectic automorphisms induced by the underlying surface. Furthermore, we determine their second Betti number, the fundamental group of their singular locus and, in the Kummer case, we determine the singularities of their universal quasiétale cover. Finally, we compare our deformation types with the examples known in literature, placing our work in the classification program proposed by Menet.
Note:
This talk is part of the activity of the MIUR Department of Excellence Project MatMod@TOV (20232027) 
10/05/24  Seminario  16:00  17:00  1201 Dal Passo  Gabriele VEZZOSI  Università di Firenze 
Algebra & Representation Theory Seminar (ARTS)
joint session with
Topology Seminar
"Analogs of BeilinsonDrinfeld's Grassmannian on a surface"
N.B.: this talk is part of the activity of the MIUR Excellence Department Project MatMod@TOV (CUP E83C23000330006)
BeilinsonDrinfeld's Grassmannian on an algebraic curve is an important object in Representation Theory and in the Geometric Langlands Program. I will describe some analogs of this construction when the curve is replaced by a surface, together with related preliminary results.
This is partly a joint work with Benjamin Hennion (Orsay) and Valerio Melani (Florence), and partly a joint work in progress with Andrea Maffei (Pisa) and Valerio Melani (Florence).

10/05/24  Seminario  14:30  15:30  1201 Dal Passo  Stefano MARINI  Università di Parma 
Algebra & Representation Theory Seminar (ARTS)
"On finitely Levi nondegenerate closed homogeneous CR manifolds"
N.B.: this talk is part of the activity of the MIUR Excellence Department Project MatMod@TOV (CUP E83C23000330006)
A complex flag manifold F = G/Q decomposes into finitely many real orbits under the action of a real form of G. Their embeddings into F define CRmanifold structures on them. We give a complete classification of all closed simple homogeneous CRmanifolds that have finitely nondegenerate Levi forms.

09/05/24  Seminario  14:30  15:30  1201 Dal Passo  Jan Grošelj  University of Ljubljana  PowellSabin splines: unstructured and structured case
A standard approach to the construction of smooth low degree polynomial splines over an unstructured triangulation is based on splitting of triangles in such a way that the refined triangulation allows the imposition of smoothness constraints without dependence on geometry. A wellestablished splitting technique is the PowellSabin 6refinement, which can be used to define C1 quadratic splines as well as splines of higher degree and smoothness.
In this talk we review the construction of splines over a PowellSabin 6refinement with a special emphasis on C1 cubic splines. We present Bsplinelike functions that enjoy favorable properties such as local support, stability, nonnegativity, and a partition of unity. In particular, we discuss what supersmoothness properties these functions possess and how they depend on geometric properties of the underlying refinement. Based on this we explain how to establish approximation spaces that are suitable for completely unstructured triangulations, partially structured triangulations, and triangulations with a high level of symmetry, e.g., threedirectional triangulations.
This talk is part of the activity of the MUR Excellence Department Project MatMod@TOV (CUP E83C23000330006).

08/05/24  Seminario  16:00  17:00  1201 Dal Passo  Roberto Conti  Sapienza Università di Roma 
Operator Algebras Seminar
Positive definite Fell bundle maps
C*algebraic bundles (nowadays simply called Fell bundles) were introduced by Fell at the end of the sixties as yet another tool to deal with the representation theory of locally compact groups. The reason why the related literature is still growing is probably due to the fact that they fit pretty well with various aspects of the theory of (twisted) actions (and coactions) of groups (and groupoids) on C*algebras. For instance, many familiar constructions like group C*algebras and crossed products can be viewed as cross sectional C*algebras of suitable Fell bundles.
In the talk we will introduce the concept of positive definite "multiplier" between Fell bundles and discuss some consequences and applications. Especially, a notion of amenability for Fell bundles naturally appears. Other applications are concerned with the construction of certain functors from the category of positive definite multipliers to the category of completely positive maps between C*algebras and with the existence of certain C*correspondences associated to left actions of Fell bundles on right
Hilbert bundles. (Joint work with E. Bedos) 
07/05/24  Seminario  14:30  15:30  1101 D'Antoni  Cinzia Casagrande  Università di Torino  Geometry Seminar Fano 4folds con fibrazioni razionali su 3folds
Sia X una varietà di Fano liscia, complessa, di dimensione 4, e rho(X) il suo numero di Picard. Inizieremo discutendo il seguente risultato: se rho(X)>12, allora X è un prodotto di superfici di del Pezzo; se rho(X)=12, allora X ha una contrazione razionale X>Y dove Y ha dimensione 3. Una contrazione razionale è una mappa data da una successione di flips seguita da un
morfismo suriettivo a fibre connesse, vedremo degli esempi espliciti.
Poi discuteremo le proprietà geometriche delle Fano 4folds che hanno una contrazione razionale su una 3fold. Un obiettivo è di determinare il massimo numero di Picard di X, ed eventualmente di classicare i casi con numero di Picard grande. Un altro obiettivo è di usare questa descrizione geometrica per costruire nuovi esempi con rho grande; questo è un progetto in corso con Saverio Secci.
NB:
This talk is part of the activity of the MIUR Department of Excellence Project MatMod@TOV (20232027) 
03/05/24  Colloquium  15:00  16:00  1201 Dal Passo  Benjamin Schlein  Universität Zürich  Colloquium di Dipartimento
Bogoliubov theory for dilute quantum systems
In the setting of manybody quantum mechanics, I am going to present a rigorous and recently developed version of Bogoliubov theory. Furthermore, I am going to show how this theory can be applied, on the one hand to study the lowenergy spectrum of dilute Bose gases (i.e. to determine the lowlying eigenvalues of their Hamilton operator) and, on the other hand, to approximate their timeevolution, capturing fluctuations around the nonlinear GrossPitaevskii equation describing the dynamics of the BoseEinstein condensate.
NB:This colloquium is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C23000330006 