| 29/05/24 | Seminario | 16:00 | 17:00 | 1201 Dal Passo | Stefaan Vaes | KU Leuven |
Operator Algebras Seminar
Ergodic states on type III_1 factors and ergodic actions
I will report on a joint work with Amine Marrakchi. Since the early days of Tomita-Takesaki theory, it is known that a von Neumann algebra that admits a state with trivial centralizer must be a type III_1 factor, but the converse remained open. I will present a solution of this problem, proving that such ergodic states form a dense G_delta set among all normal states on any III_1 factor with separable predual. Through Connes' Radon-Nikodym cocycle theorem, this problem is related to the existence of ergodic cocycle perturbations for outer group actions, which I will discuss in the second half of the talk.
Note: This talk is part of the activity of the MUR Excellence Department Project MatMod@TOV (CUP E83C23000330006) |
| 28/05/24 | Seminario | 14:30 | 16:00 | 1101 D'Antoni | Karl Christ | UT Austin | Geometry Seminar
Irreducibility of Severi varieties on toric surfaces
Severi varieties parametrize integral curves of fixed geometric genus in a given linear system on a surface. In this talk, I will discuss the classical question of whether Severi varieties are irreducible and its relation to the irreducibility of other moduli
spaces of curves. I will indicate how tropical methods can be used to answer such irreducibility questions. The new results are from ongoing joint work with Xiang He and Ilya Tyomkin.
Note:
This talk is part of the activity of the MIUR Department of Excellence Project MatMod@TOV (2023-2027) |
| 24/05/24 | Seminario | 16:00 | 17:00 | 1101 D'Antoni | Ulrich KRÄHMER | TU Dresden |
Algebra & Representation Theory Seminar (ARTS)
(N.B.: mind the change of room!)
The ring of differential operators
on a monomial curve is a Hopf
algebroid
N.B.: this talk is part of the activity of the MIUR Excellence Department Project Mat-Mod@TOV (CUP E83C23000330006)
The ring of differential
operators on a cuspidal curve
whose coordinate ring is a numerical
semigroup algebra
is shown to be a
cocommutative and cocomplete
left Hopf algebroid. If the
semigroup is symmetric so that the
curve is Gorenstein, it is a full
Hopf algebroid (admits an antipode).
Based on joint work with Myriam
Mahaman. |
| 24/05/24 | Seminario | 14:30 | 15:30 | 1101 D'Antoni | Giovanni PAOLINI | Università di Bologna |
Algebra & Representation Theory Seminar (ARTS)
joint session with
Topology Seminar
(( N.B.: mind the change of room! ))
"Dual Coxeter groups of rank three"
N.B.: this talk is part of the activity of the MIUR Excellence Department Project Mat-Mod@TOV (CUP E83C23000330006)
In this presentation, I will discuss the combinatorics of the noncrossing partition posets associated with Coxeter groups of rank three. In particular, I will describe the techniques used to prove the lattice property and lexicographic shellability. These properties can then be used to solve several problems on the corresponding Artin groups, such as the K(π,1) conjecture, the word problem, the center problem, and the isomorphism between standard and dual Artin groups.
This is joint work with Emanuele Delucchi and Mario Salvetti. |
| 24/05/24 | Seminario | 12:00 | 13:00 | 1201 Dal Passo | Vitaly Moroz | Swansea University | Seminario di Dipartimento
Nonlinear elliptic problems with nonlocal interactions
We present a survey of nonlinear elliptic equations with nonlocal interactions. These equations describe the collective behavior of self-interacting many-body systems at different scales, from atoms and molecules to the formation of stars and galaxies. What sets these models apart from classical nonlinear PDEs is the presence of nonlocal terms in the equations, introduced via Coulomb-type interactions or a fractional Laplacian term, or both. We provide an overview of typical problems with repulsive interactions originating from Density Functional Theory; and Choquard type problems with attractive gravitational interactions. We also outline recent results in problems featuring competing attractive/ repulsive terms, which create particularly complex structures.
NB:This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C23000330006
|
| 22/05/24 | Seminario | 16:00 | 17:00 | 1201 Dal Passo | Alessio Ranallo | University of Geneva |
Operator Algebras Seminar
Low energy spectrum of the XXZ model coupled to a magnetic field
I will report on recent developments concerning the control of a class of short-range perturbations of the Hamiltonian of an Ising chain. An example covered by our analysis is the celebrated XXZ chain. The talk is based on a joint work with S. Del Vecchio, J. Fröhlich, and A. Pizzo. |
| 21/05/24 | Seminario | 14:30 | 16:00 | 1101 D'Antoni | Marco D'Addezio | IRMA Strasbourg | Geometry Seminar
Edged Crystalline Cohomology
I will talk about a new cohomology theory for algebraic varieties in positive characteristic, called edged crystalline cohomology. This is a generalisation of crystalline cohomology and depends on the choice of a "decay-function''. Linear decay-functions correspond to integral versions of rigid cohomology, while logarithmic decay-functions produce the conjectured family of log-decay crystalline cohomology theories, parametrised by positive real numbers. During the talk, I will explain the construction of this theory after a brief recall of the classical crystalline and rigid cohomology theories.
Note:
This talk is part of the activity of the MIUR Department of Excellence Project MatMod@TOV (2023-2027) |
| 20/05/24 | Seminario | 16:00 | 17:00 | 1201 Dal Passo | Fabrizio Bianchi | Università di Pisa | Seminario di Sistemi Dinamici
Every complex Hénon map satisfies the Central Limit Theorem
Hénon maps were introduced by Michel Hénon as a simplified model of the Poincaré section of the Lorenz model. They are among the most studied discrete-time dynamical systems that exhibit chaotic behaviour. Complex Hénon maps have been extensively studied over the last three decades, in parallel with the development of pluripotential theory. I will present a recent result obtained with Tien-Cuong Dinh, where we show that the measure of maximal entropy of every complex Hénon map is exponentially mixing of all orders for Hölder observables. As a consequence of a recent result by Björklund-Gorodnik, the Central Limit Theorem holds for all Hölder observables.
Note:
This talk is part of the activity of the MIUR Department of Excellence Project MatMod@TOV (2023-2027) |
| 20/05/24 | Seminario | 14:30 | 15:30 | 1201 Dal Passo | Stefano Galatolo | Università di Pisa | Seminario di Sistemi Dinamici
Rare Events and Hitting Time Distribution for Discrete Time Samplings of Stochastic Differential Equations
We consider a random discrete time system in which the evolution of a
stochastic differential equation is sampled at a sequence of discrete times. We
set up a functional analytic framework for which we can prove the existence of
a spectral gap and estimate the behavior of the leading eigenvalue of the related
transfer operator as the system is perturbed by putting a ”hole” in it that cor-
responds to a rare event. By doing so, we derive the distribution of the hitting
times corresponding to the rare event and the extreme value theory associated
with it.
Note:
This talk is part of the activity of the MIUR Department of Excellence Project MatMod@TOV (2023-2027) |
| 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 Hilbert-Poincaré 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 Hilbert-Poincaré 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/home-page?authuser=0 |