29/05/24  Seminario  17:30  18:30  1201 Dal Passo  Claudio Dappiaggi  Università di Pavia 
Operator Algebras Seminar
On the stochastic SineGordon model: an AQFT perspective
We investigate the massive SineGordon model in the finite ultraviolet regime on the twodimensional Minkowski spacetime with an additive Gaussian white noise. In particular we construct the expectation value and the correlation functions of a solution of the underlying stochastic partial differential equation (SPDE) as a power series in the coupling constant, proving ultimately uniform convergence. This result is obtained combining an approach to study SPDEs at a perturbative level which a recent analysis of the quantum sineGordon model using techniques proper of the perturbative, algebraic approach to quantum field theory (pAQFT). This is a joint work with A. Bonicelli and P. Rinaldi, https://arxiv.org/pdf/2311.01558
Note: This talk is part of the activity of the MUR Excellence Department Project MatMod@TOV (CUP E83C23000330006)
The Operator Algebra Seminar schedule is here: https://sites.google.com/view/oastorvergata/homepage?authuser=0

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 TomitaTakesaki 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' RadonNikodym 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 (20232027) 
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 MatMod@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 MatMod@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 selfinteracting manybody 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 Coulombtype 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 shortrange 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 "decayfunction''. Linear decayfunctions correspond to integral versions of rigid cohomology, while logarithmic decayfunctions produce the conjectured family of logdecay 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 (20232027) 
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 discretetime 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 TienCuong 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 BjörklundGorodnik, 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 (20232027) 
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 (20232027) 