Dipartimento di Matematica -UTV-

Date	Type	Start	End	Room	Speaker	From	Title
04/06/24	Colloquium	14:30	15:30	1201 Dal Passo	Martin HAIRER	EPFL Lausanne & Imperial College, London	Colloquium Levi Civita (CMTP) “Supercritical KPZ equations” Abstract Like many discrete statistical mechanics models, stochastic PDEs can exhibit a “critical dimen-sion” beyond which their large-scale behaviour is expected to be trivial (i.e. governed by Gaussian fluc-tuations). While such sweeping heuristics allow us to formulate rather precise conjectures, there are relatively few cases where these have actually been proven. In this talk, we will mainly focus on the KPZ equation, a standard model of interface fluctuations. There has recently been substantial progress in our mathematical understanding of its large-scale behaviour in the supercritical regime.
29/05/24	Seminario	17:30	18:30	1201 Dal Passo	Claudio Dappiaggi	Università di Pavia	Operator Algebras Seminar On the stochastic Sine-Gordon model: an AQFT perspective Abstract We investigate the massive Sine-Gordon model in the finite ultraviolet regime on the two-dimensional 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 sine-Gordon 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/home-page?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 Abstract 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 Abstract 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) Abstract 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) Abstract 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 Abstract 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 Abstract 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 Abstract 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 Abstract 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)