Seminari/Colloquia
Pagina 2
Date  Type  Start  End  Room  Speaker  From  Title 

06/06/24  Seminario  14:30  15:30  1201 Dal Passo  John Pearson  University of Edinburgh  Recent Developments in the Numerical Solution of PDEConstrained Optimization Problems
Optimization problems subject to PDE constraints form a mathematical tool that can be applied to a wide range of scientific processes, including fluid flow control, medical imaging, option pricing, biological and chemical processes, and electromagnetic inverse problems, to name a few. These problems involve minimizing some function arising from a particular physical objective, while at the same time obeying a system of PDEs which describe the process. It is necessary to obtain accurate solutions to such problems within a reasonable CPU time, in particular for timedependent problems, for which the “allatonce” solution can lead to extremely large linear systems.
In this talk we consider iterative methods, in particular Krylov subspace methods, to solve such systems, accelerated by fast and robust preconditioning strategies. In particular, we will survey several new developments, including block preconditioners for fluid flow control problems, a circulant preconditioning framework for solving certain optimization problems constrained by fractional differential equations, and multiple saddlepoint preconditioners for block tridiagonal linear systems. We will illustrate the benefit of using these new approaches through a range of numerical experiments.
This talk is based on work with Santolo Leveque (Scuola Normale Superiore, Pisa), Spyros Pougkakiotis (Yale University), Jacek Gondzio (University of Edinburgh), and Andreas Potschka (TU Clausthal).
This talk is part of the activity of the MUR Excellence Department Project MatMod@TOV (CUP E83C23000330006).

06/06/24  Seminario  14:00  15:00  1101 D'Antoni  Lei Zhang  University of Florida  (Nota: Cambio di giorno, orario e aula) Asymptotic Analysis and Uniqueness of blowup solutions of nonquantized singular mean field equations
For singular mean field equations defined on a compact Riemann surface, we prove the uniqueness of bubbling solutions when blowup points are either regular points or nonquantized singular sources. In particular the uniqueness result covers the most general case extending or improving all previous works. For example, unlike previous results, we drop the assumption of singular sources being critical points of a suitably defined KirchoffRouth type functional. Our argument is based on refined estimates, robust and flexible enough to be applied to a wide range of problems requiring a delicate blowup analysis. In particular we come up with a major simplification of previous uniqueness proofs. This is a joint work with Daniele Bartolucci and Wen Yang.
Note: This talk is part of the activity of the MIUR Department of Excellence Project MatMod@TOV (20232027) 
04/06/24  Colloquium  14:30  15:30  1201 Dal Passo  “Supercritical KPZ equations”
Like many discrete statistical mechanics models, stochastic PDEs can exhibit a “critical dimension” beyond which their largescale behaviour is expected to be trivial (i.e. governed by Gaussian fluctuations). 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 largescale behaviour in the supercritical regime.
 
29/05/24  Seminario  17:30  18:30  1201 Dal Passo  Claudio Dappiaggi  Università di Pavia  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  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  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  TU Dresden  (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  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  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  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.

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