Dipartimento di Matematica -UTV-

Date	Type	Start	End	Room	Speaker	From	Title
01/04/26	Colloquium	16:00	17:00	1201 Dal Passo	Mikael Rørdam	University of Copenhagen	Colloquium "Levi-Civita" The Connes Embedding Problem, Kirchberg’s reformulations, Tsirelson’s conjecture, and MIP=RE* Abstract In his seminal classification paper from 1976, Connes remarked that every separable tracial von Neumann algebra ought to be embeddable into an ultrapower of the hyperfinite type II_1 factor, or, in other words, be approximable by matrices. Over the following decades, the Connes Embedding Problem (CEP) remained unsolved, but many interesting and deep reformulations were discovered. Prominently, Kirchberg proved in his famous 1991 Inventiones paper that CEP is equivalent to several questions concerning C-algebras and their tensor product, including his QWEP conjecture. He also showed that CEP holds if and only if there is a unique C-norm of the tensor product of two copies of the full group C*-algebra of the free group. The latter was shown (by several authors) to be equivalent to Tsirelson’s conjecture about quantum correlations. CEP also relates to the open problems in group theory if all infinite discrete groups are sofic. Recently, Ji-Natarajan-Vidick-Wright-Yuen announced a negative solution to Tsirelson’s conjecture, and hence also a negative answer to CEP by proving that two complexity classes are the same
04/03/26	Seminario	16:00	17:00	1201 Dal Passo	Stefano Galanda	University of York	Operator Algebras Seminar Construction of interacting equilibrium states for non-relativistic Bose gases with condensation Abstract In this talk I will present a recent construction of equilibrium states at positive temperature, with and without Bose-Einstein condensation, for a non-relativistic Bosonic QFT (gas of Bose particles) in the infinite volume limit, interacting through a localised two body interaction. In order to obtain this result, we use methods of quantum field theory in the algebraic formulation and of quantum statistical mechanics in the operator algebraic setting. The convergence of the interacting correlation functions is obtained constructing an equivalent perturbative series expansion introducing an auxiliary stochastic Gaussian field which mediates the interaction. Limits where the localisation of the two-body interaction is removed are eventually discussed in combination with other regimes. This talk is based on a collaboration with Nicola Pinamonti.
24/02/26	Seminario	14:30	15:30	1201 Dal Passo	Lorenzo Brasco	Università di Ferrara	Seminario di Equazioni Differenziali Eigenvalues of the $p-$Laplacian on general open sets Abstract We start by reviewing the classical spectral theory of the Dirichlet-Laplacian, on a general open set. It is well-known that the spectrum may fail to be purely discrete, in this generality. We then turn our attention to a nonlinear variant of this problem, by considering the case of the $p-$Laplacian with Dirichlet homogeneous conditions. More precisely, we analyze the minmax levels of the constrained $p-$Dirichlet integral: we show that, whenever one of these levels lies below the threshold given by the $L^p$ Poincar\'e constant ''at infinity'', it actually defines an eigenvalue. We also prove a quantitative exponential fall-off at infinity for the relevant eigenfunctions: this can be seen as a generalization of v{S}nol-Simon--type estimates to the nonlinear case. Some of the results presented have been obtained in collaboration with Luca Briani (TUM Monaco) and Francesca Prinari (Pisa). <br> <b>NB</b>: <i> This talk is part of the activity of the MUR Excellence Department Project MATH@TOV CUP E83C23000330006 </i>
24/02/26	Seminario	14:30	16:00	1101 D'Antoni	Gianluca Pacienza	Université de Lorraine	Geometry Seminar Sottovarietà di intersezioni complete di grado alto Abstract È ben noto grazie a un lavoro di Ein del 1988 che le intersezioni complete molto generali di multigrado $(d_1,...,d_c)$ nello spazio proiettivo di dimensione $n$ non contengono curve razionali non appena $d_1+...+d_c geq 2n-c-1 $. Questo risultato è stato reso ottimale ed esteso nel caso delle ipersuperfici grazie a un metodo introdotto da Voisin che ha ispirato lavori ulteriori di Clemens, Ran e miei. Nonostante lavori più recenti di Coskun, Riedl e Yang sempre nel caso delle ipersuperfici, il risultato di Ein è rimasto l’unico disponibile per intersezioni complete di codimensione arbitraria. Nel seminario parlerò di un lavoro in collaborazione con Francesco Bastianelli in cui estendiamo il lavoro di Ein, mescolando l’approccio di Voisin con quello di Coskun, Riedl e Yang. Note: This talk is part of the activity of the MIUR Department of Excellence Project MatMod@TOV (2023-2027) and the PRIN 2022 Moduli Spaces and Birational Geometry and Prin PNRR 2022 Mathematical Primitives for Post Quantum Digital Signatures
20/02/26	Seminario	16:00	17:00		Georgy SHARYGIN	IHES	Algebra & Representation Theory Seminar (ARTS) joint session with the Topology Seminar "The symmetries of the full symmetric Toda system and Lie-Bianchi" N.B.: this talk is part of the activity of the MIUR Excellence Department Project Mat-Mod@TOV (CUP E83C23000330006) Abstract   The full symmetric Toda system is a Hamilton system on the space of real symmetric matrices, given by the Lax equation <em>L'</em> = [<em>M</em>(<em>L</em>),<em>L</em>] , where <em>M</em>(<em>L</em>) is the naïve antisymmetrisation of the symmetric matrix <em>L</em> (deleting the diagonal and inverting the sign of the lower-triangular half). This system turns out to be Liouville-integrable and even super-integrable. In my talk I will prove that it satisfies one more integrability criterion, the Lie-Bianchi criterion, based on the study of its symmetries. <br>   <em><small><small> <strong><u>N.B.</u>:</strong> this talk is part of the activity of the MIUR Excellence Department Project MatMod@TOV (CUP E83C23000330006) </small></small></em>
20/02/26	Seminario	14:30	15:30	1201 Dal Passo	Yasushi IKEDA	IHES	Algebra & Representation Theory Seminar (ARTS) joint session with the Topology Seminar "Argument shift method on algebra U(gl(d))" N.B.: this talk is part of the activity of the MIUR Excellence Department Project Mat-Mod@TOV (CUP E83C23000330006) Abstract The argument shift method is a simple but efficient way to produce a commutative subalgebra in a Poisson algebra, in particular in the symmetric algebra of a Lie group. Its main ingredient is an operator on the Poisson algebra that generates the elements of the commutative subalgebra by acting on its center. In my talk I will describe an analogous operator on the universal enveloping algebra of gl(d), and show why it satisfies a similar property. N.B.: this talk is part of the activity of the MIUR Excellence Department Project MatMod@TOV (CUP E83C23000330006)
17/02/26	Seminario	14:30	15:30	1201 Dal Passo	Rafael Ruggiero	PUC Rio de Janeiro	Seminario di Equazioni Differenziali Horospherical billiards Abstract We introduce the concept of horospherical billiard in the universal covering of a compact surface without focal points and prove some rigidity results assuming the existence of some geometric first integrals. Note: This talk is part of the activity of the MIUR Department of Excellence Project MatMod@TOV (2023–2027).
17/02/26	Seminario	14:30	16:00	1101 D'Antoni	Emmanuel Kowalski	ETH Zürich	Geometry Seminar Exponential sums, jacobians and graphs Abstract Exponential sums over finite fields are essential ingredients in the solution of many arithmetic problems. Their study often relies on algebraic geometry, and especially on Deligne's Riemann Hypothesis over finite fields, which reveals deep structural features of these sums. In turn, one can exploit these to construct some remarkable combinatorial objects. The talk will provide a survey of these various aspects. (Joint works with A. Forey, J. Fresán and Y. Wigderson) <em> Note: </em> This talk is part of the activity of the MIUR Department of Excellence Project MatMod@TOV (2023-2027) and the PRIN 2022 Moduli Spaces and Birational Geometry and Prin PNRR 2022 Mathematical Primitives for Post Quantum Digital Signatures
11/02/26	Colloquium	14:30	15:30	1201 Dal Passo	Alexander Volberg	Michigan State University	Colloquium di Dipartimento Classical and quantum learning problems via harmonic analysis Abstract Recently the learning problems took the center stage in area of theoretical computer science. An amazing and beautiful thing is that they are harmonic analysis problems at heart. The lecture concerns with some natural and elementary question of learning theory and the approach to learning via harmonic analysis. Suppose you wish to find a N by N matrix by asking this matrix question that it honestly answers. For example you can ask question ''What is your (1,1) element?'' Obviously you will need $N^2$ many questions like that. But if one knows some information on Fourier side one can ask only log log N questions if they are carefully randomly chosen. Of course one pays the price: first of all one would find the matrix only with high confidence (high probability bigger than $1-delta$), secondly with the error $epsilon$. Such learning is known as PAC learning, PAC stands for 'probably approximately correct'. The origins of the problem are in theoretical computer science, but the methods are pure harmonic analysis and probability. The main ingredient is dimension free Bernstein—Remez inequality. NB: This talk is part of the activity of the MUR Excellence Department Project MATH@TOV CUP E83C23000330006
10/02/26	Seminario	14:30	15:30	1201 Dal Passo	Laurent Niederman	Université Paris-Saclay	Seminario di Equazioni Differenziali Quasi-periodic co-orbital motions in the planetary three-body problem Abstract Numerous orbits exist in the solar system or in astrodynamics with very peculiar motions. Their common feature is that they consist of two moons or satellites around a much heavier central attractor with almost equal semi-major axes, this is called a co-orbital motion. In spite of analytical theories and numerical investigations developed to describe their long-term dynamics, so far very few rigorous long-time stability results in this setting have been obtained even in the restricted three-body problem. Actually, the nearly equal semi major axes of the moons implies also nearly equal orbital periods (or 1:1 mean motion resonance), and this last point prevent the application of the usual Hamiltonian perturbation theory for the three body problem. Adapting the idea of Arnold to a resonant case, hence by an applcation of KAM theory to the planar planetary three-body problem, we provide a rigorous proof of existence of a large measure set of Lagrangian invariant tori supporting quasi-periodic co-orbital motions, hence stable over infinite times. (Joint work with L. Biasco, L. Chierchia, A. Pousse and P. Robutel) Note: This talk is part of the activity of the MIUR Department of Excellence Project MatMod@TOV (2023–2027).