Dipartimento di Matematica -UTV-

Date	Type	Start	End	Room	Speaker	From	Title
12/12/25	Seminario	16:00	17:00	1201 Dal Passo	Edoardo D'Angelo	Università di Milano	Operator Algebras Seminar A locally covariant renormalization group in Lorentzian spacetimes/em> Abstract Renormalization group flows, based on functional Polchinski or Wetterich equations, are powerful tools that give access to non-perturbative aspects of strongly coupled QFTs and gravity. I will provide an overview of a new approach, developed to construct a rigorous renormalization group (RG) flow on Lorentzian manifolds. This approach, based on a local and covariant regularization of the Wetterich equation, highlights its state dependence. I give the main ideas of a proof of local existence of solutions for the RG equation, when a suitable Local Potential Approximation is considered. The proof is based on an application of the renown Nash-Moser theorem. I will also present recent applications of the locally covariant RG equation to the non-perturbative renormalizability of quantum gravity.
25/11/25	Seminario	14:30	15:30	1201 Dal Passo	Pau Martin	UPC Barcelona	Seminario di Equazioni Differenziali Newhouse phenomena and universality in celestial mechanics Abstract McGehee introduced a compactification of the phase space of the restricted 3-body problem by gluing a manifold of periodic orbits ''at infinity''. Although from the dynamical point of view these periodic orbits are parabolic (the linearization of the Poincare map is the identity matrix), one of them, denoted here by O, possesses stable and unstable manifolds which, moreover, separate the regions of bounded and unbounded motion. This observation prompted the investigation of the homoclinic picture associated to O, starting with the work of Alekseev and Moser. We continue this research and extend, to this degenerate setting, some classical results in the theory of homoclinic bifurcations. More concretely, we prove that there exist Newhouse domains N in parameter space (the ratio of masses of the bodies) and residual subsets R subset N for which the homoclinic class of O has maximal Hausdorff dimension and is accumulated by generic elliptic periodic orbits. One of the main consequences of our work is the fact that, for a (locally) topologically large set of parameters of the restricted 3-body problem the union of its elliptic islands forms an unbounded subset of the phase space and, moreover, the closure of the set of generic elliptic periodic orbits contains hyperbolic sets with Hausdorff dimension arbitrarily close to maximal. Other instances of the restricted n-body problem such as the Sitnikov problem and the case n=4 are also considered. This is a joint work with M. Garrido and J. Paradela. Note: This talk is part of the activity of the MIUR Department of Excellence Project MatMod@TOV (2023–2027).
21/11/25	Seminario	16:00	17:00	1201 Dal Passo	Bernard LECLERC	Université de Caen	Algebra & Representation Theory Seminar (ARTS) "Cluster structures on (G,c)-bands and representations of quantum affine algebras" N.B.: this talk is part of the activity of the MIUR Excellence Department Project Mat-Mod@TOV (CUP E83C23000330006) Abstract   Let <em>G</em> be a simple simply-connected algebraic group of type <em>A</em>, <em>D</em>, <em>E</em>. In the 60's Steinberg has described cross-sections <em>A</em>(<em>c</em>) of the set of regular conjugacy classes in <em>G</em>, depending on the choice of a Coxeter element <em>c</em> in the Weyl group of <em>G</em>. We define a (<em>G</em>,<em>c</em>)-band as a sequence (<em>g</em>(<em>k</em>)) of elements of <em>G</em> such that, for every <em>k</em>, <em>g</em>(<em>k</em>+1) is equal to the product of <em>g</em>(<em>k</em>) by an element of <em>A</em>(<em>c</em>). We show that (<em>G</em>,<em>c</em>)-bands are the rational points of an infinite-dimensional affine integral scheme <em>B</em>(<em>G</em>,<em>c</em>), whose coordinate ring <em>R</em>(<em>G</em>,<em>c</em>) has the structure of a cluster algebra. <br> This is a joint work with Luca Francone. <br>   <em><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></em>
21/11/25	Seminario	14:30	15:30	1201 Dal Passo	Matilde MACCAN	Ruhr-Universität Bochum	Algebra & Representation Theory Seminar (ARTS) "Automorphisms of flag varieties with non reduced stabilizers" N.B.: this talk is part of the activity of the MIUR Excellence Department Project Mat-Mod@TOV (CUP E83C23000330006) Abstract   Alongside toric varieties, flag varieties are one of the rare classes of object in algebraic geometry whose combinatorics allow for explicit computations and testing conjectures. In positive characteristic, there are "twisted" versions of these varieties, namely quotients of the form <em>X</em>=<em>G/P</em> where <em>G</em> is semisimple and <em>P</em> is a non-reduced parabolic subgroup (scheme). Their geometry significantly differs from the one of classical flag varieties; for instance, they are almost never Fano. First we will recall the classification of non-reduced parabolics, and describe through examples the contractions of Schubert curves on <em>X</em>. This will allow us to get to a complete description of the connected automorphism group of <em>X</em> (as a group scheme), generalizing the classical results of Demazure. <br>   <em><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></em>
19/11/25	Seminario	16:00	17:00	1201 Dal Passo	Karl-Henning Rehren	Univ. of Göttingen	Operator Algebras Seminar Gauge-invariant quantum observables in non-abelian gauge theories Note:This talk is part of the activity of the MUR Excellence Department Project MatMod@TOV (CUP E83C23000330006) Abstract Classical constructions of gauge-invariant quantities, like Wilson loops, are too singular as candidates for quantum observables. We present a new construction of more regular operators (sloppily called "Wilson sausage" operators) in the Wick algebra, and discuss their algebraic properties under the operator product.
18/11/25	Seminario	14:30	15:30	1201 Dal Passo	Liangjun Weng	SNS Pisa	Seminario di Equazioni Differenziali The Gauss curvature flow and its capillary variant Abstract The Gauss curvature flow is a fully nonlinear geometric evolution equation in which a strictly convex, closed hypersurface moves with normal velocity equal to its Gauss curvature. Originating from Firey's work in 1974, it was introduced as an idealized model for the abrasion of convex stones on a beach, and has since developed deep connections with PDE and geometry. In this talk, we will discuss some recent progress on the Gauss curvature flow, including the key contributions by Andrews, Guan–Ni, Brendle–Choi–Daskalopoulos, and others. Particular attention will be given to the convergence of a convex body to a round point in finite time, and to the important roles played by the monotonicity of Firey's entropy in the asymptotic analysis of the flow. We will also discuss natural extensions of the Gauss curvature flow in the capillary setting, based on recent work with Xinqun Mei (Peking University) and Guofang Wang (University of Freiburg). NB: This talk is part of the activity of the MUR Excellence Department Project MATH@TOV CUP E83C23000330006
12/11/25	Seminario	16:00	17:00	1201 Dal Passo	Serena Cenatiempo	GSSI - Gran Sasso Science Institute	Operator Algebras Seminar Bose-Einstein Condensation and low temperature phases of Dilute Bose Gases/em> Note:This talk is part of the activity of the MUR Excellence Department Project MatMod@TOV (CUP E83C23000330006) Abstract Dilute Bose gases are unique quantum systems that exhibit a fascinating low-temperature phase known as the Bose-Einstein condensate. Over the past two decades, the mathematical understanding of these systems has improved considerably. In this talk, we will review some of these advances, with a perspective on the largely open challenge of understanding their general behaviour in the thermodynamic limit, the appropriate large-scale framework for investigating the occurrence of phase transitions. Based on a series of joint works with G. Basti, C. Boccato, C. Brennecke, A. Giuliani, A. Olgiati, G. Pasqualetti and B. Schlein.
11/11/25	Seminario	14:30	15:30	1201 Dal Passo	Cyril Letrouit	CNRS, Laboratoire d' Orsay, Paris Saclay	Seminario di Equazioni Differenziali Quantitative stability of optimal transport maps Abstract Optimal transport consists in sending a given source probability measure ρ to a given target probability measure μ in an optimal way with respect to a certain cost. Optimal transport has been widely used in many fields, including analysis, probability, statistics, geometry, and optimization. Under classical assumptions, there exists a unique optimal transport map from ρ to μ (Brenier's, McCann's theorems, etc.). In this talk based on a collaboration with Quentin Mérigot, we provide a quantitative answer to the following stability question, notably motivated by numerical analysis and statistics: if μ is perturbed, can the optimal transport map from ρ to μ change significantly? The answer depends on the properties of the source measure ρ. We will also explain some mechanisms leading to instability and present a few conjectures. NB:This talk is part of the activity of the MUR Excellence Department Project MATH@TOV CUP E83C23000330006
07/11/25	Seminario	14:30	15:30	1201 Dal Passo	Lucia BAGNOLI		Algebra & Representation Theory Seminar (ARTS) "On new classes of quantum vertex algebras" N.B.: this talk is part of the activity of the MIUR Excellence Department Project MatMod@TOV (CUP E83C23000330006) Abstract We present the construction of a new class of quantum vertex algebras associated with a normalized Yang R-matrix. They are obtained as Yangian deformations of certain S-commutative quantum vertex algebras and their S-locality takes the form of a single RTT-relation. We establish some preliminary results on their representation theory and then further investigate their braiding map. These results were obtained jointly with Slaven Kozic. If time allows, we will discuss a recent generalization of these results to the case of the type A trigonometric R-matrix. These results were obtained jointly with Marijana Butorac and Slaven Kozic. N.B.: this talk is part of the activity of the MIUR Excellence Department Project MatMod@TOV (CUP E83C23000330006)
04/11/25	Seminario	14:30	15:30	1201 Dal Passo	Livia Corsi	Università Roma Tre	Seminario di Equazioni Differenziali Asymptotically full measure sets of almost-periodic solutions for the NLS equation Abstract In the study of close to integrable Hamiltonian PDEs, a fundamental question is to understand the behaviour of “typical” solutions. With this in mind it is natural to study the persistence of almost-periodic solutions and infinite dimensional invariant tori, which are in fact typical in the integrable case. In this talk I shall consider a family of NLS equations parametrized by a smooth convolution potential and prove that for “most” choices of the parameter there is a full measure set of Gevrey initial data that give rise to almost-periodic solutions whose hulls are invariant tori. As a consequence the elliptic fixed point at the origin turns out to be statistically stable in the sense of Lyapunov. This is a joint work with L.Biasco, G.Gentile and M.Procesi. Note: This talk is part of the activity of the MIUR Department of Excellence Project MatMod@TOV (2023–2027).