| 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>
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
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). |
| 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
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)
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
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)
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
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). |
| 29/10/25 | Seminario | 16:00 | 17:00 | 1201 Dal Passo | Vedran Sohinger | University of Warwick |
Operator Algebras Seminar
Gibbs measures of 1D quintic nonlinear Schrödinger equations as limits of many-body quantum Gibbs states
Note: This talk is part of the activity of the MUR Excellence Department Project MatMod@TOV (CUP E83C23000330006)
Gibbs measures of nonlinear Schrödinger equations (NLS) are a
fundamental object used to study low-regularity solutions with random
initial data. In the dispersive PDE community, this point of view was
pioneered by Bourgain in the 1990s. We study the problem of the
derivation of Gibbs measures as mean-field limits of Gibbs states in
many-body quantum mechanics.
In earlier joint work with Jürg Fröhlich, Antti Knowles, and Benjamin
Schlein, we studied this problem for variants of the cubic NLS with
defocusing (positive) interactions. The latter models physically
correspond to pair interactions of bosons. In these works, the problem
was studied in dimensions d=1,2,3.
In this talk, I will explain how one can obtain an analogous result for
the 1D quintic NLS, which corresponds to three-body interactions of
bosons. In this setting, we consider focusing interactions,
due to which we need to add a truncation in the mass and rescaled
particle number. Our methods allow us to obtain a microscopic derivation
of the time-dependent correlation functions for the 1D quintic NLS. This
is joint work with Andrew Rout. |
| 28/10/25 | Seminario | 14:30 | 15:30 | 1201 Dal Passo | Maxime Zavidovique | Sorbonne Université (Francia) | Seminario di Equazioni Differenziali
Discounted Hamilton-Jacobi equations with and without monotonicity
We are interested in (viscosity) solutions of Hamilton-Jacobi equations of the form $G( lambda u_lambda(x),x,D_x u_lambda) = cst $ where $u_lambda : M o mathbb{R}$ is a continuous function defined on a closed manifold and $G$ verifies convexity and growth conditions in the last variables. Such solutions carry invariant sets for the contact flow associated to $G$. The parameter $lambda>0$ is aimed to be sent to $0$. It has been known that when $G$ is increasing in the first variable, $u_lambda$ exists, is unique and the family converges as $lambda o 0$. We will explain that when this hypothesis is dropped, there can be non uniqueness of solutions $u_lambda$ at $lambda>0$ fixed. Moreover, there can be coexistence of converging families of solutions $(u_lambda)_lambda$ and diverging ones. (Collaboration with Davini, Ni and Yan)
Note: This talk is part of the activity of the MIUR Department of Excellence Project MatMod@TOV (2023–2027). |
| 28/10/25 | Seminario | 14:30 | 16:00 | 1101 D'Antoni | Arne Kuhrs | Paderborn University | Geometry Seminar
Tropical principal bundles on metric graphs
Tropical geometry studies a piecewise linear, combinatorial shadow of degenerations of algebraic varieties. In many cases, usual algebro-geometric objects such as divisors or line bundles on curves have tropical analogues that are closely tied to their classical counterparts. For instance, the theory of divisors and line bundles on metric graphs has been crucial in advances in Brill–Noether theory and the birational geometry of moduli spaces. In this talk, I will present an elementary theory of tropical principal bundles on metric graphs, generalizing the case of tropical line bundles to bundles with arbitrary reductive structure group. Our approach is based on tropical matrix groups arising from the root datum of the corresponding reductive group, and leads to an appealing geometric picture: tropical principal bundles can be presented as pushforwards of line bundles along covers equipped with symmetry data from the Weyl group. Building on Fratila's description of the moduli space of semistable principal bundles on an elliptic curve, we describe a tropicalization procedure for semistable principal bundles on a Tate curve. More precisely, the moduli space of semistable principal bundles on a Tate curve is isomorphic to a natural component of the tropical moduli space of principal bundles on its dual metric graph. This is based on ongoing work with Andreas Gross, Martin Ulirsch, and Dmitry Zakharov.
<strong> Note: </strong>
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 |