| 07/11/25 | Seminario | 16:00 | 17:00 | 1201 Dal Passo | Lucia BAGNOLI | "Sapienza" Università di Roma |
Algebra & Representation Theory Seminar (ARTS)
"TBA"
N.B.: this talk is part of the activity of the MIUR Excellence Department Project MatMod@TOV (CUP E83C23000330006)
T.B.A.
<br>
<em> <strong><u>N.B.</u>:</strong> this talk is part of the activity of the MIUR Excellence Department Project MatMod@TOV (CUP E83C23000330006) </em> |
| 07/11/25 | Seminario | 14:30 | 15:30 | 1201 Dal Passo | Alessio CIPRIANI | Università di Verona |
Algebra & Representation Theory Seminar (ARTS)
"TBA"
N.B.: this talk is part of the activity of the MIUR Excellence Department Project MatMod@TOV (CUP E83C23000330006)
T.B.A.
<br>
<em> <strong><u>N.B.</u>:</strong> this talk is part of the activity of the MIUR Excellence Department Project MatMod@TOV (CUP E83C23000330006) </em> |
| 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 |
| 24/10/25 | Seminario | 16:00 | 17:00 | 1201 Dal Passo | Giovanni CERULLI IRELLI | "Sapienza" Università di Roma |
Algebra & Representation Theory Seminar (ARTS)
"Quivers with Polynomial Identities"
N.B.: this talk is part of the activity of the MIUR Excellence Department Project MatMod@TOV (CUP E83C23000330006)
Which quivers have a path algebra that is PI? What can we say about their T-ideal? And what happens if we add relations? In this talk, I will address these questions.
This is joint work with Elena Pascucci and Javier De Loera Chavez.
N.B.: this talk is part of the activity of the MIUR Excellence Department Project MatMod@TOV (CUP E83C23000330006) |
| 24/10/25 | Seminario | 14:30 | 15:30 | 1201 Dal Passo | Antonio Miti | U Roma La Sapienza |
Algebra & Representation Theory Seminar (ARTS)
Construction and Reduction of the Lie infinity Algebra of Observables associated with a BV-Module
Multisymplectic manifolds generalize symplectic manifolds by featuring a closed nondegenerate differential form of degree higher than 2. Such structures are natural candidates for a geometric formalization of classical field theories. In this context, Rogers (2010) showed that just as a symplectic manifold yields a Poisson algebra of functions, an n-plectic manifold yields an n-terms Lie infinity algebra of observables. The remarkable aspect of Rogers' construction is that it is essentially algebraic and relies only on the axioms of Cartan calculus, suggesting that this higher version of the "observable Poisson algebra" can be generalized beyond the realm of manifolds. In this talk, we propose such a generalization in the setting of Gerstenhaber algebras and Batalin–Vilkovisky (BV) modules, which provide an algebraic formulation of Cartan calculus of interests in the context of non-commutative geometry. This framework allows us to construct Lie infinity algebras of observables in a purely algebraic way, without reference to an underlying manifold. As an application, we turn to the problem of reducing multisymplectic observables in the presence of constraints or symmetries. Building on the work of Dippel, Esposito, and Waldmann, who introduced the notion of a "constraint triple" as a categorical package for coisotropic reduction, we adapt this formalism to our BV-module context and the associated Lie infinity algebras. This construction provides a conceptual framework for the algebraic reduction procedure of multisymplectic observables, as developed in our recent joint work with Casey Blacker (SIGMA 2024). The results presented here are part of a collaboration with Leonid Ryvkin, published in Differential Geometry and its Applications (2025).
This talk is part of the activity of the MIUR Excellence Department Project MatMod@TOV (CUP E83C23000330006) |
| 22/10/25 | Seminario | 16:00 | 17:00 | 1201 Dal Passo | Gandalf Lechner | FAU Erlangen-Nürnberg |
Operator Algebras Seminar
Inclusions of Standard Subspaces
Note:This talk is part of the activity of the MUR Excellence Department Project MatMod@TOV (CUP E83C23000330006)
Standard subspaces are closed real subspaces of a complex Hilbert space that appear naturally in Tomita–Takesaki modular theory and have many applications to quantum field theory. In this talk, standard subspaces are considered as a subject of interest in their own right (independently of von Neumann algebras). A particular focus are inclusions of standard subspaces, which have similarities to subfactors, and several new methods for investigating the relative symplectic complement of an inclusion will be discussed. A particular class of examples that arises from the fundamental irreducible building block of a conformal field theory on the line is analyzed in detail.
Joint work with Ricardo Correa da Silva, see https://link.springer.com/article/10.1007/s00220-025-05458-4. |
| 21/10/25 | Seminario | 14:30 | 15:30 | 1201 Dal Passo | Mattia Galeotti | Università di Bologna |
Seminario di Equazioni Differenziali
The Benamou-Brenier formulation of optimal transport on sub-Riemannian manifolds
The dynamical formulation of optimal transport between two probability measures $\mu_0,\mu_1$ on a (sub)Riemannian manifold $M$, aims at minimizing the square integral of a Borel family of vector fields
$$
\int_0^1\int_M||v_t||^2dmu_t dt,
$$
where the narrowly continuous curve of probabilities $\mu_t$ and $v_t$ must respect the continuity equation.
The equivalence between this Benamou-Brenier formulation and the Kantorovich formulation of optimal transport, is well known in Riemannian context, but still open in sub-Riemannian manifolds (in the SR case, $v_t$ is a family of {em horizontal} vector fields).
I will present some recent advancements in this problem and a joint work (with Giovanna Citti and Andrea Pinamonti), proving the equivalence under general regularity assumptions
in the case of a sub-Riemannian manifold with no non-trivial abnormal geodesics. The key idea is the formulation of a relaxed version of the dynamical problem that hinges the other two versions, and allows to prove the equivalence of the Kantorovich formulation with the relaxed and the original Benamou-Brenier formulation.
NB:This talk is part of the activity of the MUR Excellence Department Project MATH@TOV CUP E83C23000330006 |