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Settimana 02/04/2024 - 05/03/2024
Seminari
Università degli Studi Roma Tor Vergata
Dipartimento di Matematica
Operator Algebras Seminar
Date: 3th April 2024
Schedule: 16:00 - Rome Time
Where: Conference Room 1201 "R. Dal Passo"
Title: " Automorphic forms design of free group factors and quantum dynamics "
Speaker: Florin Radulescu - University of Rome Tor Vergata
Abstract:
The role of automorphic forms as intertwiners between various representations of free group factors was discovered a long time ago by Vaughan Jones, starting with a remarkable formula relating Peterson scalar product with the intrinsical trace. The intertwiner associated to an automorphic form is an eclectic object, not much can be computed, but the Muray von Neuman dimension can be used to get hints on its image. Vaughan Jones used that to settle the problem of finding analytic functions vanishing on the orbit under the modular group of a point in the upper half plane. In past work of the speaker, it was put in evidence that this is related to equivariant Berezin quantization.
This leads to a different representation of free group factors and to the existence of a quantum dynamics whose associated unbounded Hochschild 2- cocycle is related to the isomorphism problem. I will explain some concrete formulae and some new interpretation of the associated quantum dynamics
Organizing Committee:
Vincenzo Morinelli (mail to contact)
Roberto Longo (mail to contact)
Daniele Guido (mail to contact)
Giuseppe Ruzzi (mail to contact)
Further Info: Click here for Operator Algebras Seminar Page
Streaming Link (MS Teams): This seminar will be held in person
Università degli Studi Roma Tor Vergata
Dipartimento di Matematica
Topology Seminar
Date: 5th April 2024
Schedule: 14:30 Rome Time
Where: Conference Room 1102 "R. Dal Passo"
Speaker: Nicolas Guès - Université Paris 13
Title: "Capturing Brain dynamics using Topological Data Analysis "
Abstract:
Characterizing intrinsic and extrinsic transitions in cortical activity can provide an understanding of cognition, e.g.,
For many known families of algebro-geometric objets indexed by natural numbers (the symmetric groups, the braid groups,...) a phenomenon known as homological stability happens :
their homology Hd(Xn) becomes stationary when n goes to ∞. Sometimes, these objects are equipped with actions of the symmetric group Σn on Xn : in this context, the right notion of stability is that of representation stability introduced by Church and Farb in 2010. One main example is the family of ordered configuration spaces of manifolds, whose cohomology is known to be representation stable with explicit ranges. I will review in this talk the main ideas of representation stability and explain how we can take a homotopy-theoretic point of view on representation stability to generalize such stability theorems.
This talk is part of the activity of the MIUR Excellence Department Projects MatMod@TOV.
Organizing Committee:
Paolo Salvatore (Contact Mail)
Andrea Pizzi PhD ( Contact Mail)
Further Information: Click here for Topology webpage
Streaming Link (MS Teams): This seminar will be held in person
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Università degli Studi Roma Tor Vergata
Dipartimento di Matematica
DIFFERENTIAL EQUATIONS SEMINAR
Date: 02th April 2024
Schedule: 16:00 - Rome Time
Where: Conference Room "R. Dal Passo"
Title: " Asymptotically quasiperiodic solutions for time-dependent Hamiltonians with a view to celestial mechanics "
Speaker: Donato Scarcella - U.P.C. Barcelona
Abstract:
Dynamical systems subject to perturbations that decay over time are relevant in the description of many physical models, e.g. when considering the effect of a laser pulse on a molecule, in epidemiological studies, as well as in celestial mechanics.
For this reason, in the present talk, we consider a time-dependent perturbation of a Hamiltonian dynamical system having an invariant torus supporting quasiperiodic solutions. Assuming the perturbation decays polynomially fast as time tends to infinity, we prove the existence of orbits converging in time to the quasiperiodic solutions associated with the unperturbed system. This result generalizes the work of Canadell and de la Llave, where exponential decay in time was considered, and the one of Fortunati and Wiggins, where arithmetic, non-degeneracy conditions, and exponential decay in time are assumed.
We apply this result to the example of the planar three-body problem perturbed by a given comet coming from and going back to infinity asymptotically along a hyperbolic Keplerian orbit (modeled as a time-dependent perturbation).
Nota: Questo seminario fa parte delle attività finanziate dal progetto MIUR Dipartimento d'eccellenza MatMod@TOV (2023-27)
Note: This talk is part of the activity of the MIUR Excellence Department Project MatMod@TOV (2023-27)
Organizing Committee:
Riccardo Molle (mail to contact)
Alfonso Sorrentino (mail to contact)
Further Info and Program: Click here
Streaming Link (MS Teams): This seminar will be held in person
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