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Notiziario Scientifico
a cura del Dipartimento di Matematica Guido Castelnuovo, Sapienza Università di Roma
Settimana dal 17-02-2025 al 23-02-2025
Lunedì 17 febbraio 2025
Ore 11:30, Aula A, Dipartimento di Matematica e Fisica, Università di Roma Tre, Via della Vasca Navale 84
seminario di Fisica Matematica
Leonardo Goller (SISSA Trieste)
\(\pi\)-Flux Phase Stability in Z2 Lattice Gauge Theory
The Flux Problem is a famous problem in condensed matter physics, solved by Lieb. It states that the magnetic flux through each plaquette of a square lattice in 2d (with either OBC/PBC or PBC/PBC) that minimizes the ground state energy of a system of free electrons at half-filling is . Such phase, called \(\pi\)-Flux Phase, is known to display emergent Dirac-like low energy excitations. What happens when we couple the system to a dynamical 2 gauge field whose energy is minimized by 0 flux per plaquette? In this talk, we prove the stability of \(\pi\)-Flux Phase by showing, using Reflection Positivity techniques, that the energy of the fermions at half-filling in a background of N monopoles increases extensively in N. As an application, we compute explicitly the zero temperature diamagnetic susceptibility and the conductivity of the gauge theory, and we show that they coincide with the ones of massless Dirac fermions. Arxiv: https://arxiv.org/abs/2501.10065 (Join Work with Marcello Porta)
Lunedì 17 febbraio 2025
Aula Picone, Dipartimento di Matematica, Sapienza Università di Roma
Scuola del periodo tematico: Statistical Mechanics and Non Equilibrium Processes
Statistical Mechanics, Nonequilibrium Processes and Probability
All information available at https://sites.google.com/view/winterschoolsapienza/home. The school is part of the activities of the Dipartimento di Eccellenza 2023-27, Project B83C23001390001 and it is co-funded by the European Union - Next Generation EU through ERC CoG KiLiM 101125162, PRIN 2022 77WX43, and by INdAM.
Per informazioni, rivolgersi a: sergio.simonella@uniroma1.it
Lunedì 17 febbraio 2025
Ore 14:30, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
seminario di Analisi Matematica
Marco Cirant (Università di Padova)
Some results on Nash systems with several equations
Nash systems are strongly coupled systems of semilinar parabolic equations that describe closed-loop Nash equilibria in stochastic differential games. Despite existence, uniqueness and regularity for this class of systems is now classical, new questions regarding the regularity of solutions as the number of players increases have been posed within the study of large population games. It is indeed desirable to justify limiting models for these games as the number of players goes to infinity; from a PDE perspective, this amounts to obtain Lipschitz estimates (and further rather precise information on higher order derivatives) as the number of equations goes to infinity. The talk will be devoted to the presentation of some results in this direction, obtained in collaboration with D. F. Redaelli (University of Rome Tor Vergata). This seminar is part of the activities of the Excellence Department Project CUP B83C23001390001 and it is funded by the European Union – Next Generation EU.
Per informazioni, rivolgersi a: azahara.delatorrepedraza@uniroma1.it
Martedì 18 febbraio 2025
Aula Picone, Dipartimento di Matematica, Sapienza Università di Roma
Scuola del periodo tematico: Statistical Mechanics and Non Equilibrium Processes
Statistical Mechanics, Nonequilibrium Processes and Probability
All information available at https://sites.google.com/view/winterschoolsapienza/home. The school is part of the activities of the Dipartimento di Eccellenza 2023-27, Project B83C23001390001 and it is co-funded by the European Union - Next Generation EU through ERC CoG KiLiM 101125162, PRIN 2022 77WX43, and by INdAM.
Per informazioni, rivolgersi a: sergio.simonella@uniroma1.it
Martedì 18 febbraio 2025
Ore 14:30, Aula "Dal Passo", Dipartimento di Matematica, Università di Roma "Tor Vergata"
Seminario di Analisi Matematica
Pierpaolo Esposito (Università Roma3)
Exponential PDEs in high dimensions
For a quasilinear equation involving the n−Laplacian and an exponential nonlinearity, I will discuss quantization issues for blow-up masses in the non-compact situation, where the exponential nonlinearity concentrates as a sum of Dirac measures. A fundamental tool is provided here by some Harnack inequality of sup + inf type, a question of independent interest that we prove in the quasilinear context through a new and simple blow-up approach. If time permits, we will also discuss some recent progress concerning sharp sup+inf inequalities. Joint work with Marcello Lucia.
NB: This talk is part of the activity of the MUR Excellence Department Project MATH@TOV CUP E83C23000330006
Per informazioni, rivolgersi a: molle@mat.uniroma2.it
Martedì 18 febbraio 2025
Ore 14:30, aula d'Antoni, Dipartimento di Matematica, Università di Roma Tor Vergata
seminario di Geometria
Dario Weissmann (IMPAN, Warsaw)
Distinguishing algebraic spaces from schemes
We introduce local invariants of algebraic spaces and stacks which measure how far they are from being a scheme. Using these invariants, we develop mostly topological criteria to determine when the moduli space of a stack is a scheme. In the setting of a stack admitting a separated (good) moduli space this also yields a criterion for when the moduli space is a scheme. As an application we identify all separated good moduli spaces of vector bundles over a smooth projective curve which are schemes. This is joint work with Andres Fernandez Herrero and Xucheng Zhang.
Per informazioni, rivolgersi a: guidomaria.lido@gmail.com
Mercoledì 19 febbraio 2025
Aula Picone, Dipartimento di Matematica, Sapienza Università di Roma
Scuola del periodo tematico: Statistical Mechanics and Non Equilibrium Processes
Statistical Mechanics, Nonequilibrium Processes and Probability
All information available at https://sites.google.com/view/winterschoolsapienza/home. The school is part of the activities of the Dipartimento di Eccellenza 2023-27, Project B83C23001390001 and it is co-funded by the European Union - Next Generation EU through ERC CoG KiLiM 101125162, PRIN 2022 77WX43, and by INdAM.
Per informazioni, rivolgersi a: sergio.simonella@uniroma1.it
Mercoledì 19 febbraio 2025
Ore 14:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Algebra e Geometria
Valerio Proietti (University of Oslo)
Chern character and groupoid-equivariant bivariant K-theory
Building on previous work by Davis and Lück, and recent constructions of bivariant K-theory as a stable \(\infty\)-category, I will sketch the construction of a Chern character running from groupoid-equivariant K-homology to (periodicized) homology groups of the given groupoid. Under the assumption that the isotropy groupoid is torsion free, this map is a rational isomorphism, thereby establishing a modified form of Matui’s HK conjecture (after integral counterexamples have been found). This construction also computes the rational homotopy type of the algebraic K-theory spectrum of ample groupoids as defined in a recent work by X. Li. This is joint work-in-progress with M. Yamashita.
Giovedì 20 febbraio 2025
Aula Picone, Dipartimento di Matematica, Sapienza Università di Roma
Scuola del periodo tematico: Statistical Mechanics and Non Equilibrium Processes
Statistical Mechanics, Nonequilibrium Processes and Probability
All information available at https://sites.google.com/view/winterschoolsapienza/home. The school is part of the activities of the Dipartimento di Eccellenza 2023-27, Project B83C23001390001 and it is co-funded by the European Union - Next Generation EU through ERC CoG KiLiM 101125162, PRIN 2022 77WX43, and by INdAM.
Per informazioni, rivolgersi a: sergio.simonella@uniroma1.it
Giovedì 20 febbraio 2025
Aula Bandinelli (Palazzina RM015), Dipartimento SBAI, Sapienza Università di Roma
Workshop
Recent progress in PDEs
Program:
- 09:30 M. Medina (UAM) Blowing-up solutions to critical competitive systems in dimensions 3 and 4
- 10:10 A. Roncoroni (PoliMi) Rigidity results for critical elliptic equations
- 11:20 S. Almi (Federico II, Naples) Pontryagin Maximum Principle for Mean-Field Optimal Control
- 12:00 W. Gorny (Wien) Evolution equations on two overlapping random walk structures
- 14:30 G. Meglioli (Bielefeld) Uniqueness for parabolic equations on infinite graphs
- 15:10 A. Martinez-Aparicio (UAL) Existence and regularity results for 1-Laplace type problems with singular nonlinearities
- 16:20 L. Temperini (UNIVPM) Global Compactness and subcritical approximation in the critical Folland-Stein embedding
- 17:00 E. Vecchi (UniBO) Mixed local-nonlocal critical problems
Giovedì 20 febbraio 2025
Ore 12:00, Stanza 116, CNR-IAC, via dei Taurini 19
Seminario di Modellistica Differenziale Numerica
Andrea Bondesan (Università di Parma)
Diffusion asymptotics of the Boltzmann multi-species equation through perturbation of hypocoercivity
I will discuss the rigorous derivation of hydrodynamic limits of the Boltzmann multi-species equation, for Mach and Knudsen numbers vanishing at the same rate. Solutions to the kinetic system are constructed as fluctuations around local non-equilibrium Maxwellian distributions, whose physical observables solve the limit macroscopic model of interest. A general hypocoercive formalism is developed to establish a uniform (with respect to the small diffusion parameter) Cauchy theory for this perturbative setting. I will apply the method to derive the Maxwell-Stefan cross-diffusion system and present numerical results confirming this convergence. To access the IAC building you need to show an ID-card
Giovedì 20 febbraio 2025
Ore 14:30, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
P(n)/N(p) : Problemi differenziali nonlineari/Nonlinear differential problems
Claudia Bucur (Università di Milano)
S-minimal functions: existence and continuity
We discuss a nonlocal fractional problem that serves as a nonlocal counterpart of the classical problem of functions of least gradient. We show how we obtain the existence of minimizers by using their connection to nonlocal minimal sets. Additionally, we discuss the continuity of these minimizers and a weak formulation of the problem. The results presented are obtained in collaboration with S. Dipierro, L. Lombardini, J. Maz ́on and E. Valdinoci.
Per informazioni, rivolgersi a: galise@mat.uniroma1.it
Venerdì 21 febbraio 2025
Ore 10:00, Aula F, Dipartimento di Matematica, Sapienza Università di Roma
Discussione della tesi di dottorato
Agnese Pacifico (Sapienza Università di Roma)
Identification and control of unknown differential equations
Venerdì 21 febbraio 2025
Aula Picone, Dipartimento di Matematica, Sapienza Università di Roma
Scuola del periodo tematico: Statistical Mechanics and Non Equilibrium Processes
Statistical Mechanics, Nonequilibrium Processes and Probability
All information available at https://sites.google.com/view/winterschoolsapienza/home. The school is part of the activities of the Dipartimento di Eccellenza 2023-27, Project B83C23001390001 and it is co-funded by the European Union - Next Generation EU through ERC CoG KiLiM 101125162, PRIN 2022 77WX43, and by INdAM.
Per informazioni, rivolgersi a: sergio.simonella@uniroma1.it
Venerdì 21 febbraio 2025
Aula Bandinelli (Palazzina RM015), Dipartimento SBAI, Sapienza Università di Roma
Workshop
Recent progress in PDEs
Program:
- 09:15 G. Stefani (UniPD) A geometrical approach to the sharp fractional Hardy inequality on convex sets
- 09:55 F. Anceschi (UNIVPM) De Giorgi-Nash-Moser theory for kinetic integral equations
- 11:05 F. Esposito (UniCal) Symmetry results for Hardy-Sobolev nonlinear critical systems
- 11:45 M. Solera (UV) Instabilities and loss of determinism in active scalar equations
- 12:25 R. Bianchini (IAC-CNR) Ill-posedness and Instabilities in Nonhomogeneous Density Fluids
Venerdì 21 febbraio 2025
Aula 25, Facoltà di Ingegneria in San Pietro in Vincoli, Sapienza Università di Roma
Workshop
Two Days in Operator Algebras (A workshop on the occasion of Roberto Conti's 60th birthday)
Program:
- 9:30 E. Bedos Actions of Fell bundles
- 10:15 S. Carpi Holomorphic vertex operator algebras and Teichmüller modular forms
- 11:30 F. Radulescu von Neumann dimension and V.F.R Jones view on automorphic forms
- 12:15 R. Longo tba
- 14:30 L. Turowska Absolutely dilatable module maps
- 15:15 A. Brothier Moduli of representations of the Cuntz algebra
- 16:30 P. Contucci Statistical Mechanics and Artificial Intelligence
- 17:15 C. Falcolini Algoritmi e modelli parametrici da nuvole di punti: il progetto di ricostruzione degli affreschi tardo medievali dell’Abbazia di San Vincenzo al Volturno
Venerdì 21 febbraio 2025
Ore 16:00, Aula Enriques, Dipartimento di Matematica, Sapienza Università di Roma
Conferenze PLS per docenti
Stefania Gubbiotti (Sapienza Università di Roma)
La percezione delle differenze di genere: rilevazioni statistiche a cura degli studenti del liceo matematico
Venerdì 21 febbraio 2025
Ore 16:30, Aula D'Antoni, Dipartimento di Matematica, Università degli Studi di Roma Tor Vergata
DocTorV Seminar
Alessio Ranallo (Université de Genève)
Random graphs and their Spectra
This talk explores how random graphs, serving as simple models of quantum disordered systems, exhibit a delocalization-localization transition of the eigenstates of their adjacency matrices. I will present a few basic models and review well-established results concerning the above mentioned transition.
Per informazioni, rivolgersi a: doctorv.uniroma2@gmail.com
Sabato 22 febbraio 2025
Aula 25, Facoltà di Ingegneria in San Pietro in Vincoli, Sapienza Università di Roma
Workshop
Two Days in Operator Algebras (A workshop on the occasion of Roberto Conti's 60th birthday)
Program:
- 9:30 S. Rossi Non-commutative skew-products
- 10:15 V. Aiello The Motzkin subproduct system
- 11:30 F. Fidaleo Spectral Actions for Free Particles and their Asymptotics
- 12:15 R. Hillier Dynamical decoupling of open quantum systems
- 14:30 F. Brenti Combinatorics of Cuntz algebra automorphisms and their subgroups
- 15:15 C. Farsi tba
- 16:30 J. Bassi On isometries for spectral triples on AF-algebras
- 17:15 E. Vasselli Hilbert bimodules and models in Quantum Field Theory
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seminari@mat.uniroma1.it.
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