Notiziario Scientifico
a cura del Dipartimento di Matematica Guido Castelnuovo, Sapienza Università di Roma
Settimana dal 03-10-2022 al 09-10-2022
Lunedì 03 ottobre 2022
Ore 14:00, Aula M1, Dipartimento di Matematica e Fisica, Roma Tre
Mini-course in mathematical physics - Constructive Renormalization Group Approach To Lattice Gauge Theories
Prof. Jonathan Dimock (Univ. Buffalo NY USA)
The ultraviolet problem for QED in d=3
We review some recent work on quantum electrodynamics on a three dimensional Euclidean spacetime, work which culminates in a proof of ultraviolet stability in a finite volume. The model is formulated on a fine lattice and bounds are obtained uniformly in the lattice spacing. The method is a renormalization group technique due to Balaban. Topics to be covered are (1.) Introduction, (2.) Block averaging for gauge fields, (3.) Block averaging for Fermi fields, (4.) Random walk expansions, (5.) Norms and polymer functions, (6.) Renormalization group with bounded gauge fields, (7.) Renormalization, (8.) The full expansion. Program: mon-wed-fri from oct 3 to oct 14, 2022, 14:00 - 15:30; aula M1, Lungotevere Dante 376 (access also from L.go S. L. Murialdo 1), Dip.to Matematica e Fisica, Univ. Roma Tre
Per informazioni, rivolgersi a: Organizer: Alessandro Giuliani (Univ. Roma Tre) - alessandro.giuliani@uniroma3.it
Martedì 04 ottobre 2022
Ore 10:00, Aula 1B1, Dipartimento SBAI, Sapienza Università di Roma
PhD Course
Masahiro Yamamoto (The University of Tokyo - INdAM Visiting Professor)
Inverse problems and time-fractional partial differential equations 6
We consider an initial boundary value problem for time-fractional diffusion-wave equation (in the following we refer to it as system (*)). The lectures aim at self-contained concise explanations for the fundamental theory for such problems and mathematical analysis of inverse problems. The idea of fractional derivatives dates back to Leibniz and there have been many works including by Abel, Riemann, Liouville. Now the system (*) is widely recognized as more feasible model for various phenomena such as anomalous diffusion in heterogeneous media, where the anomaly cannot be well interpreted by the classical advection. diffusion equation and the conventional models often provide wrong simulation results. Thus we have to exploit more relevant models because the issues are serious, for example, for the protection of the environments , and the mathematical researches should support such practical applications. For researches on inverse problems, we need also mathematical analyses for (*). Usually in practice, we are not a priori given coefficients and other quantities in (*). The inverse problems are concerned with parameter identification, and are essential for more accurate prediction or simulations of anomalous diffusion. Therefore mathematical researches should be done for both foundations of direct problems and applications to inverse problems for (*).
Per informazioni, rivolgersi a: francesco.petitta@uniroma1.it
Martedì 04 ottobre 2022
Ore 14:30, Aula Dal Passo, Dipartimento di Matematica, Università di Roma Tor Vergata
Seminario di Geometria
Davide Veniani (University of Stuttgartt)
Symplectic rigidity of O'Grady's manifolds
Mukai classified all symplectic groups of automorphisms of K3 surfaces as possible subgroups of one of the Mathieu groups. Since then, the proof of Mukai's theorem has been simplified using lattice theoretical techniques, and extended to higher dimensional hyperkähler manifolds. In two joint works with L. Giovenzana (Loughborough), A. Grossi (Chemnitz) et C. Onorati (Roma Tor Vergata), we studied possible cohomological actions of symplectic automorphisms of finite order on the two sporadic deformation types found by O'Grady in dimension 6 and 10. In particular, we showed that, in dimension 10, all symplectic automorphisms are trivial. In my talk, I will explain the connection between our proof and the sphere packing problem, which was recently solved by Fields medalist Viazovska in dimension 8 and 24.
Per informazioni, rivolgersi a: onorati@mat.uniroma2.it
Martedì 04 ottobre 2022
Ore 16:00, Aula Dal Passo, Dipartimento di Matematica, Università di Roma "Tor Vergata"
Seminario di Equazioni Differenziali
Lei Zhang (University of Florida (US))
Non-simple Blowup solutions of singular Liouville equations
The singular Liouville equation is a class of second order elliptic partial differential equations defined in two dimensional spaces: \( \Delta u+ H(x)e^{u}=4\pi \gamma \delta_0 \) where H is a positive function, \( \gamma>-1\) is a constant and \( \delta_0 \) stands for a singular source placed at the origin. This deceptively simply looking equation has a rich background in geometry, topology and Physics. In particular it interprets the Nirenberg problem in conformal geometry and is the reduction of Toda systems in Lie Algebra, Algebraic Geometry and Gauge Theory. Even if we only focus on the analytical aspects of this equation, it has wonderful and surprising features that attract generations of top mathematicians. The structure of solutions is particular intriguing when $\gamma$ is a positive integer. In this talk I will report recent joint works with D’Aprile and Wei that give answers to some important issues of this equation. I will report the most recent results and consequences that our results may lead to. Notes: 1) The seminar will be held in presence, although the speaker will be connected remotely via MS Teams. The MS Teams link might be provided upon request to the organizers. 2) This talk is part of the activity of the MIUR Department of Excellence Project MATH@TOV CUP E83C18000100006.
Per informazioni, rivolgersi a: sorrentino@mat.uniroma2.it
Mercoledì 05 ottobre 2022
Ore 10:00, Aula 1B1, Dipartimento SBAI, Sapienza Università di Roma
PhD Course
Masahiro Yamamoto (The University of Tokyo - INdAM Visiting Professor)
Inverse problems and time-fractional partial differential equations 7
We consider an initial boundary value problem for time-fractional diffusion-wave equation (in the following we refer to it as system (*)). The lectures aim at self-contained concise explanations for the fundamental theory for such problems and mathematical analysis of inverse problems. The idea of fractional derivatives dates back to Leibniz and there have been many works including by Abel, Riemann, Liouville. Now the system (*) is widely recognized as more feasible model for various phenomena such as anomalous diffusion in heterogeneous media, where the anomaly cannot be well interpreted by the classical advection. diffusion equation and the conventional models often provide wrong simulation results. Thus we have to exploit more relevant models because the issues are serious, for example, for the protection of the environments , and the mathematical researches should support such practical applications. For researches on inverse problems, we need also mathematical analyses for (*). Usually in practice, we are not a priori given coefficients and other quantities in (*). The inverse problems are concerned with parameter identification, and are essential for more accurate prediction or simulations of anomalous diffusion. Therefore mathematical researches should be done for both foundations of direct problems and applications to inverse problems for (*).
Per informazioni, rivolgersi a: francesco.petitta@uniroma1.it
Mercoledì 05 ottobre 2022
Ore 14:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
seminario di Algebra e Geometria
Carlo Mantegazza (Università di Napoli)
Una dimostrazione della disuguaglianza di Penrose riemanniana per mezzo della teoria del potenziale nonlineare
Discuterò la disuguaglianza di Penrose riemanniana in una 3-varietà asintoticamente piatta, con curvatura scalare non negativa, e i punti principali di una nuova dimostrazione per mezzo di una formula di monotonia che vale lungo gli insiemi di livello del potenziale p-capacitario dell'orizzonte di un buco nero. Lavoro in collaborazione con Virginia Agostiniani, Lorenzo Mazzieri e Francesca Oronzio.
Per informazioni, rivolgersi a: diverio@mat.uniroma1.it
Mercoledì 05 ottobre 2022
Ore 16:00, Aula Dal Passo, Dipartimento di Matematica, Università di Roma "Tor Vergata"
Seminario
Detlev Buchholz (University of Goettingen)
Proper condensates and long range order
The usual characterization of Bose-Einstein condensates is based on spectral properties of one-particle density matrices. (Onsager-Penrose criterion). The analysis of their specific properties, such as the occurrence of long-range order between particles and peaks in momentum space densities requires, however, the transition to the thermodynamic limit, where the one-particle density matrices are no longer defined. In the present talk, we will explain a new criterion of "proper condensation" that allows us to establish the properties of bosonic systems occupying fixed bounded regions. Instead of going to the idealization of an infinite volume, one goes to the limit of arbitrarily large densities in the given region. The resulting concepts of regular and singular wave functions can then be used to study the properties of realistic finite bosonic systems, the occurrence of condensates, and their large-distance behavior, with a precise control of accuracy.
Giovedì 06 ottobre 2022
Ore 14:15, Aula M1, Dipartimento di Matematica e Fisica, Università Roma Tre
Seminario di Geometria
Gavril Farkas (Humboldt)
Resonance, Koszul modules and Chen invariants in algebraic geometry
Inspired from ideas in topology, Koszul modules turned out to have important algebro-geometric applications for instance to (i) Green's Conjecture on syzygies of canonical curves, (ii) stabilization of cohomology of projective varieties in arbitrary characteristics and (iii) a resolution of an effective form of an important conjecture of Suciu's on Chen invariants of hyperplane arrangements. I will discuss new developments related to this circle of ideas obtained in joint work with Aprodu, Raicu and Suciu.
Per informazioni, rivolgersi a: amos.turchet@uniroma3.it
Giovedì 06 ottobre 2022
Ore 14:30, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario P(n)/N(p)
Luca Battaglia (Università degli Studi Roma Tre)
New conformal metrics on the half-plane with prescribed Gaussian and geodesic curvature
We consider the problem of prescribing both the Gaussian curvature in the half plane and the geodesic curvature on its boundary. We show the existence of solutions with non-constant curvatures bifurcating from the (explicitly known) solutions to the problem with constant curvatures. The main arguments used in proofs are finite-dimensional reduction and degree theory.
Per informazioni, rivolgersi a: galise@mat.uniroma1.it
Venerdì 07 ottobre 2022
Ore 10:00, Aula 1B1, Dipartimento SBAI, Sapienza Università di Roma
PhD Course
Masahiro Yamamoto (The University of Tokyo - INdAM Visiting Professor)
Inverse problems and time-fractional partial differential equations 8
We consider an initial boundary value problem for time-fractional diffusion-wave equation (in the following we refer to it as system (*)). The lectures aim at self-contained concise explanations for the fundamental theory for such problems and mathematical analysis of inverse problems. The idea of fractional derivatives dates back to Leibniz and there have been many works including by Abel, Riemann, Liouville. Now the system (*) is widely recognized as more feasible model for various phenomena such as anomalous diffusion in heterogeneous media, where the anomaly cannot be well interpreted by the classical advection. diffusion equation and the conventional models often provide wrong simulation results. Thus we have to exploit more relevant models because the issues are serious, for example, for the protection of the environments , and the mathematical researches should support such practical applications. For researches on inverse problems, we need also mathematical analyses for (*). Usually in practice, we are not a priori given coefficients and other quantities in (*). The inverse problems are concerned with parameter identification, and are essential for more accurate prediction or simulations of anomalous diffusion. Therefore mathematical researches should be done for both foundations of direct problems and applications to inverse problems for (*).
Per informazioni, rivolgersi a: francesco.petitta@uniroma1.it
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