Notiziario Scientifico
a cura del Dipartimento di Matematica Guido Castelnuovo, Sapienza Università di Roma
Settimana dal 24-03-2025 al 30-03-2025
Lunedì 24 marzo 2025
Ore 14:30, Aula B, Dipartimento di Matematica e Fisica, Università degli Studi Roma Tre
Seminario di Analisi Matematica
Thomas Bartsch (Justus Liebig University Giessen)
Critical point theory at infinity: an abstract approach and an application
In this talk I present an abstract framework under which Morse theoretical methods can be applied to some non-compact variational problems by computing the difference of topology induced by "critical points at infinity" in the sense of Bahri. As application we sketch how to apply the abstract theorem to the Nirenberg problem of prescribing the scalar curvature on spheres.
Per informazioni, rivolgersi a: luca.battaglia@uniroma3.it
Lunedì 24 marzo 2025
Ore 14:30, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
seminario di Analisi Matematica
Fabio Cavalletti (Università di Milano)
Timelike Ricci bounds in the non-smooth setting: an optimal transport approach.
Optimal transport tools have been extremely powerful to study Ricci curvature, in particular Ricci lower bounds in the non-smooth setting of metric measure spaces (which can be been as a non-smooth extension of Riemannian manifolds). Since the geometric framework of general relativity is the one of Lorentzian manifolds (or space-times), and the Ricci curvature plays a prominent role in Einstein’s theory of gravity, a natural question is whether optimal transport tools can be useful also in this setting. The goal of the talk is to introduce the topic and to report on recent progress. More precisely: After recalling some basics of optimal transport, we will define "timelike Ricci curvature and dimension bounds" for a possibly non-smooth Lorentzian space in terms of displacement convexity of suitable entropy functions and discuss applications, including the extension of classical singularity theorems to settings of low regularity, and prove a new isoperimetric-type inequality. Based on joint works with A. Mondino. 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 25 marzo 2025
Ore 14:30, aula d'Antoni, Dipartimento di Matematica, Università di Roma Tor Vergata
Seminario di Geometria
Enrico Fatighenti (Università di Bologna)
Modular vector bundle on Hyperkahler manifolds
We exhibit examples of slope-stable and modular vector bundles on a hyperkähler manifold of K3^[2]-type. These are obtained by performing standard linear algebra constructions on the examples studied by O’Grady of (rigid) modular bundles on the Fano varieties of lines of a general cubic 4-fold and the Debarre-Voisin hyperkähler. Interestingly enough, these constructions are almost never infinitesimally rigid, and more precisely we show how to get (infinitely many) 20 and 40 dimensional families. This is a joint work with Claudio Onorati. Time permitting, I will also present a work in progress with Alessandro D'Andrea and Claudio Onorati on a connection between discriminants of vector bundles on smooth and projective varieties and representation theory of GL(n).
Per informazioni, rivolgersi a: guidomaria.lido@gmail.com
Mercoledì 26 marzo 2025
Ore 13:00, Aula Picone, Dipartimento di Matematica, Sapienza Università di Roma
Seminario del ciclo MATHtalks
Valerio Corica (Sapienza Università di Roma)
Insiemi di perimetro finito
L'obiettivo di questo seminario sarà introdurre gli studenti alle tecniche moderne del calcolo delle variazioni, cercando anche di spiegare, per quanto possibile, cosa si intenda per teoria geometrica della misura. Introdurremo quindi il metodo diretto del calcolo delle variazioni, una strategia generale per dimostrare l'esistenza di minimi in problemi variazionali. Seguendo un percorso ormai classico, sviluppato da De Giorgi, affronteremo il problema di Plateau nella classe degli insiemi di perimetro finito. Definiremo il perimetro secondo Caccioppoli, utilizzandolo come esempio di rilassamento, e successivamente vedremo l'equivalenza con la definizione più diffusa alla De Giorgi, verificando che il funzionale perimetro soddisfi tutte le ipotesi necessarie per l'applicazione del metodo diretto. Tempo permettendo, discuteremo il Teorema di struttura di De Giorgi e la connessione con la misura di Hausdorff.
Per informazioni, rivolgersi a: MATHtalks@uniroma1.it
Mercoledì 26 marzo 2025
Ore 12:00, aula dal Passo, Dipartimento di Matematica, Università di Roma Tor Vergata
Seminario di teoria dei numeri
Sachi Hashimoto (Brown University)
Rational points and p-Adic L-functions
There are finitely many rational points on a nice projective curve defined over the rationals of genus at least 2, but it is a difficult problem to explicitly determine these points. The quadratic Chabauty method is a p-adic method for determining these rational points under some constraints. In this talk, I will explain how we can leverage information from special values of p-adic L-functions to improve the quadratic Chabauty method for modular curves, leading to a new algorithm to determine rational points on certain modular curves.
Per informazioni, rivolgersi a: guidomaria.lido@gmail.com
Mercoledì 26 marzo 2025
Ore 16:00, Aula Dal Passo, Dipartimento di Matematica, Università di Roma Tor Vergata
Colloquium Levi-Civita
Raphael Bousso (Berkeley Center for Theoretical Physics, UC Berkeley)
Gravity as a Quantum Computer
Our search for a quantum theory of gravity is aided by a unique and perplexing feature of the classical theory: General Relativity already "knows" about its own quantum states (the entropy of a black hole), and about those of all matter (via the covariant entropy bound). The results we are able to extract from classical gravity are inherently non-perturbative and increasingly sophisticated. Recent breakthroughs include a derivation of the entropy of Hawking radiation, a computation of the exact integer number of states of some black holes, and the construction of gravitational holograms in our universe using techniques from single-shot quantum communication protocols. Note: Sponsored by Miur Prin project contract 2020KR4KN2 “String Theory as abridge between Gauge Theories and Quantum Gravity”
Giovedì 27 marzo 2025
Ore 11:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Modellistica Differenziale Numerica
Fabio Durastante (Dipartimento di Matematica, Università di Pisa)
Enforcing Katz and PageRank Centrality Measures in Complex Networks
Centrality measures are fundamental in the study of complex networks, offering insights into the relative importance of nodes based on different connectivity patterns. In this talk, we address the problem of enforcing a prescribed Katz [1] or PageRank [2] centrality while maintaining the network’s original structure as much as possible [3]. Specifically, we seek the minimal perturbation of edge weights necessary to achieve the desired centrality values, ensuring that modifications are both efficient and targeted. We formulate this problem as a constrained Quadratic Programming (QP) optimization task and propose scalable numerical methods [4] to solve it. Our approach leverages the structure of the optimization problem to enhance computational efficiency, making it feasible for large-scale networks. By carefully selecting which edges to modify, we ensure that the fundamental topology of the network remains largely intact while achieving the prescribed centrality objectives. Applications of our methodology span various domains. Through extensive computational experiments, we demonstrate the effectiveness of our approach in both synthetic and real-world networks. We also provide an open-source implementation Github of our algorithms, allowing for reproducibility and further research in the field. Bibliography [1] Katz, L. (1953). A new status index derived from sociometric analysis. Psychometrika, 18(1), 39–43. [2] Page , L., & Brin, S. (1998). The anatomy of a large-scale hypertextual Web search engine. Computer Networks, 30(1–7), 107–117. [3] Cipolla, S., Durastante, F., & Meini, B. (2024). Enforcing Katz and PageRank Centrality Measures in Complex Networks, arXiv 2409.02524. [4] Cipolla, S., & Gondzio, J. (2023). Proximal stabilized interior point methods and low-frequency-update preconditioning techniques. J. Optim. Theory Appl., 197(3), 1061–1103
Giovedì 27 marzo 2025
Ore 14:15, Aula B, Dipartimento di Matematica e Fisica, Università Roma Tre
Seminario di Geometria
Elisa Postinghel (Trento)
Duality of cones for Mori dream spaces
We consider the cones of divisors that are ample in codimension k on a variety of dimension n, for all possible values of k. Taking closures, for k=0 and k=n-1 we obtain the pseudoeffective and the nef cone respectively. For intermediate values of k, little is known about these cones. In this talk I will show that for Mori dream spaces (MDSs) all such cones are rational polyhedral. I will then discuss duality between such cones and cones of k-moving curves. For MDSs, a Weak Duality property holds, already proved by Payne and Choi. I will show that a Strong Duality property is satisfied by an interesting family of varieties. This is a joint work with O. Dumitrescu, C. Brambilla and L. Santana-Sánchez.
Per informazioni, rivolgersi a: amos.turchet@uniroma3.it
Giovedì 27 marzo 2025
Ore 14:30, Aula 1B1, Via Scarpa 12, Dipartimento SBAI, Sapienza Università di Roma
Seminario "PDE a Tutto SBAI"
Hans Knüpfer (University of Heidelberg, Germania)
2D Stokes Problem With a Moving Contact Line
We consider the evolution of a two–dimensional liquid droplet on a solid substrate in the,presence of a contact point. At the liquid-solid interface we assume Navier slip. At the triple point we assume a constant contact angle, given by Young’s law. The main result is well–posedness and regularity of the solution of the corresponding linearized problem in a class of weighted Sobolev spaces. This is a joint work with M. Bravin (U. Santander), M. Gnann (TU Delft), N. Masmoudi (NYU AD), F. Rodenburg (TU Delft), J. Sauer (U. Jena)
Venerdì 28 marzo 2025
Ore 12:00, Aula INdAM, INdAM
Number Theory Seminar
Lucile Devin (Université du Littoral Côte d'Opale)
Vertical distribution of zeros of \(L\)-functions, extended support
I will discuss the distribution of low-lying zeros of \(L\)-functions in families of degree two, for which, thanks to good trace formulas, we are able to extend the unconditional support in the Katz-Sarnak prediction. Joint with Martin Čech, Daniel Fiorilli, Kaisa Matomäki and Anders Södergren.
Per informazioni, rivolgersi a: cherubini@altamatematica.it
Venerdì 28 marzo 2025
Ore 14:30, Aula Dal Passo, Dipartimento di Matematica, U Roma Tor Vergata
Algebra and Representation Theory Seminar (ARTS)
Filippo Ambrosio (FSU Jena)
Étale geometry of Jordan classes closures
Let G be a connected reductive algebraic group over an algebraically closed field k. Lusztig (1984) partitioned G into subvarieties which play a fundamental role in the study of representation theory, the Jordan classes. An analogue partition of the Lie algebra Lie(G) into subvarieties called decomposition classes dates back to Borho-Kraft (1979). When k = C the study of geometric properties (e.g., smoothness) of a point g in the closure of a Jordan class J ⊂ G can be reduced to the study of the geometry of an element x in the closure of the union of finitely many decomposition classes in Lie(M), where M ≤ G is a connected reductive subgroup depending on g. The talk aims at introducing such objects and at generalizing this reduction procedure to the case char k > 0.
Venerdì 28 marzo 2025
Ore 16:00, Aula Enriques, Dipartimento di Matematica, Sapienza Università di Roma
Seminari PLS per insegnanti
Andrea Bruno (Università Roma Tre)
Ancora sui numeri di Fibonacci...
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