Notiziario Scientifico
a cura del Dipartimento di Matematica Guido Castelnuovo, Sapienza Università di Roma
Settimana dal 09-05-2022 al 15-05-2022
Lunedì 09 maggio 2022
Ore 14:30, Aula II, Dipartimento di Matematica, Sapienza Università di Roma
Baby A&G
Francesco Bei (Sapienza Università di Roma)
Grafi e topologia: alcune interazioni
Prendiamo un foglio e disegniamo due insiemi A e B, ciascuno formato da tre punti. E' possibile collegare ogni punto dell'insieme A ad ogni punto dell'insieme B senza che le linee si intreccino? Nel corso del seminario vedremo come alcuni risultati classici di topologia aiutino a trovare una risposta a questo e ad altri problemi simili.
Lunedì 09 maggio 2022
Ore 14:30, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
seminario di Analisi Matematica
Cristiana De Filippis (U. Parma)
Quasiconvexity meets nonlinear potential theory
A classical problem in the regularity theory for vector-valued minimizers of multiple integrals consists in proving their smoothness outside a negligible set, cf. Evans (ARMA ’86), Acerbi & Fusco (ARMA ’87), Duzaar & Mingione (Ann. IHP-AN ’04), Schmidt (ARMA ’09). In this talk, I will show how to infer sharp partial regularity results for relaxed minimizers of degenerate, nonuniformly elliptic quasiconvex functionals, using tools from nonlinear potential theory. In particular, in the setting of functionals with (p,q)-growth - according to the terminology introduced by Marcellini (Ann. IHP-AN ’86; ARMA ‘89) - I will derive optimal local regularity criteria under minimal assumptions on the data. This talk is partly based on joint work with Bianca Stroffolini (University of Naples Federico II)
Lunedì 09 maggio 2022
Ore 16:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Probabilità
Sebastian Andres (Manchester University)
First passage percolation with long-range correlations
In this talk we consider first passage percolation (FPP) with passage times generated by a general class of models with long-range correlations, including discrete Gaussian free fields as a prominent example. We will discuss conditions under which the associated time constant is positive and the FPP distance is comparable to the Euclidean distance. We will also present two applications to random conductance models (RCM) with possibly unbounded and strongly correlated conductances, namely a Gaussian heat kernel upper bound for RCMs with a general class of speed measures, and an exponential decay estimate for the Green function of RCMs with random killing measures. This talk is based on a joined work with Alexis Prévost (Cambridge).
Martedì 10 maggio 2022
Ore 16:00, Aula "Dal Passo" and online on this link, Dipartimento di Matematica, Università di Roma "Tor Vergata"
Seminario di Analisi Matematica
Filippo Gazzola (Politecnico di Milano)
Long-time behavior of partially damped systems modeling degenerate plates with piers
We consider a partially damped nonlinear beam-wave system of evolution PDE's modeling the dynamics of a degenerate plate. The plate can move both vertically and torsionally and, consequently, the solution has two components. We show that the component from the damped beam equation always vanishes asymptotically while the component from the (undamped) wave equation does not. In case of small energies we show that the first component vanishes at exponential rate. Our results highlight that partial damping is not enough to steer the whole solution to rest and that the partially damped system can be less stable than the undamped system. Hence, the model and the behavior of the solution enter in the framework of the so-called "indirect damping" and "destabilization paradox". These phenomena are valorized by a physical interpretation leading to possible new explanations of the Tacoma Narrows Bridge collapse. Joint work with Abdelaziz Soufyane (University of Sharjah, UAE)
NB:This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006
Per informazioni, rivolgersi a: molle@mat.uniroma2.it
Martedì 10 maggio 2022
Ore 16:00, Sala degli Affreschi, Facoltà di Ingegneria Civile e Industriale
Miles Rubin (Technion - Israel Institute of Technology)
Eulerian formulation of inelasticity -- from metal plasticity to growth of biological tissues
An Eulerian formulation of constitutive equations for inelasticity is discussed which models metal plasticity and growth of biological tissues. Motivated by the early work of Eckart (1948) and Leonov (1976) evolution equations are proposed for elastic deformation measures directly. In contrast with Lagrangian formulations of constitutive equations, the Eulerian formulation is unaffected by arbitrariness of specified reference and intermediate configurations and definitions of total and inelastic strain measures. Eulerian evolution equations for a triad of microstructural vectors model elastic deformation for fully anisotropic elastic-inelastic response. For growth of biological tissues, the evolution equations have been modified to model homeostasis, which is the inelastic process that causes a tendency for the elastic deformation measures to approach their homeostatic values. In particular, the stress in the homeostatic state can be non-zero. Robust, strongly objective numerical algorithms will also be discussed.
Per informazioni, rivolgersi a: jacopo.ciambella@uniroma1.it
Mercoledì 11 maggio 2022
Ore 14:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
seminario di Algebra e Geometria
Claudio Arezzo (ICTP)
Metriche a curvatura scalare costante su varietà algebriche e rivestimenti di Galois
In questo seminario presenterò alcuni risultati recenti ottenuti con Y. Shi e A. Della Vedova. Dopo un’introduzione generale sui metodi noti per produrre metriche di Einstein e cscK, presenterò come un recente risultato fondamentale di Cheng-Chen applicato a varietà algebriche permetta di costruire infinite nuove famiglie di metriche csck, connettendomi a varie costruzioni geometriche nel caso di rivestimenti ciclici, abeliani e non.
Per informazioni, rivolgersi a: diverio@mat.uniroma1.it
Mercoledì 11 maggio 2022
Ore 14:30, Aula 1B1, SBAI, ed. RM002
Antonio J. Fernández Sanchez (ICMAT (Madrid))
Singular limits for a half-Laplacian Liouville type equation
We consider the nonlocal Liouville type equation \( (-\Delta)^{\frac12}u = \epsilon \kappa(x) e^{u}, u > 0, \textrm{ in } I, \quad u = 0, \textrm{ in } \mathbb{R} \setminus I, \) where \(I\) is a union of \(d \geq 2\) disjoint bounded intervals, \(\kappa\) is a smooth bounded function with positive infimum and \(\epsilon > 0\) is a small parameter. For any integer \(1 \leq m \leq d\), we construct a family of solution \((u_{\epsilon})_{\epsilon}\) which blow-up at \(m\) distinct points of \(I\) and for which \(\epsilon \int_{I} \kappa(x) e^{u} \to 2m\pi\) as \(\epsilon \to 0\). Moreover, we show that, when \(d = 2\) and \(m\) is suitably large, no such construction is possible. The talk is based on a joint work with Matteo Cozzi (Milano, Italy).
Mercoledì 11 maggio 2022
Ore 14:30, aula 34 e online https://meet.google.com/dwz-gvib-uoj, Dipartimento di Scienze Statistiche, Sapienza Università di Roma
seminario di Probabilità
Giacomo Ascione (Scuola Superiore Meridionale)
A sojourn-based approach to discrete-time semi-Markov decision processes
Up to now, there is an extensive literature on stepped continuous-time semi-Markov decision processes. Such models generalize the classical continuous-time Markov chain decision processes by allowing for different distributions of interevent times. However, in such models, the decision is always taken in a change of state, so that it influences a priori the distribution of the inter-event times. For such a reason, these models do not allow for decision depending on intermediate observations of the system. In this talk we address the problem of intermediate observations by modelling the system as a finite horizon discrete-time semi-Markov process, thus assuming discrete observations of the system, and allowing possible decisions at each time step. To do this, we first provide an alternative characterization of discrete-time semi-Markov processes in terms of a bivariate Markov chain, involving both the state and the sojourn time of the process. Once this is done, one can use the dynamic programming principle to exploit optimal policies for the discrete-time semi-Markov decision process by resorting to the bivariate Markov formulation. With this approach we are able to exhibit the Bellman’s equation for both the value and the quality function. The latter is then used to develop a model-free reinforcement learning algorithm based on Watkins and Dayan’s Qlearning algorithm, together with a first naive attempt towards a deep reinforcement learning one. Two exploratory toy examples are provided. This is based on a joint work with Salvatore Cuomo from Univerisità degli Studi di Napoli Federico II.
Per informazioni, rivolgersi a: luisa.beghin@uniroma1.it
Mercoledì 11 maggio 2022
Ore 15:20, 1B1, SBAI, ed. RM002
Stefano Buccheri (University of Vienna )
An Agmon-Allegretto-Piepenbrink (AAP) principle for Schroedinger operators
It is well known that existence of nonnegative supersolutions is striclty connected with certain spectral properties of the Schrödinger operator \(-\Delta +V\). In this talk, we investigate the validity of such a relation when the potential \(V\) is assumed to be merely a Borel, sign changing function. As we shall see, the singularity of \(V\) dramaticaly affects the properties of the considered operator and of the associated functional space. This is a joint work with Luigi Orsina and Augusto Ponce.
Giovedì 12 maggio 2022
Ore 14:30, Sala di Consiglio - https://meet.google.com/ads-dekx-bgm, Dipartimento di Matematica, Sapienza Università di Roma
P(n)/N(p) : Problemi differenziali nonlineari/Nonlinear differential problems
Pietro D'Avenia (Politecnico di Bari)
On a general mixed dispersion nonlinear Schrödinger equation
I will present a multiplicity result for a mixed dispersion nonlinear Schrödinger equation where the nonlinearity g satisfies general assumptions. (joint work with Alessio Pomponio and Jacopo Schino)
Per informazioni, rivolgersi a: galise@mat.uniroma1.it
Giovedì 12 maggio 2022
Ore 15:00, Aula E - Sarà possibile partecipare al seminario anche in modalità telematica., Dipartimento di Matematica, Sapienza Università di Roma
Seminari di Ricerca in Didattica e Storia della Matematica
Pietro Di Martino (Università di Pisa)
La ricerca qualitativa sull'affect in Mathematics Education
Per informazioni, rivolgersi a: Coloro che sono interessati a partecipare in modalità telematica possono contattare Annalisa Cusi (annalisa.cusi@uniroma1.it)
Venerdì 13 maggio 2022
Ore 12:00, Aula 1B1, Palazzina RM002 (da remoto su Google Meet al seguente link: https://meet.google.com/bju-qqhk-ryd), Dipartimento di Scienze di Base e Applicate per l'Ingegneria, Sapienza Università di Roma
Javier Rodriguez Cuadrado (Universidad Politecnica de Madrid)
Fractal equilibrium configuration of a mechanically loaded binary tree
In this seminar we introduce the equilibrium mechanics problem that originates in a binary tree with infinite levels subjected to loads on its topmost branches. The application of the laws of mechanics to find the equilibrium configuration shows that the functional forms of the vertical and horizontal displacements of its end nodes converge to a Takagi curve and a linear combination of inverses of \(\beta\)-Cantor functions respectively as the number of levels tend to infinity. As a consequence, the shape of the canopy results from the combination of these two emerging fractals that were not present in the unloaded tree. Besides, our study also shows that the analytical expressions of the emerging fractals depend on the mechanical properties of the binary tree, indicating that the binary tree is a link between these two emerging fractals. In addition, we prove that the fractal dimensions of Takagi and \(\beta\)-Cantor are related in this model.
Venerdì 13 maggio 2022
Ore 15:00, Aula Dal Passo, Dipartimento di Matematica, Università di Roma "Tor Vergata"
Event "May12: Celebrating Women in Mathematics"
Michela Procesi (Università di Roma Tre)
Order and Chaos in Wave Dynamics
(Opening Address by Gabriella Tarantello) Abstract: Many physical phenomena are well described as the propagation of waves: the motion of the sea, the transmission of sound, electromagnetic waves (light, radio waves). Their mathematical description is often extremely complicated, and characterized by the coexistence of stable and chaotic behaviors. I will discuss some models of wave propagation by nonlinear Partial Differential Equations illustrating briefly the main difficulties as well as some mathematical methods used to study them. A small refreshment will be served at the end of the colloquium. Note: This talk is part of the activity of the MIUR Department of Excellence Project MATH@TOV CUP E83C18000100006. MS Teams Link for the streaming
Per informazioni, rivolgersi a: sorrentino@mat.uniroma2.it
Venerdì 13 maggio 2022
Ore 16:00, Aula III, Dipartimento di Matematica, Sapienza Università di Roma
MATH talks
Francesca Elisa Leonelli (Sapienza Università di Roma)
Variabilità climatica ed eventi estremi nell'oceano
Tra le componenti del clima, gli oceani svolgono un ruolo essenziale nella distribuzione del calore sul pianeta, e possono essere studiati tramite l'analisi di variabili, come la temperatura, forniti ad esempio da osservazioni satellitari. Nel seminario introdurremo i principali processi di variabilità climatica negli oceani, quindi vedremo alcuni metodi di analisi capaci di estrapolare i pattern corrispondenti. Infine, introdurremo gli eventi di temperatura estrema, le Marine Heat Waves, con particolare riferimento agli eventi nel Mar Mediterraneo.
Per informazioni, rivolgersi a: mathtalks@uniroma1.it
Venerdì 13 maggio 2022
Ore 17:00, Aula III, Dipartimento di Matematica, Sapienza Università di Roma
MATH talks
Elisabetta Brocchieri (Sapienza Università di Roma)
Instabilità di Turing e modelli diffusivi: formazione di pattern e sistemi di cross-diffusion
Perché il manto delle zebre è striato? Cosa determina le macchie sulla pelle del ghepardo? Sono tanti i fenomeni di pattern, cioè geometrie più o meno regolari che si manifestano in natura, in particolare sul manto di esseri viventi tra cui pesci e felini. Alan Turing ha per primo formalizzato matematicamente la reazione chimica che determina la formazione di pattern in termini di instabilità degli equilibri del modello in analisi [1]. Il talk è dedicato allo studio dell’instabilità di Turing per sistemi di equazioni di tipo Lotka-Volterra con termini diffusivi. In particolare, dimostreremo l’instabilità per una classe di sistemi di reazione-diffusione non lineari: i sistemi di cross-diffusion [2]. [1] Turing, A., The chemical basis of morphogenesis, Philosophical Transactions of the Royal Society of London B. 237 (1952), 37–72. [2] Shigesada, N., Kawasaki, K., and Teramoto, E., Spatial segregation of interacting species, J. Theor. Biol. 79 (1979), 83–99.
Per informazioni, rivolgersi a: mathtalks@uniroma1.it
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