Notiziario Scientifico
a cura del Dipartimento di Matematica Guido Castelnuovo, Sapienza Università di Roma
Settimana dal 04-03-2024 al 10-03-2024
Lunedì 04 marzo 2024
Ore 14:15, Aula B, Dipartimento di Matematica e Fisica, Università Roma Tre
Seminario di Geometria
Valery Alexeev (University of Georgia)
Enumerative geometry of the KSBA spaces
The enumerative geometry of the moduli spaces of curves, which began in the 1980s with a famous paper of Mumford, is now an extremely developed field, with perhaps thousands of papers dedicated to it. It's high time to do the higher dimensional case! The analogues of \(\overline{M}_{g,n}\) in higher dimensions are the KSBA spaces. I will introduce some characteristic classes on the KSBA spaces that are analogous to the kappa, lambda and psi classes on the moduli of curves, and present some results and speculations.
Per informazioni, rivolgersi a: amos.turchet@uniroma3.it
Lunedì 04 marzo 2024
Ore 14:30, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
seminario di Analisi Matematica
Azahara DelaTorre (Sapienza Università di Roma)
Uniqueness of least-energy solutions to the fractional Lane-Emden equation in the ball.
In this talk we will show the uniqueness of least-energy solutions for the fractional Lane-Emden equation posed in the ball under homogeneous Dirichlet exterior conditions. This is a non-local semilinear equation with a superlinear and subcritical nonlinearity. Existence of positive solutions follows easily from variational methods, but uniqueness is quite complicated. In the local case, the uniqueness of positive solutions follows from the result of Gidas, Ni and Nirenberg. Indeed, by using the moving plane method, they proved radial symmetry of the solutions which allows the application of ODE techniques. In the non-local case, these arguments don’t seem to work. Our proof makes use of Morse theory, and it is inspired by some results obtained by C. S. Lin in the ’90s. The talk is based on a joint work with Enea Parini. This seminar is part of the activities of the Dipartimento di Eccellenza CUP B83C23001390001 and it is funded by the European Union – Next Generation EU.
Per informazioni, rivolgersi a: azahara.delatorrepedraza@uniroma1.it
Lunedì 04 marzo 2024
Ore 16:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Probabilità
Ilya Losev (University of Cambridge, UK)
How long are the arms in Dielectric-Breakdown Model?
In this talk we will discuss the recent progress on such random growth models as Diffusion Limited Aggregation (DLA) and Dielectric-Breakdown Model (DBM) in 2 and 3 dimensions. These models are believed to exhibit non-equilibrium growth, producing irregular fractal patterns. The main questions about these processes include finding their scaling limits and fractal dimensions. However, almost nothing is known rigorously. The main result about these models is due to Kesten, who gave a non-trivial lower bound on the fractal dimension of DLA clusters. The main tool in his proof was the famous Beurling’s estimate. We generalize this result to DBM and give a new proof of Kesten’s Theorem. Our proof does not rely on Beurling’s estimate. Instead, we exploit the connection between DBM growth properties and multifractal spectrum of the harmonic measure. This talk is based on joint work with Stanislav Smirnov.
Per informazioni, rivolgersi a: silvestri@mat.uniroma1.it
Martedì 05 marzo 2024
Ore 14:30, Aula Dal Passo, Dipartimento di Matematica, Università di Roma "Tor Vergata"
Seminario di equazioni differenziali
Stefano Baranzini (Università di Torino)
Chaotic phenomena for singular systems on surfaces
The main focus of the talk will be a class of \(2d\) singular mechanical systems on a surface \(\Sigma\) with a potential \(V\) having a finite number of singularities \(\mathcal{C} := \{c_1,\dots, c_n\}\) of the form \( V(q) \sim C_i d(c_i,q)^{-\alpha_i}\), where \(C_i>0\), \(\alpha_i \geq 1\) \and \(q \in \mathcal{O}(c_i)\). The first result I will present is an existence one: there are periodic solutions in (infinitely) many conjugacy classes of \(\pi_1(\Sigma,\mathcal{C})\). Using this fact, I will construct an invariant set for the system which admits a semi-conjugation with a Bernoulli shift. The second result I will discuss aims at identifying some situation in which the semi-conjugation is actually a conjugation and the invariant set constructed displays a chaotic behaviour. This happens, for instance, under some negativity condition on the curvature of \(\Sigma\) and for large values of the energy. Much emphasis will be put on the interplay between geometry, topology and variational methods. This is a joint work with Gian Marco Canneori. Note: This talk is part of the activity of the MIUR Department of Excellence Project MatMod@TOV (2023-2027)
Per informazioni, rivolgersi a: sorrentino@mat.uniroma2.it
Martedì 05 marzo 2024
Ore 14:30, aula D'Antoni, Dipartimento di Matematica, Università di Roma Tor Vergata
seminario di Geometria
Víctor González Alonso (Leibniz Universität Hannover)
Embedded deformations of curves with maximal variation of Hodge structure
Given a family of complex (smooth projective) manifolds, one can measure its non-triviality by looking at how much the Hodge structures of the fibres change. This leads to the notion of maximal (infinitesimal) variation of Hodge structure (IVHS). In the case of families of curves, results of Lee-Pirola and of myself with Torelli imply that a general deformation of any curve has maximal IVHS. This is however not so clear if one wants the deformation to keep some further structure, such as the gonality of the curve or an embedding into a given surface. For example, it was only recently proved by Favale and Pirola that every smooth plane curve admits a deformation as a plane curve with maximal IVHS, and the question remains open for deformations of curves inside any other surface. In this talk I will present a joint work in progress with Sara Torelli extending this result to curves in \(\mathbb{P}^1 \times \mathbb{P}^1\), which turns out to be way more involved than the plane case.
Per informazioni, rivolgersi a: guidomaria.lido@gmail.com
Martedì 05 marzo 2024
Ore 14:30, aula piano 1, IAC-CNR, via dei Taurini 19
Seminari General dell'IAC
Matteo Paoluzzi (CNR-IAC )
Collective Behavior in Living Materials
Active Materials are collections of self-propelled particles that serve as model systems for several biological systems ranging from epithelial tissues to bacterial microfilms. Because of their non-equilibrium dynamics, active systems can show condensed phases that are prevented by fluctuations at equilibrium. For instance, active particles can condense even in the absence of any attractive force, develop collective long-ranged polar order in two spatial dimensions, and produce spontaneous currents once embedded into complex environments. In this talk, I will show how most of the peculiarities of scalar active systems can be rationalized in terms of persistent random walks. I will explore the impact of such non-equilibrium dynamics on a coarse-graining scale where it is possible to observe a phase separation driven by the noise. Link streaming: https://www.iac.cnr.it/matteo-paoluzzi-i-seminari-generali-delliac-2024
Per informazioni, rivolgersi a: roberta.bianchini@cnr.it
Martedì 05 marzo 2024
Ore 15:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Modellistica Differenziale Numerica
Simone Chiocchetti (University of Cologne)
Towards simple and affordable solutions for a unified first order hyperbolic model of continuum mechanics
The talk concerns the ongoing development of a non-standard model of continuum mechanics, originally due to Godunov, Peshkov, and Romenski (GPR), and its numerical approximation in Finite Volume and Discontinuous Galerkin methods. The main feature of the model is that it describes a general continuum, rather than a classic fluid or solid medium, with the difference between the two being specified only by a choice of parameters. In this framework, rather general closure laws can be implemented, including non-Newtonian rheologies, visco-elasto-plasticity, material damage and fractures, melting and solidification, and more. The model is cast in a first order hyperbolic form with stiff relaxation sources, which means that it requires no second order diffusive fluxes, and that it yields a theory in which all signals propagate with finite speed, including heat conduction. A clear drawback of the model is its complexity, in particular when applied to Newtonian viscous fluids and compared to the well established Navier-Stokes equations. Together with stiff sources, one has to also consider the presence of differential involutions and algebraic constraints, together with other nonlinearities and representation issues concerning the evolution of matrix-valued data. Here I outline my efforts towards closing the complexity gap and making the formalism more accessible, mainly focusing on the treatment of stiff sources, algebraic constraints, and on new resolution improvements involving the formulation and solution of a quaternion-valued PDE.
Mercoledì 06 marzo 2024 -- LEZIONE ANNULLATA
Ore 10:00, Aula E, Dipartimento di Matematica, Sapienza Università di Roma
corso di dottorato
Guido Pezzini (Sapienza)
Algebre di Hecke
Mercoledì 06 marzo 2024
Ore 10:30, Aula Dal Passo, Dipartimento di Matematica, Università degli studi di Roma "Tor Vergata"
corso di dottorato
Hartmut Prautzsch (Karlsruhe Institute of Technology)
Rational Curves and Surfaces for Geometric Modelling
Rational splines: Week 2 o Circle splines and their degree o Curvature interpolation, curvature continuous splines o Three- and four-point / tangent contacts o C^k constructions, splines (NURBS) o Quadric spline surfaces
Il materiale corso è raccolto in un canale teams dedicato a cui gli interessati possono essere aggiunti scrivendo a manni@mat.uniroma2.it
Mercoledì 06 marzo 2024
Ore 14:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Algebra e Geometria
Thomas Krämer (Humboldt Universität zu Berlin)
Arithmetic finiteness of very irregular varieties
I will discuss joint work with Marco Maculan in which we prove the Shafarevich conjecture for a large class of irregular varieties over number fields. Our proof combines the method of Lawrence-Sawin with a big monodromy theorem from previous work with Javanpeykar, Lehn and Maculan. If time permits, I will briefly sketch at the end some recent progress which uses Hodge modules to rule out exceptional groups in the monodromy theorem.
Mercoledì 06 marzo 2024
Ore 14:30, aula M2 (nuovo blocco aule), Lungotevere Dante n.376, Dipartimento di Matematica e Fisica, Università degli Studi Roma Tre
Seminario di Analisi Matematica
Mohameden Ahmedou (Giessen University)
An abstract framework for the critical point theory at infinity
In this talk we report on some new progress in setting up an abstract framework, under which Morse theoretical methods can be applied to some non compact variational problem by computing the difference of topology induced by the so called "critical points at infinity". As application we show how to apply such a method to the Nirenberg problem on spheres, recovering and improving existence results available in the literature. This is a joint work with Thomas Bartsch (Giessen University).
Per informazioni, rivolgersi a: luca.battaglia@uniroma3.it
Mercoledì 06 marzo 2024
Ore 16:00, Aula 108, Dipartimento di Matematica e Fisica, Università Roma Tre
Junior seminar
Muhammad Usman (Università degli studi Roma Tre)
3D Human Pose Estimation: Real-time Performance and Applications
Human pose estimation is a task that involves identifying the location of specific points in an image, usually referred to as keypoints. The keypoints can represent various parts of the object such as joints, landmarks, or other distinctive features. YOLO (You Only Look Once), a current state-of-the-art deep learning object detection model, simultaneously identifies and predicts the keypoints that define the human body's pose. In our talk, we will present a real-time 3D human pose estimation system by employing two cameras and triangulation methods to calculate the 3D pose from the 2D pose predicted by YOLO. Our results showcase the potential of the proposed method as a robust tool for real-time 3D human pose estimation. Beyond accuracy and efficiency, this approach opens up numerous possibilities across various domains, including human-computer interaction, sports analytics, and surveillance.
Mercoledì 06 marzo 2024
Ore 16:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
seminario di Fisica Matematica
Giulia Basti (GSSI, L'Aquila)
Upper bounds on the energy of dilute gases of hard-sphere bosons
In the last decades, since the first experimental realizations of Bose- Einstein condensates, the study of large bosonic systems has been a very active field of research both in physics and in mathematics. In experiments Bose gases are often very dilute and can be well described in the Gross-Pitaevskii limit, i.e. as quantum systems of N confined particles, interacting through a potential with scattering length of order 1/N where N tends to infinity. In this talk we present a recent result on a hard- sphere Bose gas in this regime. Namely, we prove a second order upper bound on the ground state energy matching the known expression of the energy for integrable potentials. We also discuss a new upper bound for hard-spheres in the thermodynamic limit, where the number of particles and the size of the box are sent to infinity keeping the density fixed. Our result resolves the ground state energy up to an error of the order of the so-called Lee-Huang-Yang correction. Based on joint works with S. Cenatiempo, A. Giuliani, A. Olgiati, G. Pasqualetti, B. Schlein.
Per informazioni, rivolgersi a: basile@mat.uniroma1.it, domenico.monaco@uniroma1.it
Giovedì 07 marzo 2024
Ore 14:00, Aula D'Antoni, Dipartimento di Matematica, Università degli studi di Roma "Tor Vergata"
corso di dottorato
Hartmut Prautzsch (Karlsruhe Institute of Technology)
Rational Curves and Surfaces for Geometric Modelling
Rational splines: Week 2 o Circle splines and their degree o Curvature interpolation, curvature continuous splines o Three- and four-point / tangent contacts o C^k constructions, splines (NURBS) o Quadric spline surfaces
Per informazioni, rivolgersi a: Il materiale del corso è raccolto in un canale teams dedicato a cui gli interessati possono essere aggiunti scrivendo a manni@mat.uniroma2.it
Giovedì 07 marzo 2024
Ore 14:30, Aula 1B1. RM002, Via A.Scarpa 16, Dipartimento SBAI, Sapienza Università di Roma
Seminario "PDE a tutto SBAI"
Andrea Bisterzo (Sapienza Università di Roma)
Weak maximum principles for elliptic operators on unbounded Riemannian domains and an application to a symmetry problem
The necessity of a maximum principle arises naturally when one is interested in studying qualitative properties of solutions to partial differential equations. Generally, to ensure the validity of such principles, additional assumptions on the ambient space or on the differential operator need to be considered. The talk aims to address, using both of these approaches, the problem of proving (weak) maximum principles for second-order elliptic operators acting on unbounded Riemannian domains under Dirichlet boundary conditions. At the end of the talk, we will see how to apply these maximum principles to recover a symmetry result for stable solutions to semilinear PDEs in isoparametric Riemannian domains.
Per informazioni, rivolgersi a: massimo.grossi@uniroma1.it
Giovedì 07 marzo 2024
Ore 16:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Presentazione risultati tesi di dottorato
Andrea Drago (Dipartimento di Matematica, Sapienza Università di Roma)
Entropy and curvature in low dimensional topology
In this talk we will explore the analogy between Ricci curvature and volume entropy. The Ricci curvature is a classical invariant in Riemannian geometry that has strong implications on the topology of manifolds. In particular, the topology of manifolds with a lower bound on the Ricci curvature are topologically finite, meaning that there are a finite number of diffeomorphism classes, and locally topologically rigid, meaning that two such manifolds with different topology cannot be too close. The volume entropy is an invariant of isometric group actions introduced in geometric group theory, which can be interpreted as an asymptotic, weak version of the Ricci curvature. In the spirit of this analogy, we will see two theorems, lying in the intersection between hyperbolic geometry, geometric group theory, and low dimensional topology, which show the topological finiteness and local topological rigidity for some classes of manifolds with volume entropy bounds.
Per informazioni, rivolgersi a: fiorenza@mat.uniroma1.it
Giovedì 07 marzo 2024
Ore 16:00, Aula 5, Dipartimento di Matematica, Sapienza Università di Roma
corso di dottorato
Guido Pezzini (Sapienza)
Algebre di Hecke
Venerdì 08 marzo 2024
Ore 16:00, Aula Picone, Dipartimento di Matematica, Sapienza Università di Roma
Seminari per i docenti A.A. 2023-2024
Francesca Tovena, Silvia Cerasaro (Università degli Studi di Roma Tor Vergata)
L'aritmetica modulare: una proposta laboratoriale ispirata al Liber Abbaci di Fibonacci.
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