Notiziario Scientifico
a cura del Dipartimento di Matematica Guido Castelnuovo, Sapienza Università di Roma
Settimana dal 25-03-2024 al 31-03-2024
Lunedì 25 marzo 2024
Ore 16:00, Aula 4, Dipartimento di Matematica, Sapienza Università di Roma
corso di dottorato
Guido Pezzini (Sapienza)
Algebre di Hecke
Lunedì 25 marzo 2024
Ore 12:30, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
seminario di Analisi Matematica
Antonio De Rosa (Università Bocconi)
Min-max construction of anisotropic CMC surfaces
We prove the existence of nontrivial closed smooth surfaces with constant anisotropic mean curvature with respect to elliptic integrands in closed smooth 3-dimensional Riemannian manifolds. Joint work with G. De Philippis. 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 25 marzo 2024
Ore 13:00, Aula G, Dipartimento di Matematica, Sapienza Università di Roma
Corso di dottorato
Vittoria Silvestri (Università di Roma La Sapienza)
Introduction to Random Geometry
This course wants to give an overview of active research topics in the field of Random Geometry, with a focus on growth models. We will start by discussing discrete growth models such as the Eden model, Diffusion Limited Aggregation and Internal DLA. We will then move to the continuum for the remaining part of the course. After discussing conformal invariance of Brownian motion, we will focus on the class of randomly growing domains on the complex plane which can be described via Loewner dynamics. We will introduce several random aggregation models on the complex plane, which go under the name of Hastings-Levitov models and Aggregate Loewner Evolutions, of which we will study the large-scale features, presenting existing results and several open questions.
Lunedì 25 marzo 2024
Ore 14:30, Aula Dal Passo, Dipartimento di Matematica, Università degli studi di Roma "Tor Vergata"
Seminario di Analisi Numerica
Hartmut Prautzsch (Karlsruhe Institute of Technology)
The many aspects of de Casteljau's algorithm - A historical review
Paul de Faget de Casteljau (1930-2022) was a highly gifted mathematician who worked in industry and made fundamental mathematical contributions. In this talk, I will focus on one central contribution that de Casteljau developed soon after he started working for Citroen in 1958. It is the algorithm of de Casteljau, a simple construction of polynomial curves from control points by iterated linear interpolation. This algorithm is not only very simple, very useful, and very well known, but it also has a great number of properties and generalizations that make it a fundamental and unifying theoretical tool for Geometric Design. As a tribute to an outstanding pioneer in CAGD, I will recall widely and little known generalizations and properties of this algorithm to remind us of its beauty, versatility and importance as THE algorithm and backbone of Computer Aided Geometric Design (CAGD).
Per informazioni, rivolgersi a: speleers@mat.uniroma2.it
Martedì 26 marzo 2024
Ore 14:00, 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
Dupin's cyclides: Week 5 o Power of a point, orthogonal spheres, similarity centers o Cyclides o Classes of cyclides o Smooth joints o Sphere inversions, cyclides and tori.
Il materiale del corso è raccolto in un canale teams dedicato a cui gli interessati possono essere aggiunti scrivendo a manni@mat.uniroma2.it
Martedì 26 marzo 2024
Ore 14:00, Aula G, Dipartimento di Matematica, Sapienza Università di Roma
Seminario finale ciclo di lezioni dottorato
Massimo Ostilli (Universidade Federal da Bahia, Salvador - BA - Brazil)
Absence of small-world effects at the quantum level and stability of the quantum critical point
The small-world effect is a universal feature used to explain many different phenomena like percolation, diffusion, and consensus. Starting from any regular lattice of N sites, the small-world effect can be attained by rewiring randomly O(N ) links or by superimposing O(N ) new links onto the system. In a classical system this procedure is known to change radically its critical point and behavior, the new system being always effectively mean-field. Here, we prove that at the quantum level the above scenario does not apply: when an O(N ) number of new couplings are randomly superimposed onto a quantum Ising chain, its quantum critical point and behavior both remain unchanged. In other words, at zero temperature quantum fluctuations destroy any small-world effect. The derivation is obtained by combining the quantum-classical mapping with topological arguments.
Martedì 26 marzo 2024
Ore 14:30, aula D'Antoni, Dipartimento di Matematica, Università di Roma Tor Vergata
seminario di Geometria
Luca Schaffler (Roma Tre University)
An explicit wall crossing for the moduli space of hyperplane arrangements
Given the moduli space of hyperplanes in projective space, V. Alexeev constructed a family of compactifications parametrizing stable hyperplane arrangements with respect to given weights. In particular, there is a toric compactification that generalizes the Losev–Manin compactification for the moduli of points on the line. We study the first natural wall crossing that modifies this compactification into a non-toric one by varying the weights. In particular, we prove that in dimensions two the wall crossing corresponds to blowing up at the identity of the generalized Losev–Manin space. As an application, we show that any Q-factorialization of this blow-up is not a Mori dream space for a sufficiently high number of lines. This is joint work in progress with Patricio Gallardo.
Per informazioni, rivolgersi a: guidomaria.lido@gmail.com
Martedì 26 marzo 2024
Ore 17:30, Aula Picone, Dipartimento di Matematica, Sapienza Università di Roma
YAMS - Young Algebraist Meetings in Sapienza
Nicola Ottolini (Università di Tor Vergata)
Some problems of Unlikely Intersections
Starting from Mordell, many conjectures have been put forward (and proved) about how geometry influences the behaviour of diophantine problems. It turns out that many of them can be put in a common framework about varieties that for dimensional reasons we do not expect to intersect. Whenever they do we say that this intersection is "unlikely". After some examples of problem of this type we will look at a common proof strategy due to Pila and Zannier.
Per informazioni, rivolgersi a: sabino.ditrani@uniroma1.it
Mercoledì 27 marzo 2024
Ore 10:00, stanza 1201 "R. Dal Passo", Dipartimento di Matematica, Università di Roma Tor Vergata
corso di dottorato
Guido Pezzini (Sapienza)
Algebre di Hecke
Mercoledì 27 marzo 2024
Ore 13:00, Aula G, Dipartimento di Matematica, Sapienza Università di Roma
Corso di dottorato
Vittoria Silvestri (Università di Roma La Sapienza)
Introduction to Random Geometry
This course wants to give an overview of active research topics in the field of Random Geometry, with a focus on growth models. We will start by discussing discrete growth models such as the Eden model, Diffusion Limited Aggregation and Internal DLA. We will then move to the continuum for the remaining part of the course. After discussing conformal invariance of Brownian motion, we will focus on the class of randomly growing domains on the complex plane which can be described via Loewner dynamics. We will introduce several random aggregation models on the complex plane, which go under the name of Hastings-Levitov models and Aggregate Loewner Evolutions, of which we will study the large-scale features, presenting existing results and several open questions.
Mercoledì 27 marzo 2024
Ore 14:30, Aula B, Dipartimento di Matematica e Fisica, Università di Roma Tre, Via della Vasca Navale, 84
seminario di Fisica Matematica
Giovanna Marcelli (Università degli Studi Roma Tre)
On the self-consistent Landauer-Büttiker formalism
We provide sufficient conditions such that the time evolution of a mesoscopic tight-binding open system with a local Hartree-Fock non-linearity converges to a self-consistent non-equilibrium steady state, which is independent of the initial condition from the "small sample". We also show that the steady charge current intensities are given by Landauer-Büttiker-like formulas, and make the connection with the case of weakly self-interacting many-body systems. This is a joint work with Horia D. Cornean https://arxiv.org/abs/2309.01564
Mercoledì 27 marzo 2024
Ore 16:00, Aula Dal Passo, Dipartimento di Matematica, Università di Roma Tor Vergata
Seminario di Algebre di Operatori
Yasuyuki Kawahigashi (The University of Tokyo)
Quantum 6j-symbols and braiding
Alpha-induction is a tensor functor producing a new fusion category from a modular tensor category and a Q-system. This can be formulated in terms of quantum 6j-symbols and braiding and gives alpha-induced bi-unitary connections. Last year, we showed that locality of the Q-system implies flatness of the alpha-induced connections. We now prove that the converse also holds. The Operator Algebra Seminar schedule is here: https://sites.google.com/view/oastorvergata/home-page?authuser=0
Mercoledì 27 marzo 2024
Ore 16:15, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario Volterra
Michela Procesi (Università Roma Tre)
Almost-periodic solutions for the non-linear Schrödinger equation on the circle
It is well known that for close-to-integrable finite dimensional Hamiltonian systems "most" solutions live on maximal invariant tori, so it is very natural to wonder whether such a result can hold also in infinite dimensional systems. This is a very challenging problem and mostly still wide open. I will give an overview of recent results, main difficulties and open problems, concentrating on the case of the non-linear Schrödinger equation on the circle with a convolution potential.
Giovedì 28 marzo 2024
Ore 14:15, Aula M1, Dipartimento di Matematica e Fisica, Università Roma Tre
Seminario di Geometria
Roberto Fringuelli (Sapienza)
A Support Theorem for the meromorphic Hitchin fibration
Let G be a connected reductive group over an algebraically closed field. A challenging task is the computation of the (intersection) cohomology of the moduli space of G-Higgs bundles over a curve. One way to tackle the problem is to study the derived direct image of the intersection complex of this moduli space along the G-Hitchin fibration. In the first part of the talk, we provide an overview of the G-Hitchin fibration for the moduli space of G-Higgs bundles. In the second part, we show that the derived direct image of the intersection complex for the meromorphic G-Hitchin fibration is determined by its restriction to the so-called elliptic locus, for any connected reductive group G. The cases GLn and SLn were already known thanks to the works of Chaudouard-Laumon, de Cataldo and Maulik-Shen. This is a work in progress jointly with Mark Andrea de Cataldo, Andres Fernandez Herrero and Mirko Mauri.
Per informazioni, rivolgersi a: amos.turchet@uniroma3.it
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