Notiziario Scientifico
a cura del Dipartimento di Matematica Guido Castelnuovo, Sapienza Università di Roma
Settimana dal 08-04-2024 al 14-04-2024
Lunedì 08 aprile 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 08 aprile 2024
Ore 14:30, Aula "Dal Passo", Dipartimento di Matematica, Università di Roma "Tor Vergata"
Colloquium di dipartimento
Rostislav I. Grigorychuk (University of Texas A&M)
Fractal, liftable and scale groups
Scale groups are closed subgroups of the group of isometries of a regular tree that fix an end of the tree and are vertex-transitive. They play an important role in the study of locally compact totally disconnected groups as was recently observed by P-E.Caprace and G.Willis. In the 80th they were studied by A.Figa-Talamanca and C.Nebbia in the context of abstract harmonic analysis and amenability. It is a miracle that they are closely related to fractal groups, a special subclass of self-similar groups. In my talk I will discuss two ways of building scale groups. One is based on the use of scale-invariant groups studied by V.Nekrashevych and G.Pete, and a second is based on the use of liftable fractal groups. The examples based on both approaches will be demonstrated using such groups as Basilica, Hanoi Tower Group and Group of Intermediate Growth (between polynomial and exponential). Additionally, the group of isometries of the ring of integer p-adics and group of dilations of the field of p-adics will be mentioned in the relation with the discussed topics.
NB: This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C23000330006.
Per informazioni, rivolgersi a: molle@mat.uniroma2.it
Lunedì 08 aprile 2024
Ore 14:30, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
seminario di Analisi Matematica
Manuel Friedrich (Universität Münster)
Regularity for minimizers of the Griffith energy
We discuss regularity for the crack set of a minimizer for the Griffith fracture energy, arising in the variational modeling of brittle materials. In the planar setting, we prove an epsilon-regularity result showing that the crack is locally a C^{1,1/2} curve outside of a singular set of zero Hausdorff measure. The main novelty is that, in contrast to previous results, no topological constraints on the crack are required. Joint work with Camille Labourie and Kerrek Stinson. 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
Martedì 09 aprile 2024
Ore 14:00, Aula 34, Dipartimento di Scienze Statistiche quarto piano, Dipartimento di Scienze Statistiche
An afternoon on the spectral theory of pseudo-differential operators
Atsuhide Ishida (Tokyo University of Science, Tokyo, Japan)
Mourre inequality for non-local Schrödinger operators
We consider the Mourre inequality for the following self-adjoint operator \( H=\Psi(-\Delta/2)+V\) acting on \(L^2(\mathbb{R}^d) \), where \( \Psi: [0,\infty)\rightarrow\mathbb{R} \) is an increasing function, \( \Delta \) is the Laplacian and \( V: \mathbb{R}^d\rightarrow\mathbb{R} \) is an interaction potential. Mourre inequality immediately yields the discreteness and finite multiplicity of the eigenvalues. Moreover, the Mourre inequality together with the limiting absorption principle can be used to show absence of the singular continuous spectrum. In addition, Mourre inequality is also used for the proof of the minimal velocity estimate that plays an important role in scattering theory. In this talk, we report that Mourre inequality holds under a general \( \Psi \) and \( V \) by choosing the conjugate operator \( A=(p \cdot x + x \cdot p)/2 \) with \( p= - i \nabla \), and that the discreteness and finite multiplicity of the eigenvalues hold. This talk is a joint work with J. Lőrinczi (Alfred Rényi Institute) and I. Sasaki (Shinshu University).
Per informazioni, rivolgersi a: enrico.scalas@uniroma1.it
Martedì 09 aprile 2024
Ore 14:30, aula D'Antoni, Dipartimento di Matematica, Università di Roma Tor Vergata
seminario di Geometria
Ruijie Yang (Humboldt-Universität (Berlin))
Minimal exponent of a hypersurface
In this talk, I will go back to the origin of the minimal exponent and give a brief history on how it naturally arises in the context of integration over vanishing cycles (Arnold-Varchenko), counting integer solutions of congruence equations (Igusa) and Archimedean zeta functions (Atiyah, Bernstein, Loeser). Then I will talk about some joint work in progress with Dougal Davis (on birational formula of higher multiplier ideals via Beilinson’s formula from Jansen’s conjecture in geometry representation theory) and Ming Hao Quek (on birational characterization of minimal exponents via toric geometry and multi weighted blow-ups).
Per informazioni, rivolgersi a: guidomaria.lido@gmail.com
Martedì 09 aprile 2024
Ore 15:00, aula B, Dipartimento di Matematica e Fisica, Università di Roma Tre, Via della Vasca Navale 84, Roma
seminario di astrofisica
Mauro Centrone (INAF OAR)
Come (e perchè) creare nuove stelle
La turbolenza atmosferica rappresenta una sfida importante per le osservazioni astronomiche da terra ad elevata risoluzione spaziale, poiché comporta il movimento dell'immagine (tip-tilt) e la sfocatura dell'immagine (deformazioni del fronte d'onda di ordine superiore). I sistemi di ottica adattiva mirano a correggere queste distorsioni ma sono limitati a piccole aree intorno a stelle guida naturali sufficientemente luminose, il che si traduce in solo l'1% circa di copertura del cielo. Per aumentare questa percentuale, si utilizzano sistemi di ottica adattiva con stella guida laser. Nel seminario si descriverà come funzionano le stelle guida laser e perché oggi sono fondamentali per i grandi telescopi del mondo (presenti e futuri); infine verrà presentato lo stato attuale degli strumenti CaNaPy/ALASCA, che rappresentano lo stato dell'arte per ciò che riguarda l'utilizzo delle Stelle Laser, e per i quali l’INAF - Osservatorio Astronomico di Roma sta giocando un ruolo fondamentale.
Martedì 09 aprile 2024
Ore 15:30, Aula 34, Dipartimento di Scienze Statistiche quarto piano, Dipartimento di Scienze Statistiche
An afternoon on the spectral theory of pseudo-differential operators
József Lőrinczi (Alfred Rényi Institute, Budapest, Hungary)
Embedded eigenvalues for a class of non-local Schrödinger operators
Generally, the spectrum of a non-local Schrödinger operator may be rather intricate, even when they are self-adjoint operators. In this talk I plan to discuss some explicit cases when positive or zero eigenvalues occur, and also address the problem more generally, aiming to describe potentials which can give rise to zero eigenvalues for massive or massless (fractional) relativistic Schrodinger operators. If time permits, I intend to explain how random processes with jumps can be used to analyse such properties.
Per informazioni, rivolgersi a: enrico.scalas@uniroma1.it
Martedì 09 aprile 2024
Ore 16:00, Aula "Dal Passo", Dipartimento di Matematica, Università di Roma "Tor Vergata"
Seminario di Analisi Matematica
Luigi Appolloni (University of Leeds)
Some existence results for the nonlinear Schrödinger equation on Riemannian manifolds
Over the last few decades, the study of the nonlinear Schrödinger equation on \(\mathbb{R}^N\) has been investigated by numerous researchers. However, very few results are known when the domain is non-Euclidean. In this talk, we will see some recent results regarding the existence and multiplicity of solutions for the nonlinear Schrödinger equation on non-compact Riemannian manifolds. In particular, we will focus our attention to the interplay between the necessary assumptions on the potential in the Schrödinger operator and those on the manifold.
NB: This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C23000330006.
Per informazioni, rivolgersi a: molle@mat.uniroma2.it
Martedì 09 aprile 2024
Ore 17:30, Aula Picone, Dipartimento di Matematica, Sapienza Università di Roma
YAMS - Young Algebraist Meetings in Sapienza
Matteo Micheli (Sapienza)
Some quiver grassmannians of Dynkin and Euclidean type A
In this talk we explore a few quiver grassmannians for the equioriented type A Dynkin quiver and for the equioriented cycle. These include the complete flag variety and its PBW degeneration, as well as finite dimensional approximations of the degenerate affine grassmannian and of the degenerate affine flag variety.
Per informazioni, rivolgersi a: sabino.ditrani@uniroma1.it
Mercoledì 10 aprile 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 10 aprile 2024
Ore 14:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Algebra e Geometria
Erwan Rousseau (Université de Bretagne Occidentale)
A generalization of the Bloch-Ochiai theorem
The classical Bloch-Ochiai theorem states that a complex projective manifold with irregularity larger than its dimension has no Zariski dense entire curve. I will present a generalization of this theorem in the setting of pairs. (Joint work with S. Kebekus).
Mercoledì 10 aprile 2024
Ore 14:30, Aula Dal Passo, Dipartimento di Matematica, Tor Vergata
Seminario
Federico Camia (NYU Abu Dhabi)
Towards a logarithmic conformal field theory of 2D critical percolation
Conformal field theory (CFT) provides a very powerful framework to study the large-scale properties of models of statistical mechanics at their critical point. The prototypical example of this is the continuum (scaling) limit of the two-dimensional critical Ising model. The case of critical percolation is more difficult, partly because its continuum limit is believed to be described by a relatively unusual type of CFT, called a logarithmic CFT. In this talk, I will first briefly explain the statements above. I will then present some recent results and work in progress that are part of a program aimed at fitting percolation within the logarithmic CFT framework.
Per informazioni, rivolgersi a: salvi@mat.uniroma2.it
Mercoledì 10 aprile 2024
Ore 15:30, Aula Dal Passo, Dipartimento di Matematica, Tor Vergata
Seminario
Alessandra Bianchi (Università di Padova)
Mixing cutoff for simple random walks on the Chung-Lu directed graph
In this talk, we consider a simple random walk defined on a Chung-Lu directed graph, an inhomogeneous random network that extends the Erdos Renyi random digraph by including edges independently according to given Bernoulli laws. In this non-reversible setting, we will focus on the convergence toward the equilibrium of the dynamics. In particular, under the assumption that the average degree grows logarithmically in the size n of the graph (weakly dense regime), we will establish a cutoff phenomenon at the entropic time of order log(n)/loglog(n). We will then show that on a precise window the cutoff profile converges to the Gaussian tail function. This is qualitatively similar to what was proved in a series of works by Bordenave, Caputo, Salez for the directed configuration model, where degrees are deterministically fixed. In terms of statistical ensembles, this analysis provides an extension of these cutoff results from a hard to a soft-constrained model. Joint work with G. Passuello.
Per informazioni, rivolgersi a: salvi@mat.uniroma2.it
Mercoledì 10 aprile 2024
Ore 16:00, Aula M3, Dipartimento di Matematica e Fisica, Università Roma Tre
Junior seminar
Adrien Ragot (Universitè Paris Nord)
Realisability: from constructive proofs to program specification
In a first part - after recalling some basics of proof theory, namely what is a formal proof - we will introduce the key concept of Realisability. The Brouwer-Heyting-Kolmogorov (BHK) interpretation of proofs - originally formulated for intuistionistic logic - describes fundamental properties that should enjoy proofs. In particular it implies that the space in which proofs lives should be equipped with a product and a notion of interaction. Realisability is the implementation of the BHK-interpretation inside an untyped model of computation - first inside recursive function, variants of the lambda calculus and more recently in the context of linear logic in sets of permutations, operators on an Hilbert space, or weighted graphs. We will point out how the first versions of Realisability fall short if one wants to adopt an interactive approach and how this limit relates to consistency. We exhibit the existing modern solutions that constitutes Interactive Realisability, briefly we expose how interactive realisability is relevant for program specification. In a second part, we will present parts of our current work on Realisability for Linear Logic. We show how a simple algebraic structure, a polarized self-operand, is suited to realize multiplicative linear logic. We relate the problem of completeness in realisability to the correctness criterions of proof structures for Linear Logic. In order to study correctness, we present an algebraic framework of "path algebra" to study the connectedness and acyclicity of a graph. If times allow we will discuss in particular how one can handle second order quantifiers. Maggiori informazioni sul sito: http://ricerca.mat.uniroma3.it/seminari/junior_seminars.html
Mercoledì 10 aprile 2024
Ore 16:00, Aula d'Antoni, Dipartimento di Matematica, Università di Roma Tor Vergata
Seminario Algebre di Operatori
Fabio Ciolli (Università della Calabria)
Superselection theory as a covariant cohomology
Since 1976 J.E. Roberts introduced a non-Abelian 1-cohomology of charge-transporters on the Haag-Kaster networks, and as early as 1990 he proved that this cohomology gives a category equivalent to the one of the DHR sectors of the (Haag dual) net of the observables on the Minkowski d=1+3.In the DHR framework, the covariance of the sectors by the geometric symmetry is introduced through the vacuum representation and morphisms. Quite recently, with G. Ruzzi and E. Vasselli, motivated by theories on a globally hyperbolic spacetime and by sectors with electric charges, as in the analysis by Buchholz and Roberts, we introduced a novel cohomology covariant under the geometric symmetry, for simply connected spacetimes. I will discuss these recent results and some open problems about non-simply connected spacetimes. The Operator Algebra Seminar schedule is here: https://sites.google.com/view/oastorvergata/home-page?authuser=0
Mercoledì 10 aprile 2024
Ore 9:00, Aula 1B (RM002 Via Scarpa), Dipartimento di Scienze di Base e Applicate per l'Ingegneria
Seminario di Analisi Geometrica
Marco Radeschi (Università di Torino)
A Weyl's Law for Riemannian foliations
The famous Weyl's Law computes the dimension and volume of a closed Riemannian manifold from the eigenvalue growth of its Laplacian. Bruning-Heintze and Connelly extended this theorem to manifolds with isometric actions of compact Lie groups. In this talk, I will discuss a further generalization for manifolds with singular foliations by equidistant submanifolds. When the manifold is the round sphere, this reveals new connections between the geometry, analysis, and algebra of the foliation. This is a joint work with Ricardo Mendes and Samuel Lin.
Per informazioni, rivolgersi a: luigi.provenzano@uniroma1.it
Venerdì 12 aprile 2024
Ore 11:00, Aula Dal Passo, Dipartimento di Matematica, Università di Roma Tor Vergata
corso di dottorato
Martina Lanini (Tor Vergata)
Algebre di Hecke
Venerdì 12 aprile 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.
Venerdì 12 aprile 2024
Ore 14:30, Aula Dal Passo, Dipartimento di Matematica, U Roma Tor Vergata
Algebra and Representation Theory Seminar
Willem de Graaf (U Trento)
Classifying orbits of complex and real Vinberg representations
Vinberg representations are representations of algebraic groups that arise from a cyclic grading of a semisimple Lie algebra. In the literature, they are mainly known as theta-groups or Vinberg pairs. A distinguishing feature of these representations is that it is possible to classify the orbits of the algebraic group. We sketch how this can be done when the base field is the complex numbers. This mainly uses results of Vinberg of the 1970s. Then we describe techniques for classifying the orbits when the base field is the real numbers. This talk is based on joint work with Mikhail Borovoi, Hong Van Le, Heiko Dietrich, Marcos Origlia, and Alessio Marrani (part of the activity of the MIUR Excellence Department Project Mat-Mod@TOV (CUP E83C23000330006)).
Venerdì 12 aprile 2024
Ore 16:00, Aula Dal Passo, Dipartimento di Matematica, U Roma Tor Vergata
Algebra and Representation Theory Seminar
Grant Barkley (U Harvard)
Hypercube decompositions and combinatorial invariance for elementary intervals
The combinatorial invariance conjecture asserts that the Kazhdan-Lusztig (KL) polynomial of an interval [u,v] in Bruhat order can be determined just from the knowledge of the poset isomorphism type of [u,v]. Recent work of Blundell, Buesing, Davies, Velicković, and Williamson posed a conjectural recurrence for KL polynomials depending only on the poset structure of [u,v]. Their formula uses a new combinatorial structure, called a hypercube decomposition, that can be found in any interval of the symmetric group. We give a new, simpler, formula based on hypercube decompositions and prove it holds for "elementary" intervals: an interval [u,v] is elementary if it is isomorphic as a poset to an interval with linearly independent bottom edges. As a result, we prove combinatorial invariance for Kazhdan-Lusztig R-polynomials of elementary intervals in the symmetric group, generalizing the previously known case of lower intervals. This is a joint work with Christian Gaetz (part of the activity of the MIUR Excellence Department Project Mat-Mod@TOV (CUP E83C23000330006)).
Venerdì 12 aprile 2024
Ore 16:00, Aula Picone, Dipartimento di Matematica, Sapienza Università di Roma
Seminari per i docenti A.A. 2023-2024
Giuseppe Accascina, Giovanni Margiotta, et al.
Dalle immagini ai modelli in geometria 3D. Esempi di attività
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