Notiziario Scientifico

Notiziario dei seminari di carattere matematico
a cura del Dipartimento di Matematica Guido Castelnuovo, Sapienza Università di Roma

Settimana dal 06-02-2023 al 12-02-2023

Lunedì 06 febbraio 2023
Aula Magna di Giurisprudenza (Via Ostiense, 161)
Convegno ERC
Universality in Condensed Matter and Statistical Mechanics
Schedule:

9:00-9:45 Antti Kupiainen (Helsinki) Bootstrapping Liouville Theory
9:50-10:35 Nathanael Berestycki (Vienna) Weyl law in Liouville quantum gravity
coffee break
11:10-11:55 Sébastien Ott (Fribourg) Asymptotic expansions in spin O(N) models via reﬂection positivity
12:00-12:45 Clement Erignoux (INRIA Lille Nord) Symmetric and asymmetric hydrodynamics for the facilitated exclusion process via mapping
lunch break
14:50-15:35 Daniel Ueltschi (Warwick) Characterising extremal Gibbs states
15:40-16:25 Florian Theil (Warwick) Dislocation structures and the Read-Shockley law
coffee break
17:00-17:45 Cyrill Muratov (Pisa) Magnetic skyrmions under conﬁnement
17:50-18:35 Simone Warzel (TUM Munich) The Spectral Gap and Low-Energy Spectrum in Mean-Field Quantum Spin Systems

Webpage https://tinyurl.com/UniCoSM23

Lunedì 06 febbraio 2023
Ore 14:30, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
seminario di Analisi Matematica
Andrea Marchese (Università degli Studi di Trento)
Generic uniqueness for the Plateau problem
In [Inv. Math., 1978], Morgan proved that almost every curve in R^3 is the boundary of a unique area minimizing surface. I will show how to extend Morgan's result to surfaces of any dimension and codimension. The result follows from the generic existence of boundary points with density 1/2, which exploits a boundary regularity theorem recently proved by De Lellis, De Philippis, Hirsch and Massaccesi. The argument to deduce the generic uniqueness combines a general unique continuation principle with Almgren's celebrated regularity theory, ensuring that the singular set of any area minimizing current has codimension at least two and therefore it cannot disconnect the regular part. I will then explain how to prove a generic uniqueness result for a Plateau-type problem studied in optimal transport, even if the singular set has only codimension one.
Per informazioni, rivolgersi a: azahara.delatorrepedraza@uniroma1.it

Martedì 07 febbraio 2023
Aula Magna di Giurisprudenza (Via Ostiense, 161)
Convegno ERC
Universality in Condensed Matter and Statistical Mechanics
Schedule:

9:00-9:45 Hugo Duminil-Copin (IHES and Geneva) Scaling relations for the planar random-cluster model
9:50-10:35 Christophe Garban (Lyon 1) Surface law and charge rigidity for the Coulomb gas on Z^d
coffee break
11:10-11:55 Domenico Monaco (Roma Sapienza) Purely linear response of the quantum Hall current to space-adiabatic perturbations
12:00-12:45 Marco Falconi (Politecnico Milano) A Quantum detour: regularizing classical electrodynamics by means of QED
lunch break
14:50-15:35 Sergio Conti (Bonn) Modeling of dislocations: from discrete models to the line-tension limit
15:40-16:25 Adriana Garroni (Roma Sapienza) Variational approach for grain boundaries
coffee break
17:00-17:45 Davide Fermi (Politecnico Milano) Periodic striped states in Ising models with dipolar interactions
17:50-18:35 Felix Otto (MPI Leipzig) Universality of the magnetization ripple: A singular SPDE-perspective

Webpage https://tinyurl.com/UniCoSM23

Martedì 07 febbraio 2023
Ore 14:30, Aula Dal Passo, Dipartimento di Matematica, Università di Roma Tor Vergata
seminario di Geometria
Stefano Trapani (Università di Roma Tor Vergata)
Varietà debolmente Kahler iperboliche
Nel 1991 Michael Gromov ha introdotto la nozione di varietà Kahler iperbolica, una varietà Kahler iperbolica è una varietà complessa compatta X dotata di una forma di Kahler \(\omega\) tale che il pull back \(\tilde{\omega}\) di \(\omega\) sul rivestimento universale sia esatta con una primitiva limitata rispetto allo stesso \(\tilde\omega\). Gromov prova molte proprietà delle varietà Kahler iperboliche studiando la teoria spettrale dell operatore di Laplace. In particolare prova che X è di tipo generale e che non esistono mappe olomorfe non costanti da C in X (cioè X è Kobayashi iperbolica). In questo lavoro generalizziamo la nozione di varietà Kahler iperbolica ammettendo una classe di coomologia \(\omega\) che sia big e nef e non necessariamente Kahler. Questa nozione è più adatta allo studio birazionale di X. Noi proviamo che tali varietà sono di tipo generale, che per tali varietà la congettura di Green-Griffiths è vera (cioè tutte le mappe olomorfe da C ad X hanno immagine contenuta in una fissata sottovarietà propria) e che tutte le sottovarietà (anche singolari) di varietà Kahler iperboliche sono di tipo generale. Cercherò di esporre varie tecniche usate per passare da classi Kahler a classi big e nef come la teoria spettrale, il luogo non Kahler di una classe big, le correnti di Ahlfors e le equazioni di Monge Ampere complesse.
Per informazioni, rivolgersi a: guidomaria.lido@gmail.com

Martedì 07 febbraio 2023
Ore 15:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Modellistica Differenziale Numerica
Raphaël Loubère (Université de Bordeaux)
Entropy stable and positivity preserving Godunov-type schemes for multidimensional hyperbolic systems on unstructured grid
This talk describes a novel subface flux-based Finite Volume (FV) method for discretizing multi-dimensional hyperbolic systems of conservation laws of general unstructured grids. The subface flux numerical approximation relies on the notion of simple Eulerian Riemann solver introduced in the seminal work by Gallice in 2003. The Eulerian Riemann solver is constructed from its Lagrangian counterpart by means of the Lagrange-to-Euler mapping. This systematic procedure ensures the transfer of good properties such as positivity preservation and entropy stability. In this framework, the conservativity and the entropy stability are no more locally face-based but result respectively from a node-based vectorial equation and a scalar inequation. The corresponding multi-dimensional FV scheme is characterized by an explicit time step condition ensuring positivity preservation and entropy stability. The application to gas dynamics provides an original multi-dimensional conservative and entropy-stable FV scheme wherein the numerical fluxes are computed through a nodal solver which is similar to the one designed for Lagrangian hydrodynamics. The robustness and the accuracy of this novel FV scheme are assessed through various numerical tests. We observe its insensitivity to the numerical pathologies that plague classical face-based contact discontinuity preserving FV formulations.

Martedì 07 febbraio 2023
Ore 16:00, Aula Dal Passo, Dipartimento di Matematica, Università di Roma "Tor Vergata"
Seminario di Analisi Matematica
David Ruiz (Universidad de Granada)
Symmetry results for compactly supported solutions of the 2D steady Euler equations
In this talk we present some recent results regarding compactly supported solutions of the 2D steady Euler equations. Under some assumptions on the support of the solution, we prove that the streamlines of the flow are circular. The proof uses that the corresponding stream function solves an elliptic semilinear problem \( -\Delta \phi = f(\phi)\) with \(\nabla \phi=0\) at the boundary. One of the main difficulties in our study is that \( f \)can fail to be Lipschitz continuous near the boundary values. If \( f(\phi)\) vanishes at the boundary values we can apply a local symmetry result of F. Brock to conclude. Otherwise, we are able to use the moving plane scheme to show symmetry, despite the possible lack of regularity of \( f\). We think that such result is interesting in its own right and will be stated and proved also for higher dimensions. The proof requires the study of maximum principles, Hopf lemma and Serrin corner lemma for elliptic linear operators with singular coefficients.
Per informazioni, rivolgersi a: molle@mat.uniroma2.it

Martedì 07 febbraio 2023
Ore 16:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Modellistica Differenziale Numerica
Alessia Del Grosso (Université de Bordeaux)
Numerical simulation of geophysical flows using second-order and well-balanced Lagrange-Projection methods
In this talk we aim to describe well-balanced Lagrange-projection schemes that can be exploited for the numerical simulation of not only geophysical but also biological flows. In a few words, such methods are composed of two steps: first, the mathematical model is expressed in Lagrangian coordinates. Then, once the Lagrangian solution has been found, it is projected back into Eulerian coordinates. This strategy can also easily be interpreted as a splitting: the Lagrangian step takes into account the acoustic effects of the flow, while the projection step is dedicated to the transport phenomena. This kind of acoustic-transport splitting is of particular interest in many geophysical flows as it provides a natural time scale decomposition leading to very efficient implicit-explicit (IMEX) schemes. In particular, we focus on applications to sediment transport and stratified flows. Depending on the mathematical model, we either extend the well-balanced numerical method to second-order of accuracy or develop their IMEX version.

Mercoledì 08 febbraio 2023
Aula Magna di Giurisprudenza (Via Ostiense, 161)
Convegno ERC
Universality in Condensed Matter and Statistical Mechanics
Schedule:

9:00-9:45 Bruno Nachtergaele (UC Davis) Spectral gaps and spectral gap stability for quantum lattice systems
9:50-10:35 Vieri Mastropietro (Università di Milano) Chiral lattice gauge theory, anomaly cancellation and universality
coffee break
11:10-11:55 Robin Reuvers (Roma Tre) Ground state energy of dilute Bose and Fermi gases in 1D
12:00-12:45 Rafael Greenblatt (Roma Tor Vergata) Adiabatic evolution of low-temperature many-body systems
lunch break
14:50-15:35 Marcello Porta (SISSA Trieste) Edge Transport in Interacting Hall Systems
15:40-16:25 Margherita Disertori (Bonn) Phase transition in the Integrated Density of States of the Anderson model arising from a supersymmetric sigma model
coffee break
17:00-17:45 Slava Rychkov (IHES) Towards the critical point of 2d Ising model with Tensor network renormalization group

Webpage https://tinyurl.com/UniCoSM23

Mercoledì 08 febbraio 2023
Ore 14:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
seminario di Algebra e Geometria
Frédéric Touzet (IRMAR Université de Rennes 1)
A global Weinstein splitting theorem for holomorphic Poisson manifolds
After reviewing some basic properties of holomorphic Poisson geometry, we will present a decomposition result in the Kähler case: if a compact Kähler Poisson manifold has a compact symplectic leaf with finite fundamental group, then after passing to a finite étale cover, it splits as the product of the universal cover of the leaf and some other Poisson manifold. This can be viewed as a global analogue to a theorem due to Alan Weinstein describing local Poisson structures. Joint work with Stéphane Druel, Jorge Pereira and Brent Pym.
Per informazioni, rivolgersi a: diverio@mat.uniroma1.it

Mercoledì 08 febbraio 2023
Ore 14:30, In presenza all'IAC in via dei Taurini 19 a Roma, aula seminari 116, primo piano, e sul Canale Youtube dell'IAC https://www.youtube.com/watch?v=N1_e_eLoZqc, Istituto per le Applicazioni del Calcolo, Consiglio Nazionale delle Ricerche
Seminari Generali IAC 2023
Luca Galantucci (Istituto per le Applicazioni del Calcolo, Consiglio Nazionale delle Ricerche)
Dissipation anomaly in a turbulent quantum fluid
When the intensity of turbulence is increased (by increasing the Reynolds number, e.g. by reducing the viscosity of the fluid), the rate of the dissipation of kinetic energy decreases but does not tend asymptotically to zero: it levels off to a non-zero constant as smaller and smaller vortical flow structures are generated. This fundamental property, called the dissipation anomaly, is sometimes referred to as the zeroth law of turbulence. The question of what happens in the limit of vanishing viscosity (purely hypothetical in classical fluids) acquires a particular physical significance in the context of liquid helium, a quantum fluid which becomes effectively inviscid at low temperatures achievable in the laboratory. By performing numerical simulations and identifying the superfluid Reynolds number, here we show evidence for a superfluid analogue to the classical dissipation anomaly. Our numerics indeed show that as the superfluid Reynolds number increases, smaller and smaller structures are generated on the quantized vortex lines on which the superfluid vorticity is confined, balancing the effect of weaker and weaker dissipation.
Per informazioni, rivolgersi a: maya.briani@cnr.it

Mercoledì 08 febbraio 2023
Ore 16:00, Aula 1B, Palazzina B, Dipartimento SBAI, Sapienza Università di Roma
seminario di Analisi Armonica
Eiichi BANNAI (Kyushu University, Japan)
Explicit construction of exact unitary designs
This talk is based on the joint work with Yoshifumi Nakata, Takayuki Okuda and Da Zhao. The purpose of design theory is, for a given space \(M\), to find good finite subsets \(X\) of \(M\) that approximate the whole space \(M\) well. There are many design theories for various spaces \(M\). If \(M\) is the sphere \(S^{n-1}\) then such \(X\) are called spherical designs. If \(M\) is the unitary group \(U(d)\), then such \(X\) are called unitary designs. To begin with, we discuss spherical \(t\)-designs briefly. Then we define unitary \(t\)-designs in the unitary group \(U(d)\), and discuss some fundamental properties as well as a brief overview of the history of the study (Cf. Roy-Scott). The unitary \(t\)-designs are very much interested and studied in physics. Then I will present some of our recent results on unitary \(t\)-designs, including: (i) The classification of unitary \(t\)-groups (unitary \(t\)-designs that are groups), by Bannai-Navarro-Rizo-Tiep. (ii) Explicit constructions of certain unitary \(4\)-designs from certain unitary \(3\)-groups, by Bannai-Nakahara-Zhao-Zhu. The main purpose of this talk is to explain the explicit construction of unitary \(t\)-designs in \(U(d)\) for any \(d\) and \(t\) following Bannai-Nakata-Okuda-Zhao. The proof is given by the induction on \(d\). As a by-product, we can also obtain an explicit construction of spherical \(t\)-designs in \(S^{d-1}\) for any \(d\) and \(t\). We note that this result on explicit construction of unitary \(t\)-designs has been already applied to some practical problems in experimental physics in Nakata et al.

Mercoledì 08 febbraio 2023
Ore 17:00, Aula 1B, Palazzina B, Dipartimento SBAI, Sapienza Università di Roma
seminario di Analisi Armonica
Etsuko BANNAI (Kyushu University, Japan)
Euclidean tight design of \(\mathbb R^2\)
The concept of Euclidean \(t\)-design of \(\mathbb R^n\) was defined in the paper by Neumaier and Seidel in 1988 as a generalization of spherical designs. Delsarte and Seidel studied more precise properties of Euclidean design on a union of several spheres centered at the origin. In this talk I give a brief introduction to the general theory and will survey the current situation on the classification problem of tight Euclidean \(t\)-designs. As a new result, I will give the classification of tight Euclidean \(5\)-designs of \(\mathbb R^2\). There are a lot of them than expected before.

Giovedì 09 febbraio 2023
Ore 14:15, Aula M1, Dipartimento di Matematica e Fisica, Università Roma Tre
Seminario di Geometria
Angelina Zheng (Roma Tre)
Stable cohomology of moduli spaces of low-gonality curves
The moduli space \(\mathcal{M}_g\) of curves of genus \(g\) is a central object in algebraic geometry and our main goal is to study it from the point of view of one of the most important topological invariant, its rational cohomology. For \(g\geq5\), the rational cohomology of \(\mathcal{M}_g\) is still unknown and one way to approach this problem is by computing first the rational cohomology of some locus inside \(\mathcal{M}_g\), such as the trigonal one \(\mathcal{T}_g\). In the first part of the talk, we will study the rational cohomology of \(\mathcal{T}_g\). Specifically, we prove that, similarly to the cohomology of \(\mathcal{M}_g\), the cohomology ring of \(\mathcal{T}_g\) stabilizes and it coincides with the tautological ring within the stable range. This will be done by studying the natural embedding of trigonal curves in Hirzebruch surfaces and by using Gorinov-Vassiliev's method for the cohomology of complements of discriminants. In the second part, we will inspect what happens for curves, which are also embedded in Hirzebruch surfaces but have gonality different from 3. In particular I will discuss a joint work with Jonas Bergström which describes the stable cohomology of the moduli space of gonality 2 curves, embedded on a Hirzebruch surface of fixed degree, and how this moduli space relates to the one parametrizing hyperelliptic curves with marked points.
Per informazioni, rivolgersi a: amos.turchet@uniroma3.it

Giovedì 09 febbraio 2023
Ore 14:30, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
P(n)/N(p) : Problemi differenziali nonlineari/Nonlinear differential problems
Francescantonio Oliva (Università di Napoli Federico II)
First order terms in 1-Laplace problems involving general nonlinearities
We give a brief overview of 1-Laplace type problems and then we discuss Dirichlet problems involving general nonlinearities and first order terms. In this context existence and uniqueness (when expected) of BV-solutions are shown. Examples and regularizing effects will be discussed as well as the optimality of the results.
Per informazioni, rivolgersi a: galise@mat.uniroma1.it

Giovedì 09 febbraio 2023
Ore 15:00, Aula G (e anche a distanza, tramite la piattaforma Zoom), Dipartimento di Matematica, Sapienza Università di Roma
Seminari di Ricerca in Didattica della Matematica
Annalisa Cusi (Sapienza Università di Roma)
Quale futuro per l'insegnamento della matematica? Riflessioni dei docenti a partire dall'esperienza vissuta durante il periodo dell'emergenza Covid-19
In questo seminario presenterò i principali risultati di uno studio, realizzato in Francia, Israele, Italia e Germania, con l’obiettivo di riflettere sulle sfide che hanno caratterizzato l’esperienza di insegnamento-apprendimento della Matematica durante le diverse fasi dell’emergenza Covid-19, con particolare attenzione al periodo del lockdown che ha avuto inizio in marzo 2020. La prima fase dello studio ha coinvolto 700 docenti dei quattro Paesi (sia di scuola primaria che secondaria di primo e secondo grado), che, nel periodo marzo-aprile 2020, hanno partecipato all’indagine su base volontaria, rispondendo ad un questionario costituito da 22 domande a risposta aperta. Concentrandomi, in particolare, sui dati raccolti in Italia, presenterò i principali aspetti emersi grazie all’analisi qualitativa dei dati, in relazione ad alcuni fondamentali elementi che hanno caratterizzato la gestione della didattica a distanza all’inizio dell’emergenza. Combinando questi risultati con quelli emersi durante una seconda fase dello studio, condotta in febbraio-marzo 2021 attraverso interviste semi-strutturate realizzate con un gruppo di docenti che hanno risposto al questionario, condividerò alcune riflessioni sulle possibili influenze che l’esperienza di didattica a distanza potrà avere, in futuro, sui processi di insegnamento-apprendimento della Matematica, in particolare in relazione al tema cruciale della valutazione.
Per informazioni, rivolgersi a: Chi è interessato a partecipare a distanza può rivolgersi ad Annalisa Cusi (annalisa.cusi@uniroma1.it)

Giovedì 09 febbraio 2023
Ore 16:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Probabilità e Fisica Matematica
Daniel Ueltschi (University of Warwick)
Quantum spin chains, loop representations, dimerisation
In contrast to their classical counterparts, one-dimensional quantum spin systems are interesting, they have intriguing behaviour, and they are difficult to study. I will describe a family of systems with nearest-neighbour interactions and O(n) symmetry. Its ground state phase diagram is expected to have a rich structure. For large spins it is possible to prove the occurrence of dimerisation in an open domain. The proof involves a loop representation and the method of cluster expansions. This is joint work with Jakob Bjornberg, Peter Muhlbacher, and Bruno Nachtergaele.
Per informazioni, rivolgersi a: lorenzo.taggi@uniroma1.it

Venerdì 10 febbraio 2023
Ore 11:30, Aula Dal Passo, Dipartimento di Matematica, Università di Roma Tor Vergata
seminario di Crittografia
Massimiliano Sala (Università di Trento, CryptoLabTN)
Ransomware e crittografia: proprietà generale e un'esperienza personale
In questo seminario, rivolto principalmente a studenti di crittografia, si esaminerà il ruolo della crittografia nei ransomware. I ransomware sono attacchi informatici che puntano (tra le altre cose) a cifrare i computer vittime e chiedere un riscatto per la loro "liberazione" (ovvero, per fornire la chiave di decifratura). Sono estremamenti efficaci e molto diffusi, ma in realtà sono soggetti a vincoli pratici che si riflettono su proprietà matematiche che si possono dedurre e sfruttare. Nella prima parte del seminario esaminiamo il contesto generale e nella seconda parte spiegherò (in parte) la mia attività di decrittatura, compresa qualche tecnica che uso per liberare i computer delle aziende/enti che non intendono piegarsi al ricatto informatico.
Per informazioni, rivolgersi a: guidomaria.lido@gmail.com

Venerdì 10 febbraio 2023
Ore 14:00, Aula 10, edificio RM018 (aule di Ingegneria, Via del Castro Laurenziano), Dipartimento SBAI, Sapienza Università di Roma
Mini-corso
Felix Otto (MPI-MIS, Leipzig)
Stochastic homogenization and large-scale regularity
Lectures: 10/02 14:00, 15/02 10:00, 17/02 14:00, 22/02 10:00, 24/02 14:00 In this mini-course, I will introduce the concept of large-scale regularity in case of a linear elliptic equation (or system) with heterogeneous coefficients. It is based on a smallness (on average) of the potentials of the harmonic coordinates, and proceeds via an intrinsic Campanato iteration. I will then apply this to the case of a random heterogeneous coefficient field, sampled from a stationary and ergodic ensemble. I will try to be self-contained and closely follow Theorem 1 and Lemma 1 in Gloria, Neukamm, and Otto ``A regularity theory for random elliptic operators'', Milan J Math 2020.
Per informazioni, rivolgersi a: lorenzo.giacomelli@uniroma1.it

Venerdì 10 febbraio 2023
Ore 14:30, Aula "Roberta Dal Passo", Dipartimento di Matematica, Università degli Studi di Roma "Tor Vergata"
Algebra and Representation Theory Seminar
Maxim Gurevich (Technion - Israel Institute of Technology)
Positive decompositions for Kazhdan-Lusztig polynomials
A new algorithmic approach for computation of S_n Kazhdan-Lusztig polynomials, through their restriction to lower rank Bruhat intervals, was recently presented by Geordie Williamson and DeepMind collaborators. In a joint work with Chuijia Wang we fit this hypercube decomposition into a general framework of a parabolic recursion for Weyl group Kazhdan-Lusztig polynomials. We also show how the positivity phenomena of Dyer-Lehrer and Grojnowski-Haiman come into play in such decompositions. Staying in type A, I will explain how the new approach naturally manifests through the KLR categorification of (dual) PBW and canonical bases.

Venerdì 10 febbraio 2023
Ore 16:00, Aula "Roberta Dal Passo", Dipartimento di Matematica, Università degli Studi di Roma "Tor Vergata"
Algebra and Representation Theory Seminar
Mario Marietti (Università di Ancona)
Towards Combinatorial Invariance: Kahdan--Lusztig R-polynomials
Kazhdan–Lusztig (KL) polynomials play a central role in several areas of mathematics. In the 80's, Dyer and Lusztig, independently, formulated the Combinatorial Invariance Conjecture (CIC), which states that the KL polynomial associated with two elements u and v only depends on the poset of elements between u and v in Bruhat order. With the help of certain machine learning models, recently Blundell, Buesing, Davies, Velickovic, and Williamson discovered a formula for the KL polynomials of a Coxeter group W of type A, and stated a conjecture that implies the CIC for W (see [Towards combinatorial invariance for Kazhdan–Lusztig polynomials, Representation Theory (2022)] and [Advancing mathematics by guiding human intuition with AI, Nature 600 (2021)]. In this talk, I will present a formula and a conjecture about R-polynomials of W. The advantage in considering R-polynomials rather than KL polynomials is that the corresponding formula and conjecture are less intricate and have a dual counterpart. Our conjecture also implies the CIC. This is based on joint work with F. Brenti.

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