Notiziario Scientifico
a cura del Dipartimento di Matematica Guido Castelnuovo, Sapienza Università di Roma
Settimana dal 21-06-2021 al 27-06-2021
Lunedì 21 giugno 2021
Ore 10:00, Sala di Consiglio, Dipartimento di Matematica
Corso di dottorato - Lezione 3
Nathanael Berestycki (University of Vienna)
Introduction to Gaussian Free Field, Gaussian Multiplicative Chaos and Liouville Quantum Gravity
In recent years rigorous approaches to Liouville quantum gravity have been proposed and this has led to extraordinary progress in many different directions, including our understanding of large random planar maps. These approaches are based on the Gaussian free field and its associated Gaussian multiplicative chaos. I will introduce these notions and discuss several related themes, including (time-permitting): Liouville Brownian motion, the quantum zipper and the mating of trees theorem, and applications to random planar maps.
Per informazioni, rivolgersi a: silvestri@mat.uniroma1.it
Lunedì 21 giugno 2021
Ore 14:30, Sala di Consiglio e https://meet.google.com/nie-attq-ged, Dipartimento di Matematica
seminario di Analisi Matematica
Henri Berestycki (EHESS, Paris)
Segregation in predator-prey models and the emergence of territoriality
I report here on a series of joint works with Alessandro Zilio (Université de Paris) about systems of competing predators interacting with a single prey. We focus on the analysis of stationary states, stability issues, and the asymptotic behavior when the competition parameter becomes unbounded. Existence of solutions is obtained by a bifurcation theory type approach and the segregation analysis rests on a priori estimates and a free boundary problem. We discuss the classification of solutions by using spectral properties of the limiting system. Our results shed light on the conditions under which predators segregate into packs, on whether there is an advantage to have such hostile packs, and on comparing the various territory configurations that arise in this context. These questions lead us to nonstandard optimization problems.
Martedì 22 giugno 2021
Ore 15:30, Aula C, Dipartimento di Matematica, Sapienza Università di Roma
Seminario dei dottorandi
Lorenzo Pagani (Sapienza Università di Roma)
Class number problems in cyclotomic Zp-extensions
Understanding the ideal class group of a number field is a classical problem in algebraic number theory. Solving this problem is hard, especially if the discriminant of the field is large. However, we can get interesting results focusing on the p-part of the class group for a fixed prime p rather than focusing on the full group. In this talk, we give an overview of the main tools for studying this problem when the field is abelian. We present some interesting problems regarding the stabilization of the class groups of the fields appearing in cyclotomic Zp-extensions. Among these problems, we mainly focus on Greenberg's conjecture and we give some computational results about it.
Mercoledì 23 giugno 2021
Ore 10:30, Sala di Consiglio, Dipartimento di Matematica
Corso di Dottorato - Lezione 4
Nathanael Berestycki (University of Vienna)
Introduction to Gaussian Free Field, Gaussian Multiplicative Chaos and Liouville Quantum Gravity
In recent years rigorous approaches to Liouville quantum gravity have been proposed and this has led to extraordinary progress in many different directions, including our understanding of large random planar maps. These approaches are based on the Gaussian free field and its associated Gaussian multiplicative chaos. I will introduce these notions and discuss several related themes, including (time-permitting): Liouville Brownian motion, the quantum zipper and the mating of trees theorem, and applications to random planar maps.
Per informazioni, rivolgersi a: silvestri@mat.uniroma1.it
Mercoledì 23 giugno 2021 *** ATTENZIONE: CAMBIO DI ORARIO ***
Ore 14:30, Seminario telematico via Google Meet all'URL http://meet.google.com/jjt-toji-skw, Dipartimento di Matematica, Sapienza Università di Roma
seminario di Algebra e Geometria
Anna Wienhard (Universität Heidelberg)
Where geometry meets dynamics: groups, entropy and Hausdorff dimension
I will discuss geometric and dynamical properties of actions of discrete groups on Riemannian symmetric spaces. I will highlight some aspects of the interplay between geometry and dynamics, and present some recent results which generalize theorems of Sullivan, Bridgeman-Taylor, McMullen for convex cocompact subgroups acting on hyperbolic space in the framework of discrete subgroups of Lie groups of higher rank.
Per informazioni, rivolgersi a: diverio@mat.uniroma1.it
Mercoledì 23 giugno 2021
Ore 14:30, https://meet.google.com/pip-kvzt-fkz, Dipartimento di Fisica, Sapienza Università di Roma
Seminario delle Meccaniche
Lucio Russo (Università di Roma Tor Vergata) e Stefano Isola (Università di Camerino)
Quando è nata Ipazia? Un approccio probabilistico
Anche se nell’indagine storica può sembrare privo di senso fare esperimenti sulla base di una teoria preesistente, possono invece dimostrarsi sensate e utili forme di ragionamento tipiche delle scienze esatte come ausilio per accrescere il grado di affidabilità di una particolare affermazione riguardante un evento storico. In questo seminario discuteremo un approccio probabilistico al problema della datazione della nascita di un personaggio storico quando, su quell’evento, si disponga di un insieme di informazioni indirette, sotto forma di testimonianze su vari aspetti della sua vita. In particolare, dopo aver tradotto ogni testimonianza, se ritenuta affidabile, in una distribuzione di probabilità sull’anno di nascita, illustreremo come ottenere una distribuzione di probabilità complessiva che tenga conto della possibilità che alcune delle testimonianze siano false. Il metodo è applicato alla controversa data di nascita della scienziata alessandrina Ipazia, dimostrandosi assai efficace.
Mercoledì 23 giugno 2021
Ore 16:15, Zoom Meeting https://uniroma1.zoom.us/j/84577577400?pwd=bVBKUjFVa0gvMkhBOFk4Wnd3bS9KQT09, Meeting ID: 845 7757 7400 Passcode: 694105, Dipartimento di Matematica, Sapienza Università di Roma
Seminari di Fisica Matematica
Jacob Shapiro (Princeton University)
Fredholm operators of topological insulators and their homotopies
Index theorems, i.e., expressing topological invariants of various systems in terms of Fredholm indices (a project pioneered by Jean Bellissard and collaborators in the 1990s) are extremely helpful because they allow homotopy arguments. After presenting the basics of Fredholm theory, I will show how this perspective allows one to connect invariants in various settings via homotopy, such as continuum and discrete space IQHE systems, as well as the mobility gapped (strongly disordered) IQHE and Z_2 systems.
Venerdì 25 giugno 2021
Ore 15:00, Seminario Telematico, link
Online Representation Theory Seminar
Oleksandr Tsymbaliuk (Purdue University - USA)
Shifted Yangians and quantum affine algebras revisited
In the first part of the talk, I will recall some basic results about shifted Yangians (and their trigonometric versions-the shifted quantum affine algebras), which first appeared in the work of Brundan-Kleshchev relating type A Yangians and finite W-algebras and have become a subject of renewed interest over the last five years due to their close relation to quantized Coulomb branches introduced by Braverman-Finkelberg-Nakajima.
In the second part of the talk, I will try to convince that the case of antidominant shifts (opposite to what was originally studied in the work of Brundan-Kleshchev in type A and of Kamnitzer-Webster-Weekes-Yacobi in general type) is of particular importance as the corresponding algebras admit the RTT realization (at least in the classical types).
In particular, this provides a conceptual explanation of the coproduct homomorphisms, gives rise to the integral forms of shifted quantum affine algebras, and also yields a family of (conjecturally) integrable systems on the corresponding Coulomb branches. As another application, the GKLO-type homomorphisms used to define truncated version of the above algebras provide a wide class of rational/trigonometric Lax matrices in classical types.
This talk is based on the joint works with Michael Finkelberg as well as Rouven Frassek and Vasily Pestun.
Le comunicazioni relative a seminari da includere in questo notiziario devono pervenire esclusivamente
mediante apposita form da compilare online, entro le ore 24 del giovedì precedente la settimana
interessata. Le comunicazioni pervenute in ritardo saranno ignorate.
Per informazioni, rivolgersi all'indirizzo di posta elettronica
seminari@mat.uniroma1.it.
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