Notiziario Scientifico
a cura del Dipartimento di Matematica Guido Castelnuovo, Sapienza Università di Roma
Settimana dal 11-03-2024 al 17-03-2024
Lunedì 11 marzo 2024
Ore 14:30, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Analisi Matematica
Alessandro Pigati (Università Bocconi)
Topology of three-dimensional Ricci limits and RCD spaces
Starting from the second half of the nineteenth century, it was understood that curvature, which is infinitesimal (geo)metric information on a space, integrates to give global structure results (in spite of its nonlinear nature), specifically yielding topological rigidity of the space. It was further observed by Gromov that a lower bound on the Ricci curvature is the essential ingredient in order to control the number of degrees of freedom at a metric level as well, allowing to compactify (in a very weak sense) the set of n-dimensional Riemannian manifolds obeying a Ricci lower bound. It was later understood that singular spaces belonging to this compactification (Ricci limits), are special cases of a more general analytic notion (RCD spaces), more stable with respect to certain natural operations, and thus they also inherit a rich analytic structure, allowing to do calculus on them. In this talk, based on joint work with Elia Bruè and Daniele Semola, we will review some previously known structural results for Ricci limits and RCDs in the non-collapsed case, as well as some instructive examples and counterexamples, and we will see a new, more elementary proof that Ricci limits of dimension three are generalized manifolds, enjoying in particular uniform contractibility. Our tools, together with some results in geometric topology, give an alternative proof that they are in fact topological manifolds. We will also see a new result for tangent cones in higher dimension. If time allows, we will also mention a new structural theorem for RCDs in dimension three. 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 11 marzo 2024
Ore 15:30, Sala delle Bandiere, Sezione di Matematica - Uninettuno
Daniele Funaro, Artur Ishkhanyan, Enzo Orsingher
Special Functions in Mathematical Physics
Lunedì 11 marzo 2024
Ore 16:00 (Attenzione al cambio di orario!), Aula 4, Dipartimento di Matematica, Sapienza Università di Roma
corso di dottorato
Guido Pezzini (Sapienza)
Algebre di Hecke
Martedì 12 marzo 2024
Ore 14:30, aula D'Antoni, Dipartimento di Matematica, Università di Roma Tor Vergata
seminario di Geometria
Andrea Di Lorenzo (Humboldt University (Berlin))
The importance of being a weighted blow-up
Blow-ups are fundamental tools in algebraic geometry, and there are several results (e.g the famous Castelnuovo's theorem) that can be used to determine when a variety is obtained as a blow-up of a smooth variety along a smooth center. Weighted blow-ups play a similar role for stacks. In this talk I will present a criterion for finding out if a smooth DM stack is a weighted blow-up. I will apply this result for showing that certain alternative compactifications of moduli of marked elliptic curves are obtained via weighted blow-ups (and blow-downs). This in turn will prove to be useful in order to compute certain invariants, like Chow rings or Brauer groups. First part of this talk is a joint work with Arena, Inchiostro, Mathur, Obinna and Pernice; the second part of this talk is a joint work with L. Battistella.
Per informazioni, rivolgersi a: guidomaria.lido@gmail.com
Martedì 12 marzo 2024
Ore 17:30, Aula Picone, Dipartimento di Matematica "G.Castelnuovo"
YAMS - Young Algebraist Meetings in Sapienza
Luca Casarin (Sapienza - Università di Roma)
From derived categories to infinity categories
The goal of the talk will be to justify the use of infinity categories in modern mathematics and to see some pros and cons when working with such objects. The theory has been around for some time and it was fully developed in Jacob Lurie's works "Higher Topos Theory" and "Higher Algebra". It is notably technical and therefore we will only provide an intuitive exposition. We will start with the more familiar theory of derived/triangulated categories and see some of the undesired behaviours that it inherently has. We will provide the definition of infinity category, stable infinity category and see how these kind of objects resolve some of the issues of derived categories. Time permitting we will discuss the following problem: given a differential graded commutative/associative algebra A (i.e. an algebra object in the category of chain complexes) and a quasi-isomorphic complex B is it possible to give to B some structure of a commutative/associative algebra? This will lead to the notion of a monoidal infinity category and algebra objects in it.
Per informazioni, rivolgersi a: yamsapienza@gmail.com
Mercoledì 13 marzo 2024
Ore 10:00, Aula E, Dipartimento di Matematica, Sapienza Università di Roma
corso di dottorato
Guido Pezzini (Sapienza)
Algebre di Hecke
Mercoledì 13 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 surfaces in homogenous Bézier form: Week 3 o Triangular Bézier form, weight points and lines, reparametrizations o Complimentary segments, base curves, projective de Casteljau algorithm o Rational de Casteljau algorithm, dual Bézier form, offset surfaces o C^k constructions, free form spline surfaces, projective structures o Ruled and developable surfaces: lines of regression, class and degree o Primal and dual representation, joining developable surfaces smoothly o Developable surfaces with cubic duals
Il materiale del corso è raccolto in un canale teams dedicato a cui gli interessati possono essere aggiunti scrivendo a manni@mat.uniroma2.it
Mercoledì 13 marzo 2024
Ore 14:00, Aula 1B1, RM002, Via A.Scarpa 16, Dipartimento SBAI, Sapienza Università di Roma
Seminario di PDE e Analisi Geometrica
Alberto Enciso (ICMAT, Madrid, Spagna)
The fearful symmetry of Neumann eigenfunctions
We will discuss some recent results and open problems on the spectral geometry of planar domains that exhibit certain geometric properties. We will be mostly interested in how the “roundness” of the domain may have a qualitative impact (or not) on the structure of the eigenfunctions. Simple geometric ideas will be emphasized throughout
Per informazioni, rivolgersi a: massimo.grossi@uniroma1.it
Mercoledì 13 marzo 2024
Ore 14:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Algebra e Geometria
Dror Varolin (Stony Brook)
Metric Positivity for Holomorphic Vector Bundles
Holomorphic line bundles play many important roles in complex analytic geometry. In the higher rank case, much less is known, but there have been important advances in the last 15 years. After a review of notions of positivity and their consequences, I will discuss some of the more recent results in the subject, often comparing with the rank-1 case.
Mercoledì 13 marzo 2024
Ore 14:15, online (zoom), registrazione disponibile alla pagina https://indico.gssi.it/event/410/
ciclo Mathematical Challenges in Quantum Mechanics
Søren Fournais (Università di Copenhagen, Danimarca)
The dilute Bose gas at positive temperature
In this talk, I will report on recent work concerning the free energy of the dilute Bose gas in the case of strong interactions. In particular hard sphere potentials are allowed. When combining recent progress on Neumann bracketing for this many-body problem with the “completion-of-the-square” approach used previously on the hard-sphere case at zero-temperature, one obtains a short and simple proof of a lower bound for the free energy in the dilute limit up to temperatures of magnitude ρ a. Here ρ is the particle density and a is the scattering length of the interaction. This is joint work with T. Girardot, L. Junge, L. Morian, M. Olivieri, and A. Triay.
Per informazioni, rivolgersi a: monaco@mat.uniroma1.it
Mercoledì 13 marzo 2024
Ore 16:00, Aula Dal Passo, Dipartimento di Matematica, Università di Roma Tor Vergata
Seminario di Algebre di Operatori
Boris Bolvig Kjær (University of Copenhagen)
The double semion model in infinite volume
According to physics literature, topologically ordered gapped ground states of 2-dimensional spin systems can be described by a topological quantum field theory. Many examples arise from microscopic models with local commuting projector Hamiltonians, namely Levin-Wen models. In this talk, I will describe the general framework for classifying infinite volume gapped ground states (by Naaijkens, Ogata, et.al.) in the simple context of abelian Levin-Wen models. This framework is heavily inspired by the DHR analysis in relativistic quantum field theory. It applies to the doubled semion model whose anyon theory is a braided fusion category equivalent to the representation category of the twisted Drinfeld double of Z_2. Based on joint work with Alex Bols and Alvin Moon, https://arxiv.org/abs/2306.13762. Seminar schedule here: https://sites.google.com/view/oastorvergata/home-page.
Mercoledì 13 marzo 2024
Ore 16:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
seminario di Fisica Matematica
Jacob Shapiro (Princeton)
Classification of disordered insulators in 1D
In this talk I will describe some of the mathematical aspects of disordered topological insulators. These are novel materials which insulate in their bulk but (may) conduct along their edge; the quintessential example is that of the integer quantum Hall effect. What characterizes these materials is the existence of a topological index, experimentally measurable and macroscopically quantized. Mathematically this is explained by applying algebraic topology to the space of appropriate quantum mechanical Hamiltonians; I will survey some recent results mainly concentrating on the classification problem in one dimension, where the problem reduces to studying spaces of unitaries (resp. orthogonal projections) which essentially-commute with a fixed projection. Joint with Jui-Hui Chung.
Finanziato dall'Unione europea – Next Generation EU.
Per informazioni, rivolgersi a: domenico.monaco@uniroma1.it
Giovedì 14 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 surfaces in homogenous Bézier form: Week 3 o Triangular Bézier form, weight points and lines, reparametrizations o Complimentary segments, base curves, projective de Casteljau algorithm o Rational de Casteljau algorithm, dual Bézier form, offset surfaces o C^k constructions, free form spline surfaces, projective structures o Ruled and developable surfaces: lines of regression, class and degree o Primal and dual representation, joining developable surfaces smoothly o Developable surfaces with cubic duals
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 14 marzo 2024
Ore 14:15, Aula M1, Dipartimento di Matematica e Fisica, Università Roma Tre
Seminario di Geometria
Francesco Ballini (Oxford)
Unlikely Double Intersections
The Zilber-Pink Conjecture, which should rule the behaviour of intersections between an algebraic variety and a countable family of "special varieties", does not take into account double intersections; some results related to tangencies with special subvarieties have been obatined by Marché-Maurin in 2014 in the case of the square of the multiplicative group and by Corvaja-Demeio-Masser-Zannier in 2019 in the case of elliptic schemes. We prove that any algebraic curve contained in \(Y(1)^2\) is tangent to finitely many modular curves (which are the one-codimensional special subvarieties) and, together with Capuano, we generalize the result of Marché-Maurin to arbitrary powers of the multiplicative group. No previous knowledge of the topic is required: we will explain the general Zilber-Pink Conjecture philosophy, we will describe the main tools used in this context and we will see what are the differences in the double intersection case.
Per informazioni, rivolgersi a: amos.turchet@uniroma3.it
Giovedì 14 marzo 2024
Ore 14:30, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
P(n)/N(p) : Problemi differenziali nonlineari/Nonlinear differential problems
Fabio Punzo (Politecnico di Milano)
A general nonlinear characterization of stochastic incompleteness
The talk is concerned with the equivalence between stochastic incompleteness of a Riemannian manifold and the existence of nonnegative, nontrivial bounded solutions to certain semilinear elliptc equations with a general nonlinearity, posed on the manifold. We also discuss the conncection with nonuniqueness of nonnegative bounded solutions to the filtration equation. Such results have been obtained jointly with Gabriele Grillo, Kazuhiro Ishige and Matteo Muratori.
Per informazioni, rivolgersi a: galise@mat.uniroma1.it
Giovedì 14 marzo 2024
Ore 16:00, Aula C, Dipartimento di Scienze, Università Roma Tre, Via della Vasca Navale 84
Seminario di Matematiche Complementari
Marco Liverani (Università Roma Tre)
Calcolo e calcolabilità. Approcci contemporanei e prospettive per l'insegnamento elementare della matematica
La "teoria della calcolabilità" si occupa di distinguere ciò che può essere calcolato per via automatica da ciò che invece non può essere calcolato per via automatica. I modelli di Von Neumann, Turing e Church servivano, prima ancora di poter disporre materialmente di strumenti di calcolo automatico, a ragionare sulla possibilità di risolvere automaticamente qualsiasi problema o meno. Con ragionamenti per nulla semplici si arriva così a dimostrare che esistono dei problemi che non possono essere risolti attraverso strumenti automatici (come la macchina di Turing, ad esempio). Quale impatto può avere questa prospettiva teorica novecentesca su un insegnamento elementare della matematica rinnovato? Nelle scuole primarie ancora le ore di matematica ruotano attorno al calcolo, e le operazioni in colonna, che sono uno dei più antichi esempi di algoritmo (si descrivono in un celebre trattato del matematico al-Khwarizmi dal cui nome deriva questo termine) costituiscono ancora per ogni alunno il primo contatto con la matematica, parte della biografia matematica di coloro che trovano in aula i docenti delle scuole secondarie. Nel seminario, con il quale il Seminario Enriques festeggia il giorno de pi greco, si offrono alcuni spunti su tale prospettiva, quale condizione di ogni proposta susseguente di innovazione didattica. Nel libro Qual'è il problema? (per la casa editrice Mimesis) ho affrontato alcuni temi relativi a problemi che invece sono calcolabili. Si potrebbe dire: per chi progetta algoritmi, i problemi non calcolabili non sono affatto interessanti! Piuttosto è interessante, nell'ambito dei problemi calcolabili, distinguere tra problemi facilmente (velocemente) calcolabili e problemi che, pur essendo calcolabili, richiedono tempi enormi (giorni, mesi, anni, milioni di anni, ...). Di questo si occupa l'analisi della complessità computazionale di un problema o di un algoritmo (da qui vengono fuori le classi di complessità P, NP, NP-completi, ...).
Per informazioni, rivolgersi a: paola.magrone@uniroma3.it
Giovedì 14 marzo 2024
Ore 16:00, Sala di Consiglio (e anche a distanza, tramite la piattaforma Zoom), Dipartimento di Matematica, Sapienza Università di Roma
Seminari di Ricerca in Didattica della Matematica
Claudio Bernardi (Sapienza Università di Roma)
Teoremi, dimostrazioni, assiomi, teorie assiomatiche. Riflessioni logiche e didattiche.
Per informazioni, rivolgersi a: annalisa.cusi@uniroma1.it
Venerdì 15 marzo 2024
Ore 14:30, Aula Dal Passo, Dipartimento di Matematica, U Roma Tor Vergata
Algebra and Representation Theory Seminar
Anna Michael (U Magdeburg)
Folded galleries --- a museum tour through 192 years of math history
Folded galleries, as introduced by Peter Littelmann in the 1990s, are combinatorial objects related to certain (subsets of) elements of Coxeter groups. They have shown to have versatile applications in algebra and geometry, making them an object of interest for current research. In this talk, we will retrace the roots of their invention 192 years back in history, contemplate colorful illustrations of examples, and discover open questions for future applications.
Venerdì 15 marzo 2024
Ore 16:00, Aula Dal Passo, Dipartimento di Matematica, U Roma Tor Vergata
Algebra and Representation Theory Seminar
Christophe Hohlweg (U Montréal)
Shi arrangements in Coxeter groups
Given an arbitrary Coxeter system (W,S) and a nonnegative integer m, the m-Shi arrangement of (W, S) is a subarrangement of the Coxeter hyperplane arrangement of (W,S). The classical Shi arrangement (m = 0) was introduced in the case of affine Weyl groups by Shi to study Kazhdan-Lusztig cells for W. As two key results, Shi showed that each region of the Shi arrangement contains exactly one element of minimal length in W and that the union of their inverses form a convex subset of the Coxeter complex. The set of m-low elements in W were introduced to study the word problem of the corresponding Artin-Tits (braid) group and they turn out to produce automata to study the combinatorics of reduced words in W. In this talk, I will discuss how to extend Shi’s results to any Coxeter system and show that the minimal elements in each Shi region are in fact the m-low elements. This talk is based on joint work with Matthew Dyer, Susanna Fishel, and Alice Mark.
Venerdì 15 marzo 2024
Ore 16:00, Aula Picone, Dipartimento di Matematica, Sapienza Università di Roma
Seminari per i docenti A.A. 2023-2024
Nicoletta Lanciano (Sapienza Università di Roma)
La catalogazione dei materiali della Biblioteca Emma Castelnuovo
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.
Coloro che desiderano ricevere questo notiziario via e-mail sono pregati
di comunicare il proprio indirizzo di posta elettronica a
seminari@mat.uniroma1.it.