Notiziario Scientifico
a cura del Dipartimento di Matematica Guido Castelnuovo, Sapienza Università di Roma
Settimana dal 06-05-2024 al 12-05-2024
Lunedì 06 maggio 2024
Ore 14:00, Aula M6, Dipartimento di Matematica e Fisica, Università di Roma 3, Lungotevere Dante 376, e via Teams al seguente link
seminario di Fisica Matematica
Zhituo Wang (Harbin Institute of Technology)
Constructive renormalizations of the 2-D Honeycomb-Hubbard model
In this talk I will present some recent progress on the construction of ground state of the two-dimensional Hubbard model, which is a prototypical model for studying phase transitions in quantum many-body systems. Using fermionic cluster expansions and constructive renormalization theory, we proved that the ground state of the 2-d Hubbard model on the honeycomb lattice with triangular Fermi surfaces is not a Fermi liquid in a mathematical precise sense (Salmhofer criterium). I will also discuss the crossover phenomenon in the 2D square lattice Hubbard model and universality. This presentation is based on the work CMP 401, 2569–2642(2023) and arXiv:2303.13628.
Lunedì 06 maggio 2024
Ore 14:30, Aula 1B/1 in via Scarpa 16, S.B.A.I.- Sapienza
Corso di dottorato
Ralf Schiffler (University of Connecticut)
Quiver Representations
This is the first lecture of the course financed by INDAM on "quiver representations". This course is an introduction to quivers and their representations, with a focus on applications to the representation theory of finite dimensional algebras. Topics covered in the course include: representations of quivers, direct sums, morphisms, kernels, exact sequences, projective and injective representations, Auslander-Reiten quiver, algebras, modules, idempotents, path algebras, Auslander-Reiten theory. We will use the language of category theory throughout the course.
Per informazioni, rivolgersi a: giovanni.cerulliirelli@uniroma1.it
Lunedì 06 maggio 2024
Ore 14:30, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
seminario di Analisi Matematica
María del Mar González (Universidad Autónoma de Madrid)
A gluing construction of singular solutions for a fully non-linear equation in conformal geometry
We produce complete, non-compact, Riemannian metrics with positive constant \(\sigma_2\)-curvature on a sphere of dimension \(n > 4\), with a prescribed singular set given by a disjoint union of closed submanifolds whose dimension is positive and strictly less than \((n−n−\sqrt 2)/2\). The \(\sigma_2\)-curvature in conformal geometry is defined as the second elementary symmetric polynomial of the eigenvalues of the Schouten tensor, which yields a fully non-linear PDE for the conformal factor. We show that the classical gluing method of Mazzeo-Pacard (JDG 1996) for the scalar curvature still works in the fully non-linear setting. This is a consequence of the conformal properties of the equation, which imply that the linearized operator has good mapping properties in weighted spaces. This is joint work with María Fernanda Espinal. 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 06 maggio 2024
Ore 14:30, Aula Dal Passo, Dipartimento di Matematica, Università di Roma Tor Vergata
Corso di dottorato
Alessio Bottini (University of Bonn)
Sheaves on hyper-Kähler manifolds
Abstract: Constructing hyper-Kähler manifolds is a hard problem. Up to deformation, all the known examples are built from moduli spaces of stable sheaves on a K3 (or abelian) surface. It is natural to wonder if moduli spaces of sheaves on high dimensional HK manifolds could be HK themselves. Already thirty years ago, Kobayashi and Verbitsky studied vector bundles on HK manifolds, and noticed that they have symplectic moduli spaces. Unfortunately, while on K3 surfaces the theory is well-understood, in high dimension it is much harder, and for now, we can handle only very special cases. In this course, I will describe the state of the art of the theory of sheaves on HK manifolds, focusing especially on the recent developments due to the works of Beckmann, Markman and O’Grady. I will start with a review of sheaves on K3 surfaces, and I will try to highlight the important properties which we want to generalize. Later, I will discuss the various classes of sheaves on HK manifolds, which emerge by trying to generalize from K3 surfaces. Lastly, I will discuss some explicit examples in dimension four.
Per informazioni, rivolgersi a: guidomaria.lido@gmail.com
Martedì 07 maggio 2024
Ore 10:30, sala conferenze , INdAM Piazzale Aldo Moro, 5 – Roma
LYSeMinar, Seminari of LYSM
Eitan TADMOR (University of Maryland and Fondation Sciences Mathématiques de Paris & Laboratoire Jacques-Louis Lions – CNRS – Sorbonne Université/Université Paris Cité)
Emergent Behavior in Alignment Dynamics
A fascinating aspect of collective dynamics is self-organization of small-scale interactions into high-order structures with larger-scale patterns. In different contexts these are clusters which take the form of flocks, swarms, consensus, synchronized states etc. In this talk I will survey recent mathematical developments in alignment dynamics, which is driven by the tendency of steering towards average headings. A main question of interest is how different alignment kernels affect the large-crowd, long-time dynamics. We discuss how short- vs. long-range interactions dictate the large-crowd emergent behavior, and the role of pressure away thermal equilibrium
Per informazioni, rivolgersi a: lysm.eu
Martedì 7 maggio 2024
Ore 11:00, aula D'Antoni, Dipartimento di Matematica, Università di Roma Tor Vergata
corso di dottorato
Martina Lanini (Tor Vergata)
Algebre di Hecke
Martedì 07 maggio 2024
Ore 14:30, aula D'Antoni, Dipartimento di Matematica, Università di Roma Tor Vergata
seminario di Geometria
Cinzia Casagrande (Università di Torino)
Fano 4-folds con fibrazioni razionali su 3-folds
Sia X una varietà di Fano liscia, complessa, di dimensione 4, e \(\rho(X)\) il suo numero di Picard. Inizieremo discutendo il seguente risultato: se \(\rho(X)>12\), allora X è un prodotto di superfici di del Pezzo; se \(\rho(X)=12\), allora X ha una contrazione razionale X-->Y dove Y ha dimensione 3. Una contrazione razionale è una mappa data da una successione di flips seguita da un morfismo suriettivo a fibre connesse, vedremo degli esempi espliciti. Poi discuteremo le proprietà geometriche delle Fano 4-folds che hanno una contrazione razionale su una 3-fold. Un obiettivo è di determinare il massimo numero di Picard di X, ed eventualmente di classicare i casi con numero di Picard grande. Un altro obiettivo è di usare questa descrizione geometrica per costruire nuovi esempi con rho grande; questo è un progetto in corso con Saverio Secci.
Per informazioni, rivolgersi a: guidomaria.lido@gmail.com
Martedì 07 maggio 2024
Ore 15:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Modellistica Differenziale Numerica
Eitan Tadmor (Fondations Sciences Mathematiques de Paris and University of Maryland)
Swarm-Based Gradient Descent Methods for Non-Convex Optimization
We discuss a novel class of swarm-based gradient descent (SBGD) methods for non-convex optimization. The swarm consists of agents, each is identified with position, x, and mass, m. There are three key aspects to the SBGD dynamics. (i) persistent transition of mass from agents at high to lower ground; (ii) mass-dependent marching in directions randomly aligned with gradient descent; and (iii) time stepping protocol which decreases with m. The interplay between positions and masses leads to dynamic distinction between 'leaders' and 'explorers': heavier agents lead the swarm near local minima with small time steps; lighter agents use larger time steps to explore the landscape in search of improved global minimum, by reducing the overall 'loss' of the swarm. Convergence analysis and numerical simulations demonstrate the effectiveness of SBGD method as a global optimizer.
Per informazioni, rivolgersi a: giuseppe.visconti@uniroma1.it
Martedì 07 maggio 2024
Ore 15:15 Aula d'Antoni, Dipartimento di Matematica, Università di Roma Tor Vergata
Corso di dottorato
Alessio Bottini (University of Bonn)
Sheaves on hyper-Kähler manifolds
Abstract: Constructing hyper-Kähler manifolds is a hard problem. Up to deformation, all the known examples are built from moduli spaces of stable sheaves on a K3 (or abelian) surface. It is natural to wonder if moduli spaces of sheaves on high dimensional HK manifolds could be HK themselves. Already thirty years ago, Kobayashi and Verbitsky studied vector bundles on HK manifolds, and noticed that they have symplectic moduli spaces. Unfortunately, while on K3 surfaces the theory is well-understood, in high dimension it is much harder, and for now, we can handle only very special cases. In this course, I will describe the state of the art of the theory of sheaves on HK manifolds, focusing especially on the recent developments due to the works of Beckmann, Markman and O’Grady. I will start with a review of sheaves on K3 surfaces, and I will try to highlight the important properties which we want to generalize. Later, I will discuss the various classes of sheaves on HK manifolds, which emerge by trying to generalize from K3 surfaces. Lastly, I will discuss some explicit examples in dimension four.
Per informazioni, rivolgersi a: guidomaria.lido@gmail.com
Mercoledì 8 maggio 2024
Ore 10:00, aula E, Dipartimento di Matematica, Sapienza Università di Roma
corso di dottorato
Martina Lanini (Tor Vergata)
Algebre di Hecke
Mercoledì 08 maggio 2024
Ore 10:00, Aula 1B/1, via Scarpa 16, S.B.A.I.- Sapienza
Corso di dottorato
Ralf Schiffler (University of Connecticut)
Quiver representations
This is the second lecture of the course financed by INDAM on "quiver representations". This course is an introduction to quivers and their representations, with a focus on applications to the representation theory of finite dimensional algebras. Topics covered in the course include: representations of quivers, direct sums, morphisms, kernels, exact sequences, projective and injective representations, Auslander-Reiten quiver, algebras, modules, idempotents, path algebras, Auslander-Reiten theory. We will use the language of category theory throughout the course.
Per informazioni, rivolgersi a: giovanni.cerulliirelli@uniroma1.it
Mercoledì 08 maggio 2024
Ore 14:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Algebra e Geometria
Gabriele Viaggi (Sapienza Università di Roma)
Hausdorff dimension of hyperconvex representations of surface groups
A discrete and faithful representation of a surface group in PSL(2,C) is said to be quasi-Fuchsian when it preserves a Jordan curve on the Riemann sphere. Classically these objects lie at the intersection of several areas of mathematics and have been studied (for example) using complex dynamics, Teichmüller theory, and 3-dimensional hyperbolic geometry. From a dynamical perspective, an important invariant of such representations is the Hausdorff dimension of the invariant Jordan curves (typically a very fractal object). It is elementary to see that this number is always at least 1. A celebrated result of Bowen establishes it is equal to 1 if and only if the quasi-Fuchsian representation is Fuchsian, that is, it is conjugate in PSL(2,R). I will first describe this classical picture and then report on recent joint work with James Farre and Beatrice Pozzetti where we prove a generalization of Bowen's result for the much larger class of hyperconvex representations of surface groups in PSL(d,C) (where d is arbitrary).
Mercoledì 08 maggio 2024
Ore 14:30, Aula Seminari (Palazzina RM004, via Antonio Scarpa 16), Dipartimento di Scienze di Base e Applicate per l'Ingegneria, Sapienza Università di Roma
Seminario di Analisi Matematica
Chérif Amrouche (Pau University)
Dirichlet problem for the Laplacian and the Bilaplacian in Lipschitz domains
We are interested here in questions related to the maximal regularity of solutions of elliptic problems with Dirichlet boundary condition (see [1]). For the last 40 years, many works have been concerned with questions when \( \Omega \) is a Lipschitz domain. Some of them contain incorrect results that are corrected in the present work. We give here new proofs and some complements for the case of the Laplacian (see [3]), the Bilaplacian ([2] and [6]) and the operator div \( A\nabla \) (see [5]), when \( A \) is a matrix or a function. And we extend this study to obtain other regularity results for domains having an adequate regularity. We give also new results for the Dirichlet-to-Neumann operator for Laplacian and Bilaplacian. Using the duality method, we can then revisit the work of Lions-Magenes [4], concerning the so-called very weak solutions, when the data are less regular. [1] C. Amrouche and M. Moussaoui. The Dirichlet problem for the Laplacian in Lipschitz domains. Submitted. See also the abstract in https://arxiv.org/pdf/2204.02831.pdf [2] B.E.J. Dahlberg, C.E. Kenig, J. Pipher and G.C. Verchota. Area integral estimates for higher order elliptic equations and systems. Ann. Inst. Fourier, 47-5, 1425–1461, (1997). [3] D. Jerison and C.E. Kenig. The Inhomogeneous Dirichlet Problem in Lipschitz Domains, J. Funct. Anal. 130, 161–219, (1995). [4] J.L. Lions and E. Magenes. Problèmes aux limites non-homogènes et applications, Vol. 1, Dunod, Paris, (1969). [5] J. Necas. Direct methods in the theory of elliptic equations. Springer Monographs in Mathematics. Springer, Heidelberg, (2012). [6] G.C. Verchota. The biharmonic Neumann problem in Lipschitz domains. Acta Math., 194-2, 217–279, (2005).
Mercoledì 08 maggio 2024
Ore 14:30 Aula d'Antoni, Dipartimento di Matematica, Università di Roma Tor Vergata
Corso di dottorato
Alessio Bottini (University of Bonn)
Sheaves on hyper-Kähler manifolds
Abstract: Constructing hyper-Kähler manifolds is a hard problem. Up to deformation, all the known examples are built from moduli spaces of stable sheaves on a K3 (or abelian) surface. It is natural to wonder if moduli spaces of sheaves on high dimensional HK manifolds could be HK themselves. Already thirty years ago, Kobayashi and Verbitsky studied vector bundles on HK manifolds, and noticed that they have symplectic moduli spaces. Unfortunately, while on K3 surfaces the theory is well-understood, in high dimension it is much harder, and for now, we can handle only very special cases. In this course, I will describe the state of the art of the theory of sheaves on HK manifolds, focusing especially on the recent developments due to the works of Beckmann, Markman and O’Grady. I will start with a review of sheaves on K3 surfaces, and I will try to highlight the important properties which we want to generalize. Later, I will discuss the various classes of sheaves on HK manifolds, which emerge by trying to generalize from K3 surfaces. Lastly, I will discuss some explicit examples in dimension four.
Per informazioni, rivolgersi a: guidomaria.lido@gmail.com
Mercoledì 08 maggio 2024
Ore 16:00, Aula Dal Passo, Dipartimento di Matematica, Università di Roma Tor Vergata
Seminario di Algebre di Operatori
Roberto Conti (Sapienza Università di Roma)
Positive definite Fell bundle maps
C*-algebraic bundles (nowadays simply called Fell bundles) were introduced by Fell at the end of the sixties as yet another tool to deal with the representation theory of locally compact groups. The reason why the related literature is still growing is probably due to the fact that they fit pretty well with various aspects of the theory of (twisted) actions (and coactions) of groups (and groupoids) on C*-algebras. For instance, many familiar constructions like group C*-algebras and crossed products can be viewed as cross sectional C*-algebras of suitable Fell bundles. In the talk we will introduce the concept of positive definite "multiplier" between Fell bundles and discuss some consequences and applications. Especially, a notion of amenability for Fell bundles naturally appears. Other applications are concerned with the construction of certain functors from the category of positive definite multipliers to the category of completely positive maps between C*-algebras and with the existence of certain C*-correspondences associated to left actions of Fell bundles on right Hilbert bundles. (Joint work with E. Bedos) The Operator Algebra Seminar schedule is here: https://sites.google.com/view/oastorvergata/home-page?authuser=0
Mercoledì 08 maggio 2024
Ore 16:00, Aula primo piano, Istituto per le Applicazioni del Calcolo "M. Picone" IAC-CNR Roma, via dei Taurini 19
Seminari Vito Volterra
Michael Goldman (CNRS-Ecole Polytechnique)
Recent progress on the optimal matching problem
In this talk I will review some recent progress in the understanding of the optimal matching problem. While the work of Ajtai-Komlos-Tusnady in the 80's on this classical optimization problem attracted a lot of attention from the probability community (see the book by Talagrand), this problem has seen a renewed interest from the PDE community thanks to the ansatz proposed by Caracciolo Lucibello, Parisi and Sicuro in 2014. I will explain to which extent this ansatz can be rigorously justified and show how it leads to a deeper understanding of this problem.
Per informazioni, rivolgersi a: lucia.deluca777@gmail.com
Mercoledì 08 maggio 2024
Ore 16:30, Aula M6, Dipartimento di Matematica e Fisica, Università di Roma Tre, Lungotevere Dante 376
Seminario di Analisi Matematica
Zhiqiang Wang (Università degli Studi Roma Tre)
Dynamics of Hamiltonian PDEs
In this talk I will discuss some results about long time behaviors of solutions to Hamiltonian PDEs (Schrödinger, Kirchhoff, etc). In particular I will focus on a recent result where we (with J. Bernier, N. Camps and B. Grébert) prove exponential stability of small typical solutions of Schrödinger-Poisson equation by the so-called Rational Normal Form. For these resonant Hamiltonian PDEs the linear frequencies are fully resonant and we have to use the nonlinearity to avoid the resonances, which leads to a kind of new small divisors compared to Birkhoff Normal Form.
Giovedì 09 maggio 2024
Ore 14:15, Aula M1, Dipartimento di Matematica e Fisica, Università Roma Tre
Seminario di Geometria
Kenneth Ascher (Irvine)
Moduli of K3 Surfaces, Wall-crossing, and the Hassett-Keel Program
I will survey some results from the study of moduli spaces of higher dimensional varieties as well as the Hassett—Keel program for the moduli space of curves. I will then discuss applications of these techniques to the study of moduli spaces of K3 surfaces of low degree. Most of the original work presented in this talk will be based on joint work with Kristin DeVleming and Yuchen Liu.
Per informazioni, rivolgersi a: amos.turchet@uniroma3.it
Giovedì 09 maggio 2024
Ore 14:30, Aula 1B1, RM002 Via A.Scarpa 16, Dipartimento SBAI, Sapienza Università di Roma
Seminario "PDE a tutto SBAI"
Alberto Saldana ( Universidad Nacional Autonoma de México)
Asymptotic analysis of Lane-Emden systems
Lawrence C. Evans once wrote: “One important principle of mathematics is that extreme cases reveal interesting structure.” In this talk, we put this piece of mathematical wisdom to the test. First, we recall some known results on elliptic problems with power nonlinearity as the exponent tends to infinity. Then we consider the case of the Lane-Emden system and study the profile of least-energy solutions as one of the exponents tends to infinity. In this case, the limit profile can be characterized as a least-energy solution of a p-biharmonic nonlinear equation which can be studied with tools from nonsmooth analysis. These results were obtained in collaboration with Nicola Abatangelo (Università di Bologna) and Hugo Tavares (Universidade de Lisboa).
Per informazioni, rivolgersi a: massimo.grossi@uniroma1.it
Giovedì 09 maggio 2024
Ore 14:30, Aula Dal Passo, Dipartimento di Matematica, Università degli studi di Roma "Tor Vergata"
Seminario di Analisi Numerica
Jan Grošelj (University of Ljubljana)
Powell-Sabin splines: unstructured and structured case
A standard approach to the construction of smooth low degree polynomial splines over an unstructured triangulation is based on splitting of triangles in such a way that the refined triangulation allows the imposition of smoothness constraints without dependence on geometry. A well-established splitting technique is the Powell-Sabin 6-refinement, which can be used to define C1 quadratic splines as well as splines of higher degree and smoothness. In this talk we review the construction of splines over a Powell-Sabin 6-refinement with a special emphasis on C1 cubic splines. We present B-spline-like functions that enjoy favorable properties such as local support, stability, nonnegativity, and a partition of unity. In particular, we discuss what super-smoothness properties these functions possess and how they depend on geometric properties of the underlying refinement. Based on this we explain how to establish approximation spaces that are suitable for completely unstructured triangulations, partially structured triangulations, and triangulations with a high level of symmetry, e.g., three-directional triangulations. This talk is part of the activity of the MUR Excellence Department Project MatMod@TOV (CUP E83C23000330006).
Per informazioni, rivolgersi a: speleers@mat.uniroma2.it
Giovedì 09 maggio 2024
Ore 14:30, Aula L, Dipartimento di Matematica e Fisica, Università di Roma Tre, Lungotevere Dante 376
seminario di Probabilità
Camille Tardif (Sorbonne Universite, LPSM Paris)
Persistence problem for additive functionals of one-dimensional diffusion processes
I will present a joint work with Quentin Berger and Loïc Bethencourt. We study the asymptotic of the probability that a signed additive functional of a recurrent one-dimensional diffusion stays below some constant level for a long time. Under our hypothesis we prove that this persistence probability decreases polynomially and we find the persistence exponent. For that we decompose the diffusion into excursions and the problem is reduced to study the fluctuations of some Lévy process naturally associated with the additive functional.
Giovedì 09 maggio 2024
Ore 16:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminari di Ricerca in Didattica della Matematica
Laura Branchetti (Università degli Studi di Milano)
Curve e dimostrazioni come boundary objects tra matematica e fisica: dall'analisi epistemologica alla formazione degli insegnanti e alle sperimentazioni in aula
In questo contributo si presenteranno alcuni risultati di un progetto di ricerca internazionale (IDENTITIES) sul tema dell'educazione all'interdisciplinarità tra matematica e fisica nella scuola secondaria, che si basa su un approccio storico-epistemologico alla ricostruzione del sapere in ottica interdisciplinare e ha come fine la promozione dell'interdisciplinarità nel pieno rispetto del contributo culturale e educativo delle discipline. Verrà presentato un framework messo a punto all'interno del progetto (Satanassi et al., 2023) e un caso di studio concreto sul tema delle coniche e del moto parabolico. Verranno mostrati i principi di progettazione di attività per la formazione degli insegnanti e in particolare l'uso della nozione di curva e di dimostrazione come boundary objects (Akkerman & Bakker, 2011), i risultati della co-progettazione coi docenti di attività da condurre in classi di scuola secondaria di secondo grado (Liceo matematico) e i primi risultati preliminari relativi agli apprendimenti degli studenti e delle studentesse nelle classi in cui sono state effettuate le prime sperimentazioni.
Per informazioni, rivolgersi a: annalisa.cusi@uniroma1.it
Venerdì 10 maggio 2024
Ore 11:00, aula D'Antoni, Dipartimento di Matematica, Università di Roma Tor Vergata
corso di dottorato
Martina Lanini (Tor Vergata)
Algebre di Hecke
Venerdì 10 maggio 2024
Ore 14:30, Aula Dal Passo, Dipartimento di Matematica, U Roma Tor Vergata
Algebra and Representation Theory Seminar
Stefano Marini (U Parma)
On finitely Levi nondegenerate closed homogeneous CR manifolds
A complex flag manifold F= G /Q decomposes into finitely many real orbits under the action of a real form of G. Their embeddings into F define CR manifold structures on them. We give a complete classification of all closed simple homogeneous CR manifolds that have finitely nondegenerate Levi forms.
Venerdì 10 maggio 2024
Ore 16:00, Aula Dal Passo, Dipartimento di Matematica, U Roma Tor Vergata
Algebra and Representation Theory Seminar
Gabriele Vezzosi (U Firenze)
Analogues of Beilinson-Drinfeld's Grassmannian on a surface
The Beilinson-Drinfeld's Grassmannian on an algebraic curve is an important object in Representation Theory and in the Geometric Langlands Program. I will describe some analogues of this construction when the curve is replaced by a surface, together with related preliminary results. This is partly joint work with Benjamin Hennion (Orsay) and Valerio Melani (Florence), and partly joint work in progress with Andrea Maffei (Pisa) and Valerio Melani (Florence).
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