Notiziario Scientifico

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

Settimana dal 21-02-2022 al 27-02-2022

Lunedì 21 febbraio 2022
Ore 14:30, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
seminario di Analisi Matematica
Lucia De Luca (IAC-CNR)
Crystallization results for pairwise interaction energies in two dimensions
I will discuss some recent crystallization results for pairwise interaction energies of systems of particles in the plane. I will focus on the so-called Heitmann-Radin (HR) sticky disc potential that - in its classic form - is defined by \(V(r)=+\infty\) for \(r<1\), \(V(r)=-1\) for \(r=1\), \(V(r)=0\) elsewhere. For the classic HR functional it has been proven that minimizing configurations are subsets of the regular triangular lattice. First, I will show how this result extends in a suitable sense to the class of quasi-minimizers. Furthermore, I will enrich the classic HR model in order to deal with vectorial crystallization problems arising in mathematical biology. Specifically, associating a vectorial orientation to each particle of the configuration and enforcing threshold criteria for the interactions between particles, I will show that minimizing configurations exhibit the so-called diamond formation (typical in fish schooling).


Lunedì 21 febbraio 2022
Ore 14:30, Aula Dal Passo, Dipartimento di Matematica, Università di Roma Tor Vergata e online a questo link
Corso di Dottorato
Emanuele Macrì (Laboratoire de Mathématiques d’Orsay)
Bridgeland stability conditions
I will discuss some recent crystallization results for The subject of the course in the theory of Bridgeland Stability conditions. In particular, I will explain some applications to algebraic geometry. Specifically, I will cover the following topics:

  1. 1. Foundational material and Bridgeland's deformation theorem
  2. 2. Examples: curves and surfaces
  3. 3. Moduli spaces and variation of stability conditions
Per informazioni, rivolgersi a: pareschi@math.uniroma2.it

Martedì 22 febbraio 2022
Ore 11:00, Aula Dal Passo, Dipartimento di Matematica, Università di Roma Tor Vergata e online a questo link
Corso di Dottorato
Emanuele Macrì (Laboratoire de Mathématiques d’Orsay)
Bridgeland stability conditions
I will discuss some recent crystallization results for The subject of the course in the theory of Bridgeland Stability conditions. In particular, I will explain some applications to algebraic geometry. Specifically, I will cover the following topics:

  1. 1. Foundational material and Bridgeland's deformation theorem
  2. 2. Examples: curves and surfaces
  3. 3. Moduli spaces and variation of stability conditions
Per informazioni, rivolgersi a: pareschi@math.uniroma2.it

Martedì 22 febbraio 2022
Ore 14:30, Aula Dal Passo, Universita' di Roma Tor Vergata
Seminari di Geometria
Roberto Fringuelli (Universita' di Roma Tor Vergata)
The automorphism group of the moduli space of principal bundles on a smooth curve
Let G be a complex (connected) reductive group and C be a complex smooth projective curve of genus at least four. It is known that the moduli space of semistable G-bundles over C is a projective variety. The automorphism group of this variety contains the so-called tautological automorphisms: they are induced by the automorphisms of the curve C, outer automorphisms of G and tensorization by Z-torsors, where Z is the center of G. It is a natural question to ask if they generate the entire automorphism group. Kouvidakis and Pantev gave a positive answer when G=SL(n). An alternative proof has been given by Hwang and Ramanan. Later, Biswas, Gomez and Muñoz, after simplifying the proof for G=SL(n), extended the result to the symplectic group Sp(2n). All the proofs rely on the study of the singular fibers of the Hitchin fibration. In this talk, we present a recent work where, by adapting the Biswas-Gomez-Muñoz strategy, we describe the automorphism group of the connected components of the moduli space of semistable G-bundles over C, for any almost-simple group G.
Per informazioni, rivolgersi a: onorati@mat.uniroma2.it


Martedì 22 febbraio 2022
Ore 16:00, Aula Dal Passo + Streaming via MS Teams, Dipartimento di Matematica, Università degli Studi di Roma "Tor Vergata"
Seminario di Equazioni differenziali
Cristian Mendico (Università degli Studi di Roma "Tor Vergata")
Asymptotic behavior of solutions to Hamilton-Jacobi-Bellmann equations
The analysis of the ergodic behavior of solutions to Hamilton-Jacobi-Bellmann equations has a long history going back to the seminal paper by [Lions, P.-L., Papanicolaou, G. and Varadhan,S.R.S]. Since this work, the subject has grown very fast and when the Hamiltonian is of Tonelli type a large number of results have been proved. A full characterization of the ergodic behavior of solutions to Tonelli Hamilton-Jacobi equations can be found in the celebrated weak KAM theory and Aubry-Mather theory. However, few results are available if the Hamiltonian fails to be Tonelli, i.e., the Hamiltonian is neither strictly convex nor coercive with respect to the momentum variable. In particular, such results cover only some specific structure and so, the general problem is still open. In this talk, I will present some recent results obtained in collaboration with Piermarco Cannarsa and Pierre Cardaliaguet concerning the long time-average behavior of solutions to Hamilton-Jacobi-Bellman equations. We will look, first, to the case of control of acceleration and, then, to sub-Riemannian control systems. Finally, we conclude this talk showing how the previous analysis applies to mean field game systems. Note: This talk is part of the activity of the MIUR Department of Excellence Project MATH@TOV CUP E83C18000100006 MS Teams Link for the streaming
Per informazioni, rivolgersi a: sorrentino@mat.uniroma2.it


Mercoledì 23 febbraio 2022
Ore 14:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Algebra e Geometria
Lewis Topley (University of Bath)
Dirac reduction for shifted Yangians
Finite W-algebras are a finite collection of filtered algebras associated to each complex semisimple Lie algebra, which have interesting applications to the classification of primitive ideals in enveloping algebras. One of the key challenges in the theory is to find an explicit presentation for a finite W-algebra. This problem was solved comprehensively for the general linear algebras by Brundan--Kleshchev, by relating them to shifted Yangians, with further important work by Kac--De Sole and their collaborators. Extending this to other classical Lie algebras has proved to be extremely difficult. A good approximation to the problem is describing the Poisson structure on the semiclassical limit of the W-algebra. In this seminar I will describe some new progress in extending the Yangian description to types B, C, D in the semiclassical setting, using the theory of Dirac reduction.
Per informazioni, rivolgersi a: pezzini@mat.uniroma1.it


Giovedì 24 febbraio 2022
Ore 12:00, Seminario online https://uniroma1.zoom.us/j/81135419795, Dipartimento di Scienze di Base e Applicate per l'Ingegneria
Seminario
Michel Mehrenberger (Aix-Marseille Université )
Semi-Lagrangian schemes for Vlasov type equations
In this talk we give an overview of some semi-Lagrangian schemes that are applied to the numerical resolution of the Vlasov equation. The latter equation models typically the time evolution of charged particles (ions, electrons) with self consistant electric field and external magnetic field; it is still quite challenging to solve due in particular to the high dimensionality (6D phase space), the different scales and the filamentation process.
Per informazioni, rivolgersi a: annachiara.lai@uniroma1.it


Giovedì 24 febbraio 2022
Ore 12:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario
Loïc Foissy (Université du Littoral Cote d'Opale, Calais)
Cointeracting bialgebras
Pairs of cointeracting bialgebras appear recently in the literature of combinatorial Hopf algebras, with examples based on formal series, on trees (Calaque, Ebrahimi-Fard, Manchon and Bruned, Hairer, Zambotti), graphs (Manchon), posets... We will give several results obtained on pairs of cointeracting bialgebras: actions on the group of characters, antipode, morphisms to quasi-symmetric functions... and we will give applications to Hopf algebras of graphs, posets, multigraphs or mixed graphs.


Giovedì 24 febbraio 2022
Ore 14:00, Aula Picone, Dipartimento di Matematica, Sapienza-Università di Roma
Seminario di presentazione della tesi dei dottorandi
David Rios Ortiz (Dottorando-Matematica-Sapienza)
Linear Systems on Hyperkähler Manifolds.
In this talk I will give some results in the theory of linear systems of divisors on Hyperkähler manifolds. A relationship between linear systems on Hilbert squares on a K3 surface and Gaussian maps is established, then is used for the study of Gaussian maps on canonical curves. An infinite family of non-divisorial base loci for ample divisors is constructed for Hilbert schemes of points on K3 surfaces. The formulae for the Euler characteristic of divisors is completed for the last two known examples of Hyperkähler manifolds. In addition, a general theorem will be proved on the asymptotic base loci of big divisors on Hyperkähler manifolds.
Per informazioni, rivolgersi a: rios@mat.uniroma1.it


Giovedì 24 febbraio 2022
Ore 14:15, Aula M1, Dipartimento di Matematica, Università Roma Tre
Seminario di Geometria
Giulio Codogni (Università degli Studi di Roma Tor Vergata)
Characterizing Jacobians via the KP equation and via flexes and degenerate trisecants to the Kummer variety: an algebra-geometric approach.
I will present completely algebro-geometric proofs of a theorem by T. Shiota, and of a theorem by I. Krichever, characterizing Jacobians of algebraic curves among all irreducible principally polarized abelian varieties. Shiota's characterization is in terms of the KP equation. Krichever's characterization is in terms of trisecant lines to the Kummer variety, and I will discuss only the degenerate case of his result. The proofs rely on a new theorem asserting that the base locus of a complete linear system on an abelian variety is reduced. This is a joint work with E. Arbarello and G. Pareschi.
Per informazioni, rivolgersi a: amos.turchet@uniroma3.it


Giovedì 24 febbraio 2022
Ore 14:15, online, disponibile alla pagina https://www.mcqm.it/talks/registration.html
ciclo "Mathematical Challenges in Quantum Mechanics"
Zied Ammari (IRMAR Rennes)
On Well-posedness for the Gross-Pitaevskii and Hartree Hierarchy Equations
Gross-Pitaevskii and Hartree hierarchies are infinite systems of coupled PDEs related to mean field theory of Bose gases. Due to their physical and mathematical relevance, the issues of well-posedness and uniqueness for these hierarchies have recently been studied thoroughly using specific nonlinear and combinatorial techniques. In this talk I will introduce a new approach based on a duality between hierarchies and Liouville equations. Several new results are obtained as an outcome of this approach.
Per informazioni, rivolgersi a: monaco@mat.uniroma1.it


Giovedì 24 febbraio 2022
Ore 14:30, Sala di Consiglio - https://meet.google.com/ads-dekx-bgm, Dipartimento di Matematica, Sapienza Università di Roma
P(n)/N(p): Problemi differenziali nonlineari/Nonlinear differential problems
Sergio Cruz Blázquez (Scuola Normale Superiore, Pisa)
Conformal Metrics with Prescribed Scalar and Mean Curvature
We consider the case with boundary of the classical Kazdan- Warner problem in dimension greater or equal than three, i.e. the prescription of scalar and boundary mean curvatures via conformal deformations of the metric. We deal in particular with negative scalar curvature and boundary mean curvature of arbitrary sign, which to our knowledge has not been treated in the literature. We employ a variational approach to prove new existence results, especially in three dimensions. One of the principal issues for this problem is to obtain compactness properties, due to the fact that bubbling may occur with profiles of hyperbolic balls or horospheres, and hence one may lose either pointwise estimates on the conformal factor or the total conformal volume. We can sometimes prevent them using integral estimates, Pohozaev identities and domain-variations of different types.
Per informazioni, rivolgersi a: galise@mat.uniroma1.it


Giovedì 24 febbraio 2022
Ore 14:45, Aula Picone, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di presentazione delle tesi dei dottorandi
Filippo Fagioli (Dottorando-Matematica-Sapienza)
Positivity of characteristic forms via pointwise universal push-forward formulae
In the last few years there has been a renewed interest around a conjecture by Griffiths which states that the positive cone spanned by the Schur forms of a Griffiths positive vector bundle consists of positive differential forms. This conjecture can be interpreted as the differential geometric counterpart of the celebrated Fulton-Lazarsfeld theorem on numerically positive polynomials for ample vector bundles. In this talk, I present some results that confirm the above conjecture for several positive linear combinations of Schur forms. The positivity of such characteristic forms is obtained as a consequence of a result that provides the pointwise, Hermitian version of a universal push-forward formula for flag bundles valid in cohomology. Some of the results presented in this talk were obtained in collaboration with Simone Diverio.
Per informazioni, rivolgersi a: fagioli@mat.uniroma1.it


Giovedì 24 febbraio 2022
Ore 15:00, Il seminario sarà tenuto in modalità telematica, Il link per partecipare al seminario sarà condiviso con gli interessati
Seminari di Ricerca in Didattica e Storia della Matematica
Alessandro Gambini (Sapienza Università di Roma)
Numeri primi e polinomi irriducibili: il ruolo della rappresentazione

Per informazioni, rivolgersi a: annalisa.cusi@uniroma1.it


Giovedì 24 febbraio 2022
Ore 15:45, Aula Picone, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di presentazione delle tesi dei dottorandi
Marco Trevisiol (Dottorando-Matematica-Sapienza)
Normality of closure of nilpotent conjugacy classes
In this work the author studies the geometry of the conjugacy classes in the space of matrices and in its subspaces of symmetric and skew-symmetric matrices under the actions of the general linear group, the orthogonal group and the symplectic group. An extensive and self-contained review of the current state of the art concerning the description of nilpotent conjugacy classes and their closures is provided. Many geometrical properties of the closure of a conjugacy class are interesting from a representation theoretic viewpoint; in particular, their normality. A complete discussion of the normality of the closures of the conjugacy classes for the stated actions takes a prominent role in this work. The main new result completes the picture and it states that a nilpotent symmetric conjugacy class for the orthogonal group has normal closure if and only if the associated partition has consecutive parts of length differing by at most one.
Per informazioni, rivolgersi a: trevisiol@mat.uniroma1.it


Giovedì 24 febbraio 2022
Ore 16:30, Aula Picone, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di presentazione delle tesi dei dottorandi
Marco Valerio Giannone (Dottorando-Matematica-Sapienza)
Twisting quantum groups at the roots of unity
Let \(G\) be a simply connected compact Lie group and \(\mathfrak g\) be its complexified Lie algebra. Building on the work of H. Wenzl, we present a weak tensor structure on the unitary modular categories arising from quantum groups \(U_q(\mathfrak g)\) specialised at the root of 1 \(q\), following the work about weak quasi-tensor categories by S. Carpi, S. Ciamprone, C. Pinzari and myself. The theory therein developed allows us to reconstruct these categories as representation categories of discrete unitary coboundary weak Hopf algebras. Furthermore, we consider the twisted categories obtained by modifying the associator using 3-cocycles on the dual of the centre of \(G\) and reconstruct them as representation categories of suitable discrete unitary weak Hopf algebras; this is done by adaptation of a result by S. Neshveyev and M. Yamashita in the analogous scenario of the compact quantum group corresponding to \(U_q(\mathfrak g)\) for \(q>1\), i.e. for generic values of \(q\).
Per informazioni, rivolgersi a: giannone@mat.uniroma1.it


Venerdì 25 febbraio 2022
Ore 11:00, Aula Dal Passo, Dipartimento di Matematica, Università di Roma Tor Vergata e online a questo link
Corso di Dottorato
Emanuele Macrì (Laboratoire de Mathématiques d’Orsay)
Bridgeland stability conditions
I will discuss some recent crystallization results for The subject of the course in the theory of Bridgeland Stability conditions. In particular, I will explain some applications to algebraic geometry. Specifically, I will cover the following topics:

  1. 1. Foundational material and Bridgeland's deformation theorem
  2. 2. Examples: curves and surfaces
  3. 3. Moduli spaces and variation of stability conditions
Per informazioni, rivolgersi a: pareschi@math.uniroma2.it

Venerdì 25 febbraio 2022
Ore 12:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario MoMA
Francisco Facchinei (Sapienza Università di Roma)
Newton's method: past, present and a bit of future
We review recent developments in Newton's method. Newton's method for the solution of systems of equations has a long and glorious history; after reviewing it we describe the latest advancements aimed at dealing with nonsmooth functions and non-isolated solutions. These developments are at the core of many successful applications of the method in a wide range of interesting contemporary problems which, in turn, offered the motivation for studying new methods expanding the range of applicability of Newton's basic algorithm.


Venerdì 25 febbraio 2022
Ore 14:30, Aula "Roberta Dal Passo", Dipartimento di Matematica, Università degli Studi di Roma "Tor Vergata"
Algebra and Representation Theory Seminar
Jacopo Gandini (Università di Bologna)
Fully commutative elements and spherical nilpotent orbits
Let \(\mathfrak g\) be a simple Lie algebra, with a fixed Borel subalgebra \(\mathfrak b = \mathfrak t+\mathfrak n\), and let \(W\) be the associated Weyl group. The Steinberg map associates to any element of \(W\) a nilpotent orbit in \(\mathfrak g\), which is defined by the corresponding set of inversions. Extending on previous work of Fan and Stembridge, in this talk I will compare two different notions of "smallness", one available in the Weyl group and the other one for nilpotent orbits.
Link per seguire seminario in streaming


Venerdì 25 febbraio 2022
Ore 16:00, Aula "Roberta Dal Passo", Dipartimento di Matematica, Università degli Studi di Roma "Tor Vergata"
Algebra and Representation Theory Seminar
Eugenio Giannelli (Università di Firenze)
On Sylow Branching Coefficients
In this talk we will discuss the nature of the relationship between the representations of a finite group G and those of a Sylow subgroup P of G. We will introduce Sylow Branching Coefficients (SBCs) and we will show how the study of these numbers led us to prove a conjecture proposed by Malle and Navarro in 2012. We will conclude by presenting new results on SBCs in the case where G is the symmetric group. The talk is based on joint works with Law, Long, Navarro, Vallejo and Volpato.
Link per seguire seminario in streaming


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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