Notiziario Scientifico
a cura del Dipartimento di Matematica G. Castelnuovo, Sapienza Università di Roma
Settimana dal 17-02-2020 al 23-02-2020
Lunedì 17 febbraio 2020
Ore 10:00, Aula SEMINARI (Palazzina E) , SBAI, Sapienza Università di Roma
Alexander A. Ivanov (IC London)
Locally Projective Graphs, Majorana Theory, and the Monster Group
Let \(\Gamma\) be a graph with an edge-transitive automorphism group \(G\) such that (a) \(\Gamma\) is bipartite with vertices in one part having valency \(\alpha \in \{2, 3\}\) (they are called lines), and the vertices in the other part having valency \(2^n - 1\) for some \(n \geq 2\) (they are called points); (b) the stabilizer in \(G\) of a point induces the natural doubly transitive action of \(L_n(2)\) on the set of lines containing this point. The ultimate goal is to classify the amalgams \(\{G(p), G(l)\}\) formed by the stabilizers of adjacent point-line pairs \((p, l)\). For \(n = 2\) there are \(15\) such amalgams as proved in the ground breaking paper by D. Goldschmidt. For every Goldschmitd's amalgam the order of \(G(p)\) divides \(2^7 \cdot 3\) and the largest amalgam is realized in the automorphism group of the Mathieu group \(M_{12}\). For \(n \geq 3\) the known examples come from point-line incident graphs of classical and sporadic flag-transitive geometries. The classical examples are associated with the linear and symplectic geometries over \(GF(2)\) along with the Hamming graphs over the alphabet with \(3\) letters and automorphism group \(S_3 \wr L_n(2)\). The sporadic examples include the exceptional \(A_7\)-geometry, Cooperstein's geometry of \(G_2(3)\), and tilde geometries of the Mathieu group \(M_{24}\), the Held group \(He\), the Conway group \(Co_1\), culminating at the Monster group \(M\). The similar problem with lines having valency \(2\) was accomplished by S.V. Shpectorov and the author with essential use of V.I. Trofimov's results announced in 1991 and published in numerous subsequent papers along with the classification of Petersen geometries. A special case of \(n = 3\) problem with lines of valency \(3\) was settled recently, where the amalgams coming from \(M_{24}\)- and He-geometries were characterized (and proved to be isomorphic to each other), and a new amalgam realized in \(A_{16}\) was discovered.
Lunedì 17 febbraio 2020
Ore 14:00, aula Conversi, Dipartimento di Fisica, Università di Roma La Sapienza
seminario delle meccaniche
Giovanni Gallavotti (Università di Roma La Sapienza)
Viscosity, Reversibility, Statistical Ensembles: in a Navier-Stokes fluid
Microscopic equations for a fluid are reversible: however imply irreversible macroscopic equations. Is the possible that the same fluid could be described via reversible equations? A positive answer is proposed in analogy with the ensembles equivalence in mechanics; the role of the container volume is played by a regularization parameter N , the temperature by the viscosity and the energy by the fluid enstrophy. The thermodynamic limit will correspond to the removal of the regularization (N → ∞). A statistical interpretation of viscosity emerges which maintains the equation reversible while retaining the physical consequences of irreversibility which is realized as a spontaneous symmetry breakdown.
Lunedì 17 febbraio 2020
Ore 14:30, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
seminario di Analisi Matematica
Sara Daneri (GSSI L'Aquila)
On the sticky particle solutions to the pressureless Euler system in general dimension
I n this talk we consider the pressureless Euler system in dimension greater than or equal to two. We look for solutions satisfying the following adhesion or sticky particle principle: if two particles of the fluid do not interact, then they move freely keeping constant velocity, otherwise they join with velocity given by the balance of momentum. For initial data given by a finite number of particles pointing each in a given direction, in general dimension, it is easy to show that a global sticky particle solution always exists and is unique. In dimension one, sticky particle solutions have been proved to exist and be unique. In dimension greater or equal than two, it was shown that as soon as the initial data is not concentrated on a finite number of particles, it might lead to non-existence or non-uniqueness of sticky particle solutions. In collaboration with S. Bianchini, we show that even though the sticky particle solutions are not well-posed for every measure-type initial data, there exists a comeager set of initial data in the weak topology giving rise to a unique sticky particle solution. Moreover, for any of these initial data the sticky particle solution is unique also in the larger class of dissipative solutions (where trajectories are allowed to cross) and is given by a trivial free flow concentrated on trajectories which do not intersect. In particular for such initial data there is only one dissipative solution and its dissipation is equal to zero. Thus, for a comeager set of initial data the problem of finding sticky particle solutions is well-posed, but the dynamics that one sees is trivial. Our notion of dissipative solution is lagrangian and therefore general enough to include weak and measure-valued solutions.
Martedì 18 febbraio 2020
Ore 14:30, Aula Dal Passo, Dipartimento di Matematica, Universita' di Roma "Tor Vergata"
Seminario di Analisi Matematica
Margherita Nolasco (Universita' dell'Aquila)
Least energy solution for the relativistic electron in a Coulomb external potential
We study the normalized solutions of a nonlinear eigenvalue problem for a model of a self-interacting spin-\(1/2\) relativistic particle in an external electrostatic field generated by a heavy nucleus. The model is described by the Maxwell-Dirac equations coupled with an external Coulomb potential term. The first (positive) eigenvalue is the Lagrange multiplier lying in the positive part of the spectral gap of the essential spectrum of the Dirac-Coulomb operator. We prove the existence of a normalized least (positive) energy solution and we give a variational characterization for the lowest (positive) energy critical value (the "ground state" of the system).
Martedì 18 febbraio 2020
Ore 14:30, Dipartimento di Matematica e Fisica, Universita' degli Studi Roma Tre, Largo San Leonardo Murialdo,1 - Pal.C - Aula 311
Seminario di Fisica Matematica
Alberto Maiocchi (Universita' degli Studi di Padova)
Freezing of the optical-branch energy in a diatomic nonlinear chain
We show that the dynamics of nonlinear dynamical systems with many
degrees of freedom (possibly infinitely many) can be similar to that
of ordered system in a surprising fashion. To this aim, in the
literature techniques from perturbation theory are typically used,
such as KAM theorem or Nekhoroshev theorem. Unfortunately they are
known to be ill-suited for obtaining results in the case of many
degrees of freedom. We present here a probabilistic approach, in which
we focus on some observables of physical interest (obtained by
averaging on the probability distribution on initial data) and for
several models we get results of stability on long times similar to
Nekhoroshev estimates. We present the example of a nonlinear chain of
particles with alternating masses, a hyper-simplified model of
diatomic solid. In this case, which is similar to the celebrated
Fermi-Pasta-Ulam model and is widely studied in the literature, we
show the progress with respect to previous results, and in particular
how the present approach permits to obtain theorems valid in the
thermodynamic limit, as this is of great relevance for physical
implications.
Martedì 18 febbraio 2020
Ore 15:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Modellistica Differenziale Numerica
Caterina Balzotti (SBAI, Sapienza)
Evaluation of NOx emissions and ozone production due to vehicular traffic via second-order models
The aim of this talk is to introduce a method to estimate the production of ozone due to vehicular traffic. The traffic flow is modeled via the second-order Collapsed Generalized Aw-Rascle-Zhang model, choosing a special velocity function and calibrating it on the NGSIM dataset. Then we introduce an emission model to estimate the emission rates of nitrogen oxides (NOx), which are precursors of the ozone in atmosphere. Such a model correlates the emission rate to velocity and acceleration of vehicles. Finally, we consider the photochemical smog cycle, described by three chemical reactions which involve NOx gases and lead to the production of ozone. These reactions are modeled via a system of ODEs, with the source term given by vehicular traffic. We analyze the ozone impact of various traffic scenarios and describe the effect of traffic light timing on such impact.
Martedì 18 febbraio 2020
Ore 16:00, Dal Passo, Dipartimento di Matematica, Università di Roma "Tor Vergata"
Seminario
Karen Strung (The Czech Academy of Sciences)
The classification programme for C*-algebras and its interactions with topological dynamics
The classification programme has determined that infinite dimensional simple separable unital C*-algebras with finite nuclear dimension can be classified by the so-called “Elliott Invariant”, under the mild assumption that they satisfy the UCT. It becomes an interesting question to determine what classes of “naturally occurring” C*-algebras are covered by the classification, as well as the range of the invariant for such classes. I will discuss C*-algebras arising from topological dynamical systems and their relation to the classification program for C*-algebras.
Martedì 18 febbraio 2020
Ore 16:00, Aula D'Antoni, Dipartimento di Matematica, Università di Roma "Tor Vergata"
Seminario di Analisi Complessa
Finnur Larusson (Adelaide)
Legendrian holomorphic curves in complex projective 3-space and superminimal surfaces in the 4-sphere
I will describe new joint work with Antonio Alarcon and Franc Forstneric. Complex projective 3-space CP^3 carries an essentially unique complex contact structure, which is of interest for a number of reasons. We study holomorphic immersions and general holomorphic maps from Riemann surfaces to CP^3 that are Legendrian with respect to this structure. For example, we prove approximation and interpolation theorems for such maps, and we prove that every Riemann surface admits a complete injective Legendrian holomorphic immersion into CP^3. We use the twistor projection from CP^3 onto the 4-sphere to derive corollaries for superminimal surfaces in the 4-sphere.
Mercoledì 19 febbraio 2020
Ore 14:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
seminario di Algebra e Geometria
Daniele Agostini (Humboldt Universität Berlin)
On the Schottky problem for genus five Jacobians with a vanishing theta null
In this talk, I will present a solution to the weak Schottky problem for genus five Jacobians with a vanishing theta null, extending a result of Grushevsky and Salvati Manni in genus four. More precisely, I will show that if an abelian fivefold has a vanishing theta null with a quadric tangent cone of rank at most three, then it is in the Jacobian locus, up to extra irreducible components. This is joint work with Lynn Chua.
Mercoledì 19 febbraio 2020
Ore 15:00, Aula M3, Dipartimento di Matematica e Fisica, Lungotevere Dante 376
Seminario di Crittografia
Roberto Civino (Università degli Studi dell'Aquila)
Differential attacks using alternative operations
Block ciphers and their security are the main subjects of this seminar, where it is described the impact of differential cryptanalysis, a powerful statistical attack against block ciphers, when operations different from the one used to perform the key addition are considered on the message space. It is proven that when an alternative difference operation is carefully designed, a cipher that is proved secure against classical differential cryptanalysis can instead be attacked using this alternative difference. Nota: L'attività fa parte del ciclo di seminari atti a raggiungere i requisiti per ottenere la Borsa di Studio dell'Advisory Board della De Componendis Cifris (Bando AA 2019-2020), prevista per gli studenti del Corso di laurea in Scienze Computazionali iscritti al curriculum Gestione e Protezione dei Dati e risultati idonei al concorso
Mercoledì 19 febbraio 2020
Ore 16:00, Aula Dal Passo, Dipartimento di Matematica di Tor Vergata
Minicorso di Dottorato
Yasuyuki Kawahigashi (University of Tokyo)
"Relative boundary-bulk duality and orbifold subfactors" Seconda e terza lezione
Giovedì 20 febbraio 2020
Ore 15:00, Aula B, Dipartimento di Matematica, Sapienza Università di Roma
Seminari di ricerca in Didattica della Matematica
Alessandro Gambini (Sapienza Università di Roma)
La valutazione in matematica
Venerdì 21 febbraio 2020
Ore 10:00, Dal Passo , Dipartimento di Matematica, Università di Roma "Tor Vergata"
Seminari di Teoria Geometrica della Misura
Paolo De Donato (Sapienza), Chen Liang (Tor Vergata), Fabio De Regibus (Sapienza)
Seminars on the Theory of Currents
The speakers will present some classical problems in the Calculus of Variations related to the theory of Cartesian Currents. 10:00-11:00 Paolo De Donato (Sapienza) “Lower semicontinuity results for polyconvex integrals: a critical example in dimension two” 11:30-12:30 Chen Liang (Tor Vergata) “On the area of the graph of a singular map from the plane to the plane taking three values” 14:00-15:00 Fabio De Regibus (Sapienza) “Variational problems for maps from the plane into the sphere” The three seminars are in fulfillment for the exam of the course “Introduction to the theory of currents” held at Tor Vergata by Dr. Gianluca Orlando (TU Munich).
Venerdì 21 febbraio 2020
Ore 12:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario MoMA
Sidney Redner
Is Basketball Scoring Just a Random Walk?
Watching basketball is nearly the same as watching repeating coin tossings! By analyzing recently available data from recent National Basketball Association (NBA) basketball seasons, basketball scoring during a game is well described by a continuous-time anti-persistent random walk, with essentially no temporal correlations between successive scoring events. We show how to calibrate this model to account for many statistical season-long metrics of NBA basketball. As further illustrations of this random-walk picture, we show that the distribution of times when the last lead change occurs and the distribution of times when the score difference is maximal are both given by the celebrated arcsine law--a beautiful and surprising property of random walks. We also use the random-walk picture to construct the criterion for when a lead of a specified size is "safe" as a function of the time remaining in the game. The obvious application to game-time betting is left as an exercise for the interested.
Venerdì 21 febbraio 2020
Ore 14:00, Aula "Claudio D'Antoni", Università di Roma "Tor Vergata" - dipartimento di Matematica
Algebra & Representation Theory Seminar (ARTS)
Alessandro D'ANDREA ("Sapienza" Università di Roma)
Irreducible representations of primitive Lie pseudoalgebras of type H
Lie pseudoalgebras are a “multivariable” generalization of Lie algebras. Their classification follows Cartan’s 1909 classification of simple infinite dimensional linearly compact Lie algebras, in terms of four infinite families, called of type W, S, K, H. Finite irreducible representations in type W, S, and K have already been classified by exploiting a common strategy, which, however, remarkably fails, in multiple points, in case H. In this talk I will explain all of the above issues and how to obtain a classification in type H as well. This is a joint work with B. Bakalov and V. G. Kac.
Venerdì 21 febbraio 2020
Ore 16:00, Aula Picone, Dipartimento di Matematica, Sapienza Università di Roma
Seminari per docenti (PLS)
Fabio Spizzichino (Sapienza Università di Roma), Donatella Ricalzone (Liceo Pascal), Erminia Izzo (Liceo Lucrezio Caro), Francesca Ruzzi (Liceo Lucrezio Caro)
I numeri complessi, con qualche sguardo al passato, al presente, e al futuro
Venerdì 21 febbraio 2020
Ore 16:00, Dal Passo, Dipartimento di Matematica di Tor Vergata
Minicorso di Dottorato
Yasuyuki Kawahigashi (University of Tokyo)
"Relative boundary-bulk duality and orbifold subfactors" Quarta e quinta lezione
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