Notiziario Scientifico
a cura del Dipartimento di Matematica G. Castelnuovo, Sapienza Università di Roma
Settimana dal 08-04-2019 al 14-04-2019
Lunedì 08 aprile 2019
Ore 14:15, Aula Consiglio, Dipartimento di Matematica
Seminario di Analisi Matematica
Giuseppe Savare' (Universita' di Pavia)
Contraction and smoothing properties of the heat flow with respect to entropic and transport distances
Since the pioneering contribution by F. Otto, contraction properties of second order diffusion equations with respect to the Kantorovich-Rubinstein-Wasserstein distance played an important role, from both the geometric and the analytic point of view. We will discuss their connections with lower curvature bounds (in the sense of Bakry-Emery) and new developements involving Csiszar divergences, the Hellinger distance and the optimal Entropy-Transport problems.
Lunedì 08 aprile 2019
Ore 14:30, Aula Dal Passo, Dipartimento di Matematica, Università degli Studi di Roma "Tor Vergata"
Algebra and Representation Theory Seminar
Martina Lanini (Tor Vergata)
Combinatorial Fock Space and Representations of Quantum Groups at Roots of Unity
The classical Fock space arises in the context of mathematical physics, where one would like to describe the behaviour of certain configurations with an unknown number of identical, non-interacting particles. By work of Leclerc and Thibon, it(s q-analogue) has a realisation in terms of the affine Hecke algebra of type A and it controls the representation theory of the corresponding quantum group at a root of unity. In joint work with Arun Ram and Paul Sobaje, we produce a generalisation of the q-Fock space to all Lie types. This gadget can also be realised in terms of affine Hecke algebra and captures decomposition numbers for quantum groups at roots of unity.
Martedì 09 aprile 2019
Ore 14:00, 27, Dipartimento di Matematica, Università di Roma Tor Vergata
Ciclo di 30 ore di Lezione per il Dottorato di Ricerca in Matematica - Geometria Algebrica
Barbara Bolognese (University of Sheffield)
Stabilità di Bridgeland
Prima lezione corso (di 30 Ore). Proponente scientifico: C. Ciliberto. Lezioni in Aula 27 dalle 14 alle 17 (con pausa di 30 minuti al centro di ogni lezione), secondo il seguente programma: APRILE: giorni 9, 11, 16, 18, 23, 24 GIUGNO: giorni 11, 13, 18, 20, 25, 27. Argomenti: richiami di stabilità per fasci e spazi di moduli, categorie triangolate e derivate, condizioni di stabilità su categorie triangolate, la varietà di stabilità, il caso delle curve ellittiche e curve in generale, superficie in generale e in particolare superficie K3, risultati di Bayer e Macrì sulla classe di divisori nef sullo spazio dei moduli dei complessi stabili, superficie regolari ed altri esempi. Link http://www.mat.uniroma2.it/~ricerca/geomet/LectBolognese.html
Martedì 09 aprile 2019
Ore 14:30, Dal Passo, Dipartimento di Matematica, "Tor Vergata"
Seminario
Vilmos Komornik (Université de Strasbourg)
Moving and oblique observations of beams and plates
We report on a recent joint work with P. Jaming. We study the observability of linear beam and plate equations by moving or oblique observations. Applying different versions and adaptations of Ingham's theorem on nonharmonic Fourier series, we obtain various observability and non-observability theorems. Several interesting problems remain open.
Martedì 09 aprile 2019
Ore 15:00, Aula di Consiglio, Dipartimento di Matematica Guido Castelnuovo, Sapienza Università di Roma
Seminario di Modellistica Differenziale Numerica
Hendrik Speleers (Dipartimento di Matematica, Università degli Studi di Roma “Tor Vergata”)
Smooth B-spline construction on meshes with polar singularities
Representing arbitrary surfaces with a finite number of polynomial patches requires the introduction of polar points for high-valence neighborhoods in quadrilateral meshes. Such holes can be filled by means of polar spline surfaces, where the basic idea is to use periodic spline patches with one collapsed boundary. Building splines over such singularities requires special rules to ensure smoothness; ensuring suitability for design and analysis imposes further constraints. In this talk, we focus on C^k polar spline parametric patches of arbitrary degree and with arbitrary number of elements at the hole boundary. We present a simple, geometric construction of smooth B-spline basis functions over such polar parametric domains possessing interesting properties as non-negativity and partition of unity. In addition, the constructed spline spaces show optimal approximation behavior, even at the polar singular point. We end with some applications of the technology to free-form modelling and the solution of high-order PDEs, such as the Cahn-Hilliard equations, where the smoothness afforded by the spline basis allows straightforward numerical discretization and implementation.
Martedì 09 aprile 2019
Ore 16:30, aula di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
seminario di Fisica Matematica
Matthias Erbar (University of Bonn)
A variational characterization of the Sine-β point process
The one-dimensional log gas in finite volume is a system of particles interacting via a repulsive logarithmic potential and confined by some external field. When the number of particles goes to infinity, their macroscopic empirical distribution approaches a deterministic limit shape. When zooming in one sees microscopic fluctuations around this limit which are described in the limit by a stationary point process, the Sine-β process constructed by Valko and Virag. Leblé and Serfaty have established a large deviation principle for the microscopic configurations governed by a rate function which is the sum of a specific entropy and a renormalized interaction energy. Thus the typical microscopic behavior of the gas is described by the minimizers of this free energy functional, one of which is the Sine-β. We show that this is indeed the unique minimizer. Our argument is based on optimal transport of random point configurations and exploits strict displacement convexity in the free energy functional. This is joint work with Martin Huesmann and Thomas Leblé.
Mercoledì 10 aprile 2019
Ore 14:00, Aula di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Algebra e Geometria
Olivier Benoist (DMA/ENS Paris)
On the Clemens-Griffiths method over non-closed fields
The Lüroth problem asks whether every unirational variety is rational. Over C, it has a positive answer for curves and surfaces, but fails in higher dimensions. In this talk, I will consider the Lüroth problem for geometrically rational varieties over a non-algebraically closed field k. Adapting in this context the strategy implemented by Clemens and Griffiths over C, I will describe new examples of k-varieties that are geometrically rational, k-unirational, but not k-rational. This is joint work with Olivier Wittenberg.
Mercoledì 10 aprile 2019
Ore 14:00, Aula riunioni IAC - 1 piano, IAC, Via dei Taurini 19, Roma
Charlotte Perrin (CNRS, Marseille)
Fluid systems under maximal density constraint
This talk addresses the mathematical analysis of fluid models including a maximal density constraint. These equations arise naturally for instance in the modeling of mixtures like suspensions. I will present recent theoretical existence results on two classes of PDEs systems which correspond to two modeling approaches: the "soft" approach based on compressible equations with singular constitutive laws (pressure and/or viscosities) close to the maximal constraint; and the "hard" approach based on a free boundary problem between a congested domain with incompressible dynamics and a free domain with compressible dynamics. The seminar is partially funded by the Gnampa project 2019: "Partially dissipative hyperbolic systems"
Mercoledì 10 aprile 2019
Ore 15:00, 1B1, Pal. RM002, Dipartimento di Scienze di Base e Applicate per l'Ingegneria
Incontri di Algebra e Geometria allo SBAI
Luigi Provenzano (Università di Padova)
On the spectral behavior of a biharmonic Neumann problem
We consider an eigenvalue problem for the biharmonic operator on bounded domains of Riemannian manifolds with Neumann boundary conditions. We will discuss classical boundary conditions as well as the weak formulation of the problem. Then, we will present a few properties of the eigenvalues. In particular, we will discuss upper bounds which are compatible with the Weyl's law. Also, we shall provide examples where, differently from the corresponding biharmonic Dirichlet problem (on manifolds) or the analogous biharmonic Neumann problem on Euclidean domains, there exist negative eigenvalues. If time permits, we shall present a few more examples describing some peculiar behavior of the eigenvalues, as well as a number of open questions. Based on a joint work with Bruno Colbois (Université de Neuchâtel).
Giovedì 11 aprile 2019
Ore 11:00, Aula 211, Dipartimento di Matematica e Fisica largo S.L. Murialdo, 1
Pre-Seminario Geometria
Martin Ulirsch ((University of Frankfurt))
Geometry of tropical curves
One of the starting points of tropical geometry is the deep analogy between Riemann surfaces and metric graphs, or more generally of tropical curves. Many constructions on the side of Riemann surfaces have natural counterparts on the side of tropical curves and vice versa. In this talk I will focus on two topics: the moduli space of tropical curves and the theory of harmonic maps between tropical curves. After explaining the basic story, I will, in particular, focus on the process of tropicalization which connects this to the world of Riemann surfaces.
Giovedì 11 aprile 2019
Ore 14:30, Aula 211, Dipartimento di Matematica e Fisica Largo S. L. Murialdo, 1
Seminario di Geometria
Martin Ulirsch ((University of Frankfurt))
What is the fundamental group of a tropical curve?
An tropical curve is a finite metric graph (possibly with further decorations such as integer vertex weights or a sheaf of harmonic functions). The topological fundamental group of the underlying graph is a finitely generated free group that classifies all topological covers. One might suspect that this is all there is. In this talk I intend to convince you that there are at least two other different candidates that answer the question in the title: one that classifies tropical admissible covers, and another that classifies realizable tropical admissible covers. This gives a new perspective on the classical correspondence theorem for algebraic and tropical Hurwitz numbers and allows us to (re-)construct tropical/logarithmic compactifications of the moduli space of curves with level structures and of profinite Teichmueller space. This talk surveys joint work in progress with Yoav Len, Mattia Talpo, and Dmitry Zakharov.
Venerdì 12 aprile 2019
Ore 15:00, Aula 32, Facoltà di Ingegneria Civile e Industriale Sapienza, via Eudossiana 18, Roma
Amy Shen (Okinawa Institute of Science and Technology, Japan)
New observations of hydrodynamic instabilities around junctions by using microfluidics
Microfluidics has emerged as a powerful platform of investigating flow instabilities at small lengh scales,as it provides access to regimes of low inertia and high elasticity and allows for the study of purely elastic flow instabilities and elastic turbulence,which occur at low Reynolds numbers but high Weissenberg numbers.By employing a state-of-the-art microfabrication technique (selective laser-induced etching) to fabricate glass microfluidic devices, we create platforms for discovering new insights on flow instabilties of complex fluids, assisted by a number of flow visualization and diagnostic techniques.In this talk,I will focus on an example of using cross-slot microfluidics to explore how fluid elasticity affects inertial flow instability: Simple fluids often display flow instabilities involving the production of vortices.However,studying how polymers and vortices interact is challenging because vortices generally fluctuate significantly and polymer effects at low concentrations can be subtle.A better understanding of these interactions is needed to optimize the use of polymer additives in industrial and biomedical applications ranging from lab-on-a-chip devices to large pipelines.We fabricated unique glass microfluidic devices containing junctions to make measurements on a single, steady, stationary vortex by direct visualization at high frame rates.By adding increasing amounts of a flexible polymer to water-based solvents,we discovered that the addition of the polymer is destabilizing and lowers the threshold flow rate needed for vortex formation.At the same time, we found that the polymer significantly reduces the strength of the resulting vortex.Our discoveries provide new insight regarding the competing effects of inertial and elastic instabilities on vortex formation and dynamics at small length scales.If time permits,I will also show some ongoing work of flow around microfluidic cylinders using both polymer and surfactant wormlike micellar solutions.
Venerdì 12 aprile 2019
Ore 9:30:, Aula Magna, Rettorato, Sapienza Università di Roma
Convegno sui Licei Matematici del Lazio
Il Convegno sui Licei Matematici del Lazio si propone di far conoscere il progetto Liceo Matematico e di promuovere un confronto fra le varie scuole che hanno aderito al progetto. Interverranno, tra gli altri, Claudio Bernardi (Dipartimento di Matematica, Sapienza Università di Roma), Stefania Gubbiotti (Dipartimento di Scienze Statistiche, Sapienza Università di Roma), Annalisa Malusa (Dipartimento di Matematica, Sapienza Università di Roma), Marta Menghini (Dipartimento di Matematica, Sapienza Università di Roma), Giovanni Organtini (Dipartimento di Fisica, Sapienza Università di Roma).
Venerdì 12 aprile e sabato 13 aprile 2019
Aula I - Gini, Dipartimento di Statistica, Sapienza Universita' di Roma
Workshop Nonlocal and Fractional Operators
The purpose of the meeting is to create new bridges, bringing together collaborators and researchers, in theoretical and applied mathematics, who are interested in fractional calculus. Topics include probability, mathematical physics, analysis and numerical analysis.
Dedicated to Prof. Renato Spigler (Dept. Mathematics and Physics, Roma Tre University).
Informations and programme at
https://sites.google.com/view/lfo12-13aprile2019/home
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