Notiziario Scientifico
a cura del Dipartimento di Matematica G. Castelnuovo, Sapienza Università di Roma
Settimana dal 25-02-2019 al 03-03-2019
Lunedì 25 febbraio 2019
Ore 14:15, Aula di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Analisi Matematica
Luca Rossi (Universita' di Padova)
Analisi di stabilità per problemi di Neumann in domini illimitati
Esistono differenti concetti di stabilità nel quadro delle equazioni ellittiche e paraboliche in domini illimitati. Qual è il legame tra di loro e quali condizioni le garantiscono? Affronteremo tali questioni con l'ausilio della nozione di autovalore principale generalizzato, ispirato ad una serie di lavori in collaborazione con H. Berestycki. Come applicazione, mostreremo la validità dell'effetto "hair-trigger" per equazioni di tipo Fisher-KPP in domini generali.
Lunedì 25 febbraio 2019
Ore 14:30, Aula D'Antoni, Dipartimento di Matematica, Università degi Studi di Roma "Tor Vergata"
Algebra and Representation Theory Seminar
Ghislain Fourier (RWTH Aachen)
Recent developments on degenerations of flag and Schubert varieties
I'll recall flag varieties and Schubert varieties, and building on that PBW and linear degenerations. This first part is meant to be an introduction for Master and Phd-students. I'll proceed with recent results on PBW degenerations of Schubert varieties, explaining triangular and rectangular Weyl group elements. The talk will end with several open questions, discussing the current limit of generalizations.
Martedì 26 febbraio 2019
Ore 14:30, Dal Passo, Dipartimento Matematica "Tor Vergata"
Seminario
Claudio Bonanno (Universita' di Pisa)
Asymptotic behaviour of chains of interacting particles
One interesting problem in the study of chains of particles with nonlinear interactions is to describe and classify the possible asymptotic behaviours. The possible behaviours obviously depends on the nature of the interactions, but there are similarities in large classes of systems. Considering Hamiltonian systems I will discuss the role played by the existence of a conservation law independent from energy, and introduce a characterization of the asymptotic behaviours based on a notion of complexity.
Martedì 26 febbraio 2019
Ore 15:00, Aula di Consiglio, Dipartimento di Matematica Guido Castelnuovo, Sapienza Università di Roma
Seminario di Modellista Differenziale Numerica
Ourania Giannopoulou (Dipartimento di Matematica Guido Castelnuovo, Sapienza Università di Roma)
Chorin’s approaches revisited: Particle Vortex Method vs Finite Volume Method
In this work a Vortex Particle Method is combined with a Boundary Element Method for the study of viscous incompressible planar flow around solid bodies. The method is based on Chorin’s operator splitting approach, consisting of an advection step followed by a diffusion step. The evaluation of the advection velocity exploits the Helmholtz-Hodge Decomposition, while the no–slip condition is enforced by an indirect boundary integral equation. No mesh is used for the solution of the Poisson equation for the velocity (advection step) and the diffusion step is performed on a Regular Point Distribution with no topological connection; therefore, the resulting algorithm is completely meshless. We also revise the use of the same decomposition for the solution of the Navier–Stokes equations in primitive variables and its role in maintaining the divergence–free constraint. The results are compared with those obtained by a mesh-based Finite Volume Method, where the pseudo-compressible iteration is exploited to enforce the solenoidal constraint on the velocity field. Several benchmark tests were performed for verification and validation purposes; in particular, the unsteady flow past a circular cylinder, an ellipse with incidence and an equilateral triangle was simulated for several values of the Reynolds number.
Martedì 26 febbraio 2019
Ore 16:00, Aula D'Antoni, Dipartimento di Matematica dell'Università di Roma "Tor Vergata"
Seminario di Analisi Complessa
Samuele Mongodi (Politecnico di Milano)
Holomorphicity of slice-regular functions
In 2010, Ghiloni and Perotti showed how a slice-regular function f from a real alternative algebra A to itself is induced, in a suitable sense, by a holomorphic function F from the complex numbers to the complexification of A; however, there is no evident "holomorphic" link between the values of f and the values of F. I want to show, in the particular case where A is the algebra of quaternions H, how the set of values of F which induce a zero of f is actually a complex subspace of the complexification of H and how a number of properties of slice-regular functions can be therefore deduced from the classical properties of holomorphic functions. Moreover, this approach gives an identification of the set of imaginary units of H with a complex submanifold of a (complex) grassmannian, or, in other words, how we obtain a natural complex structure on such set which is compatible with slice-regularity; this point of view is linked to the work of Gentili, Salamon, Stoppato on the twistorial lift of a slice-regular function. If time permits, I'll hint also to the general approach for the case of an associative algebra.
Mercoledì 27 febbraio 2019
Ore 11:00, Aula 1b1 Palazzina RM 002, Dipartimento di Scienze di Base e Applicate per l’Ingegneria, , Sapienza Università di Roma
Incontri di Analisi MaTÈmatica
Giusi Vaira (Università della Campania "Luigi Vanvitelli")
On an elliptic equation with critical growth and Hardy potential
I will discuss classification results for the critical p-Laplace equation in the whole space. In particular I shall present some new results in collaboration with F. Oliva and B. Sciunzi regarding the doubly critical equation involving the Hardy potential.
Mercoledì 27 febbraio 2019
Ore 12:15, Aula 1b1 Palazzina RM 002, Dipartimento di Scienze di Base e Applicate per l’Ingegneria, Sapienza Università di Roma
Incontri di Analisi MaTÈmatica
Michal Kowalczyk (Universidad de Chile)
Maximal solution of the Liouville equation in doubly connected domains
In this talk I will discuss a new existence result for the widely studied Liouville problem \(\Delta u+\lambda2 e^{\,u}=0\)in a bounded, two dimensional, doubly connected domain with Dirichlet boundary conditions. I will show that for a sequence of \(\lambda_n\to 0\) this equation has solutions that blow-up in in the whole domain. Profiles of the blowing-up solutions are related to a free boundary problem which gives a solution to an optimal partition problem for the given domain. I will also describe the role of the free boundary problem in other classical equations such as the mean field model or the prescribed Gaussian curvature equation.
Mercoledì 27 febbraio 2019
Ore 14:00, Aula di Consiglio, Dipartimento di Matematica
Seminario di Algebra e Geometria
Peter Teichner (MPIM / Berkeley)
The group of two 2-spheres linked in 4-spaces
We’ll give an introduction to the mathematics of 4-dimensional knot theory, i.e. of embedded 2-spheres in 4-space, usually called 2-knots. We’ll start with a simple construction that spins a knotted arc in 3-space into such a 2-knot. Then we’ll discuss in how many ways a second 2-knot can lie in the complement of the first. Finally, we’ll report on recent joint work with Rob Schneiderman, in which we proved the non-existence of a 4-dimensional Hopf link: Given any (possibly singular) 2-sphere in the complement of a 2-knot, there is always a deformation (link homotopy) to the trivial situation in such a way that both components stay disjoint at all times.
Mercoledì 27 febbraio 2019
Ore 14:30, Aula Dal Passo, Dipartimento di Matematica, Università di Roma "Tor Vergata"
Colloquium di Dipartimento
Alberto Abbondandolo (Ruhr-Universität Bochum)
On short closed geodesics, shadows of balls and polar bodies
How long is the shortest closed geodesic on a Riemannian sphere? How large is the shadow of a symplectic ball? How large is the volume of the polar of a centrally symmetric convex body? I will discuss how these seemingly different problems can be addressed within the setting of Reeb dynamics.
Mercoledì 27 febbraio 2019
Ore 15:00, Aula B, Dipartimento di Matematica, Sapienza
Esame finale di Dottorato
Stefano Buccheri (Sapienza)
Elliptic boundary value problems with measurable coefficients and explosive boundary conditions
In this talk I present the main results contained in my Phd thesis. It follows two different directions, always related to elliptic boundary value problems. The first one concerns existence and regularity results for a wide class of non coercive operators with convection or drift lower order terms. The second one focuses on asymptotic behaviour of large solutions, namely solutions that blows up to infinity at the boundary of the domain, to semilinear elliptic problems.
Mercoledì 27 febbraio 2019
Ore 16:30, aula di Consiglio, Dipartimento di Matematica
seminario di Fisica Matematica
Claudio Cacciapuoti (Università degli Studi dell'Insubria)
Scattering from local deformations of a semitransparent plane
I will discuss the scattering problem for a quantum particle in dimension three in the presence of a semitransparent unbounded obstacle, modeled by a surface. The generator of the dynamics is the operator formally defined as the Laplacian plus a delta-interaction supported by the surface. I will consider the case in which the surface is obtained through a local deformation of a plane, it can be identified by the graph of a compactly supported, Lipschitz continuous function. In this configuration, the reference dynamics is the one generated by the Laplacian plus a delta-interaction supported by the plane. I will discuss existence and asymptotic completeness of the wave operators, provide a representation formula for the scattering matrix, and show that the scattering matrix converges to the identity as the deformation goes to zero (with a quantitative estimate on the rate of convergence). The talk is based on the joint paper with Davide Fermi and Andrea Posilicano: J. Math. Anal. Appl. 473 (2019) 215–257.
Giovedì 28 febbraio 2019
Ore 14:30, 211, Dip. Matematica e Fisica Universita' Roma Tre Largo S. L. Murialdo 1 Palazzina C
Seminario di Geometria
Prof. Fabrizio Barroero (Universita' di Roma Tre)
Some Results on Unlikely Intersections in Semiabelian Schemes
The Zilber-Pink conjectures on unlikely intersections predict the behaviour of subvarieties of families of (semi)abelian varieties or of Shimura varieties when intersected with special subvarieties and generalises many well-known conjectures/results like Manin-Mumford, Mordell-Lang and André-Oort. After introducing the problem and giving different versions of the conjectures I will talk about recent results for curves in families of abelian varieties (joint work with L. Capuano) and in semiabelian varieties (joint work with H. Schmidt). All of these results have been proved for varieties over the algebraic numbers. In joint work in progress with G. Dill we are extending some of the known results to varieties over fields of characteristic 0.
Giovedì 28 febbraio 2019
Ore 14:30, Aula di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario P(n)/N(p)
Giulio Tralli (Università di Padova - Dipartimento di Ingegneria Civile, Edile e Ambientale (ICEA))
(Almost) Wiener criteria for parabolic equations starting from Gaussian bounds
In this talk we will discuss the regularity of boundary points for the Dirichlet problem related to (possibly degenerate) parabolic equations. We will show the validity of a Wiener-type characterization for a class of linear operators with a fundamental solution satisfying suitable two-sided Gaussian bounds. The Wiener condition is expressed, in analogy with a result by Landis for the heat equation, in terms of a series of balayages. The results I will present have been obtained in collaboration with A.E. Kogoj, E. Lanconelli, and F. Uguzzoni.
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