Notiziario Scientifico

Notiziario dei seminari di carattere matematico
a cura del Dipartimento di Matematica G. Castelnuovo
Sapienza Università di Roma

Settimana dal 19 al 25 novembre 2018

Lunedì 19 novembre 2018
Ore 14:15, aula di Consiglio
seminario di Analisi Matematica
Samuel Nordmann (CAMS, PSL Université, Paris)
Stable solutions of semilinear elliptic equations in unbounded domains
We consider a general semilinear elliptic equation with Neumann boundary condition. A seminal result of Casten-Holland (1978) states that, if the domain is convex and bounded, all stable bounded solutions are constant. In this talk, we will investigate whether this result extends to convex unbounded domains.

Martedì 20 novembre 2018
Ore 14:30, aula di Consiglio
seminario di Modellistica Differenziale Numerica
Gerardo Toraldo (Dipartimento di Matematica e Applicazioni "Renato Caccioppoli" dell'Università di Napoli Federico II)
Proportionality based two-phase gradient methods for large scale quadratic programming problems
We propose a two-phase gradient-based method for general Quadratic Programming (QP) problems. Such kind of problems arise in many real-world applications, such as Support Vector Machines, multicommodity network flow and logistics or in variational approaches to image deblurring. Moreover, an effective QP solver is the basic building block in many algorithms for the solution of nonlinear constrained problems. The proposed approach alternates between two phases: an identification phase, which performs Gradient Projection iterations until either a candidate active set is identified or no reasonable progress is made, and an unconstrained minimization phase, which reduces the objective function in a suitable space defined by the identification phase, by applying either the conjugate gradient method or any spectral gradient method. A critical issue about a two-phase method stands in the design of an effective way to switch from phase 1 to phase 2. In our method, this is based on a comparison between a measure of optimality in the reduced space and a measure of bindingness of the active variables, defined by extending the concept of proportional iterate, which was proposed by some authors for box-constrained problems. If the objective function is bounded, the algorithm converges to a stationary point. For strictly convex problems, the algorithm converges to the optimal solution in a finite number of steps even in the case of degeneracy. Extensive numerical experiments show the effectiveness of the proposed approach. This talk is based on joint work with Daniela di Serafino (Dipartimento di Matematica e Fisica dell'Università della Campania "Luigi Vanvitelli") and Marco Viola (Dipartimento di Ingegneria Informatica Automatica e Gestionale "Antonio Ruberti" della Sapienza Università di Roma).

Martedì 20 novembre 2018
Ore 14:30, aula Dal Passo, dipartimento di Matematica, Università di Roma Tor Vergata, via della Ricerca Scientifica 1
colloquium di Dipartimento
Masayasu Mimura (Musashino University/Meiji University)
Transient Self-Organization: Closed Systems vs. Open systems of Reaction and Diffusion
After Turing's theoretical prediction on biological pattern formation, various types of patterns related to self-organization can be discovered in open systems due to the interaction of reaction with diffusion. Turing said in his paper "The model will be a simplification and an idealization, and consequently a falsification. It is to be hoped that the features retained for discussion are those of greatest importance in the present state of knowledge". Nevertheless, mathematical communities have been much influenced by his theory. We already recognize that open systems of reaction and diffusion have generated enormous rich behaviors. On the other hand, closed systems have been gradually less interesting. However, I would like to emphasize that new biological pattern formation can be observed even in closed systems as the consequence of transient self-organization, and that the theoretical understanding of such patterns is a very important subject in nonlinear mathematics. This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006

Mercoledì 21 novembre 2018
Ore 14:00, aula L
seminario di Algebra e Geometria
Lidia Angeleri Hügel (Verona)
Silting complexes over hereditary rings
I will report on joint work with Michal Hrbek. Given a hereditary ring, we use the lattice of homological ring epimorphisms to construct compactly generated t-structures in its derived category. This leads to a classification of all (not necessarily compact) silting complexes over the Kronecker algebra.

Mercoledì 21 novembre 2018
Ore 14:00, aula 311 - Pal.C, Università di Roma Tre, largo san Leonardo Murialdo 1
seminario di Analisi Matematica
Nicola Soave (Politecnico di Milano)
The nodal set of solutions to some sublinear and singular elliptic equations

Mercoledì 21 novembre 2018
Ore 15:15, aula B
seminario di Fisica Matematica
Mathieu Lewin (CNRS, Université Paris-Dauphine)
Nonlinear Gibbs measures and their derivation from many-body quantum mechanics
In this talk I will define and discuss some probability measures in infinite dimensions, which play an important role in (S)PDE, in Quantum Field Theory and for Bose-Einstein condensates. Those are Gibbs measures associated with the Gross-Pitaevskii and Hartree energies. In dimensions larger than or equal to 2, the measures are concentrated on distribution spaces, and the nonlinear term has to be renormalized. I will then present some recent results in collaboration with Phan Thanh Nam and Nicolas Rougerie about the derivation of these measures from many-body quantum mechanics in a mean-field type limit.

Giovedì 22 novembre 2018
Ore 14:30, aula di Consiglio
seminario P(n)/N(p)
Luca Martinazzi (Università di Padova)
News on the Moser-Trudinger inequality
The existence of critical points for the Moser-Trudinger inequality for large energies has been open for a long time. We will first show how a collaboration with G. Mancini allows to recast the Moser-Trudinger inequality and the existence of its extremals (originally due to L. Carleson and A. Chang) under a new light, based on sharp energy estimate. Building upon a recent subtle work of O. Druet and P-D. Thizy, in a work in progress with O. Druet, A. Malchiodi and P-D. Thizy, we use these estimates to compute the Leray-Schauder degree of the Moser-Trudinger equation (via a suitable use of the Poincaré-Hopf theorem), hence proving that for any bounded non-simply connected domain the Moser-Trudinger inequality admits critical points of arbitrarily high energy. In a work in progress with F. De Marchis, O. Druet, A. Malchiodi and P-D. Thizy, we expect to use a variational argument to treat the case of a closed surface.

Venerdì 23 novembre 2018
Ore 16:00, aula Picone
seminario per insegnanti (Piano Lauree Scientifiche)
Nicoletta Lanciano (Sapienza Università di Roma)
La Luna a 50 anni dal primo sbarco

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