## Weekly Bulletin (it)

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**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*

Tutte le informazioni relative a questo notiziario devono pervenire
esclusivamente all'indirizzo di posta elettronica
*seminari@mat.uniroma1.it*
entro le ore 24 del giovedì precedente la settimana interessata.
Le comunicazioni pervenute in ritardo saranno ignorate.
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invitati a comunicare il proprio indirizzo di posta elettronica a
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Il Direttore