Notiziario Scientifico
Notiziario dei Seminari di carattere matematico
a cura del Dipartimento 'G. Castelnuovo'
Sapienza Università di Roma
Settimana dal 21 al 27 novembre 2016
Lunedì 21 novembre 2016
Ore 11:15, aula B
Incontro di lavoro su Calcolo delle Variazioni e Γ-convergenza/
Working seminar on Calculus of Variations and Γ-convergence
Alfie Mimum (Sapienza Università di Roma)
Dimension reduction for discrete disordered elastic systems: a case study
I describe the overall behavior of variational stochastic pair-interaction systems defined
on thin domains of Rd, that is, domains consisting on a finite number of
mutually interacting overlaid copies of a portion of a stochastic lattice in Rd-1.
One of the reasons for this research lies in the fact that this kind of systems can be used to
model thin rubber objects.
Lunedì 21 novembre 2016
Ore 14:30, aula di Consiglio
seminario di Analisi Matematica
Carlo Orrieri (Sapienza Università di Roma)
A variational approach to mean field games
We present a class of mean field games with local congestion cost which have a
variational structure. The dynamical interpretation of these problems is strictly
related to the Eulerian formulation of mass transportation introduced by Benamou
and Brenier.
In this talk we are particularly interested in the vanishing viscosity limit of
the second order planning problem towards the first order one. The idea is to
combine a variational approach with a Γ-convergence argument.
This is a work in progress in collaboration with A. Porretta and G. Savaré.
Lunedì 21 novembre 2016
Ore 15:30, aula B
corso di Dottorato
Mauro Mariani (Sapienza Università di Roma)
An introduction to Symbolic Dynamics I
Lunedì 21 novembre 2016
Ore 16:00, aula C
seminario BSD
Simone Diverio (Sapienza Università di Roma)
Elementi di geometria hermitana e kaehleriana II
Martedì 22 novembre 2016
Ore 14:00, aula di Consiglio
seminario di Probabilità e Statistica Matematica
Carlo Orrieri (Sapienza Università di Roma)
Controlled Vlasov-type dynamics
The aim of the talk is to connect the optimal control of Vlasov-type PDEs with large
systems of controlled interacting particles/agents. The main difference towards the
classical mean-field theory, where the particle are freely interacting with each other,
is the presence of a central planner influencing the dynamics. In this situation it
is not obvious that the mean field limit should commute with the optimization.
In order to develop a rigorous limit theory for this problem we employ the well-known
concept of Γ-convergence.
The talk is based on a work in project with M. Fornasier, S. Lisini and G. Savaré
Martedì 22 novembre 2016
Ore 14:00, aula Dal Passo, Università di Roma Tor Vergata
seminario di Equazioni Differenziali
Daniele Bartolucci (Università di Roma Tor Vergata)
Global bifurcation analysis of mean field equations and the Onsager microcanonical
description of two-dimensional turbulence
We discuss the solution of two long standing open problems closely related
to the mean field Liouville-type equation. On one side, we find
the global behaviour of the entropy for the mean field Microcanonical
Variational Principle ((MVP) for short), as it arise in the Onsager
description of two-dimensional turbulence on strictly starshaped domains
of second kind.
Among other things we find a region of strict convexity of the entropy. On
the other side, to achieve that goal, we have to catch the global
bifurcation diagram of solutions of the mean field equation, emanating from
λ=0 and crossing λ=8π.
The (MVP) suggests the right variable (which is the energy) to be used to
obtain a global parametrization of solutions. In particular a crucial
spectral simplification is obtained by using the fact that, by definition,
solutions of the (MVP) maximize the entropy at fixed energy and total vorticity.
Martedì 22 novembre 2016
Ore 14:30, aula D'Antoni, Università di Roma Tor Vergata
seminario di Geometria Algebrica
Thomas Dedieu
Enumerazione di curve in superficie toriche mediante geometria tropicale
secondo Mikhalkin e Brugallé I
Martedì 22 novembre 2016
Ore 16:00, aula F
minicorso
Marco Falconi (Università di Roma Tre)
An introduction to semiclassical analysis in infinite dimensions, and its
applications to mean and quantum field theories I
In this short course we introduce the basic tools of semiclassical analysis, for
systems with an infinite dimensional phase space. In order to do so, we will touch
upon many interesting topics of modern analysis, from operator algebras to optimal
transportation. Some physical applications will also be discussed, in particular
Bohr's correspondence principle for bosonic quantum field theories, and the mean
field evolution of general quantum states.
Mercoledì 23 novembre 2016
Ore 09:00, aula F
minicorso
Marco Falconi (Università di Roma Tre)
An introduction to semiclassical analysis in infinite dimensions, and its
applications to mean and quantum field theories II
Mercoledì 23 novembre 2016
Ore 14:30, aula di Consiglio
seminario di Algebra e Geometria
Niels Kowalzig (Sapienza Università di Roma)
When Ext is a Batalin-Vilkovisky algebra
We show under what conditions the complex computing general Ext-groups carries the
structure of a cyclic operad such that Ext becomes a Batalin-Vilkovisky algebra.
This is achieved by transferring cyclic cohomology theories for the dual of a (left)
Hopf algebroid to the complex in question, which asks for the notion of contramodules
introduced along with comodules by Eilenberg-Moore half a century ago. Another crucial
ingredient is an explicit formula for the inverse of the Hopf-Galois map on the dual,
by which we illustrate recent categorical results and answering a long-standing open
question. As an application, we prove that the Hochschild cohomology of an associative
algebra A is Batalin-Vilkovisky if A itself is a contramodule over its enveloping algebra.
This is, for example, the case for symmetric algebras and Frobenius algebras with
semisimple Nakayama automorphism. We also recover the construction for Hopf algebras.
Mercoledì 23 novembre 2016
Ore 16:30, aula di Consiglio
seminario di Fisica Matematica
Marco Falconi (Università di Roma Tre)
External Potentials Generated by the Interaction with a Semiclassical Boson
Field
In physical experiments of condensed matter, quantum particles (atoms) are immersed
in controllable external potentials, such as harmonic traps and optical lattices.
These potentials are obtained using finely tuned lasers, or magnetic fields, acting
on the atoms. In this talk I will present some results, obtained in collaboration
with Michele Correggi, that shed light on the procedure above. We consider a coupled
system consisting of N quantum particles in (linear) interaction with a scalar boson
field. Using tools of infinite dimensional semiclassical analysis, a partially
classical limit on the scalar field is studied. We prove the convergence of the
partial trace of the full Hamiltonian to an effective reduced Hamiltonian on the
particles alone (in the strong resolvent sense). The effective Hamiltonian contains
an induced external potential, that has an explicit form that depends only on the
state of the field. We also prove the convergence of the ground state energy of the
full quantum system to the infimum on all possible classical field configurations of
the ground state energy of the effective Hamiltonian.
Giovedì 24 novembre 2016
Ore 14:00, aula B
minicorso
Marco Falconi (Università di Roma Tre)
An introduction to semiclassical analysis in infinite dimensions, and its
applications to mean and quantum field theories III
Giovedì 24 novembre 2016
Ore 14:30, aula di Consiglio
seminario PDN
Eleonora Cinti (Università di Torino)
Sharp energy estimates and flatness results for nonlocal phase transitions
We present some recent results in the study of two, closely related, nonlocal problems:
the fractional Allen-Cahn equation and the nonlocal minimal surfaces. More precisely,
we show sharp energy estimates for minimizers and stable objects for both problems and,
as a consequence, we deduce some flatness results in low dimensions. These results are
contained in several works in collaborations with X. Cabré, J. Serra and E. Valdinoci.
Venerdì 25 novembre 2016
Ore 09:30, aula Magna, Gran Sasso Science Institute, viale F. Crispi 7, L'Aquila
'Prima Giornata DinAmica' Incontro del network 'DinAmicI: young italian dynamicists'
Mauro Artigiani (SNS Pisa) 'Lagrange spectrum of Veech translation surfaces'
Anna Miriam Benini (Roma Tor Vergata) 'Singular values and periodic points'
Marcello Seri (Reading, UK) 'Quantum Confinement on Non-Complete Riemannian Manifolds'
Venerdì 25 novembre 2016
Ore 11:30, Biblioteca - Sala Ingegneria Geotecnica, Dipartimento di Ingegneria Strutturale
e Geotecnica (DISG), via Eudossiana 18
seminario
Stefano Vidoli
Quasi-static and dynamic actuation of multistable shells
Venerdì 25 novembre 2016
Ore 19:30, libreria Assaggi, via degli Etruschi 4
Percorsi d'autore: Ennio De Giorgi, genio della matematica
Presentazione del libro: Uno spirito puro di Andrea Parlangeli
Intervengono: Giovanni Bellettini (Università Roma Tor Vergata)
Andrea Braides (Università Roma Tor Vergata)
Maria Giovanna Garroni Platone (Sapienza Università Roma),
Andrea Parlangeli (autore)
Modera: Roberta Fulci (Rai Radio3 Scienza)
Ennio De Giorgi è stato uno dei matematici più straordinari del secolo
scorso. Nel 1957, quando era a Roma, a soli 29 anni risolse uno dei grandi problemi
del '900, il 19o problema di Hilbert, battendo sul tempo John Nash, protagonista
del libro e del film A Beautiful Mind.
In seguito De Giorgi ha rivoluzionato lo studio delle superfici minime come le bolle di sapone
e ha aperto nuovi orizzonti alla matematica. Si è battuto anche in difesa dei diritti
umani ed è stato uno dei personaggi più carismatici della Scuola Normale di Pisa,
dove ha vissuto per quasi quarant'anni. Quest'anno si celebrano i vent'anni dalla sua scomparsa.
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