|24/04/18||Seminario||14:30||15:30||1201 Dal Passo||Fabio Camilli||Sapienza, Università di Roma||Time-fractional Mean Field Games|
We consider a Mean Field Games model where the dynamics of the agents is subdiffusive. According to the optimal control
interpretation of the problem, we get a
system involving Hamilton-Jacobi-Bellman and Fokker-Planck equations with time-fractional derivatives.
We first discuss separately the well-posedness of each of the two equations and
then of the Mean Field Games system.
|19/04/18||Colloquium||15:30||16:30||1201 Dal Passo||Maciej ZWORSKI||Berkeley||From classical to quantum and back
Microlocal analysis exploits mathematical manifestations of the classical/quantum (particle/wave) correspondence and has been a very successful tool in spectral theory and partial differential equations. We can say that these two fields lie on the "quantum/wave side".
In the last few years microlocal methods have been applied to the study of classical dynamical problems, in particular of chaotic flows. That followed the introduction of specially tailored spaces by Blank--Keller--Liverani, Baladi--Tsujii and other dynamicists and their microlocal interpretation by Faure--Sjoestrand.
I will explain how it works in the context of Ruelle resonances, decay of correlations and meromorphy of dynamical zeta functions and will also present some recent advances by Dyatlov--Guillarmou, Dang--Riviere and Hadfield.
The talk will be non-technical and is intended as an introduction to both microlocal analysis and to chaotic dynamics.
|17/04/18||Seminario||15:00||16:00||1201 Dal Passo||Marco Mazzola||Univ. Pierre et Marie Curie (Paris VI)||Necessary optimality conditions for infinite dimensional state constrained control problems
We consider semilinear control systems in infinite dimensional Banach spaces, in the presence of constraints for the state of the system. Necessary optimality conditions for a Mayer problem associated to such systems will be discussed. In particular, a simple proof of a version of the constrained Pontryagin maximum principle, relying on infinite dimensional neighbouring feasible trajectories results, will be provided. This proof includes sufficient conditions for the normality of the maximum principle. Some applications to control problems governed by PDEs will be discussed. This talk is based on a joint work with Hélène Frankowska and Elsa Maria Marchini.
|13/04/18||Seminario||16:00||17:00||1101 D'Antoni||René SCHOOF||Università di Roma "Tor Vergata"||Il teorema di Lagrange per schemi in gruppi piatti e finiti
Il teorema di Lagrange dice che in un gruppo di cardinalità n la potenza n-esima di ogni elemento è uguale all’elemento neutro. Una congettura classica afferma che un risultato simile vale per schemi in gruppi piatti e finiti. Spiegherò la dimostrazione di un caso speciale della congettura.
|13/04/18||Seminario||14:30||15:30||1101 D'Antoni||Velleda BALDONI||Università di Roma ||Multiplicities & Kronecker coefficients
Multiplicities of representations appear naturally in different contexts and as such their description could use different languages. The computation of Kronecker coefficients is in particular a very interesting problem which has many
I will describe an approach based on methods from symplectic geometry and residue calculus (joint work with M. Vergne and M. Walter). I will state the general formula for computing Kronecker coefficients and then give many examples computed using an algorithm that implements the formula.
The algorithm does not only compute individual Kronecker coefficients, but also symbolic formulas that are valid on an entire polyhedral chamber. As a byproduct, it is possible to compute several Hilbert series.
|10/04/18||Seminario||14:30||15:30||1201 Dal Passo||Massimo Grossi||Universita' di Roma "La Sapienza"||Radial nodal solution for Moser-Trudinger problems|
We study the asymptotic behavior of least-energy nodal solutions for suitable Moser-Trudinger problems. We will show that appear different phenomena with respect to other nonlinearities (for example power or sinh-type nonlinearites).
|27/03/18||Seminario||14:30||15:30||1201 Dal Passo||Alessio Pomponio||Politecnico di Bari||The Born-Infeld equation: solutions and equilibrium measures|
In this talk, we deal with the Born-Infeld equation which appears in the Born-Infeld nonlinear electromagnetic theory.
In the first part of the talk, we discuss existence, uniqueness and regularity of the solution of the Born-Infeld equation. In the second part, instead, we study existence of equilibrium measures, namely distributions that produce least-energy potentials among all the possible charge distributions, and properties of the corresponding equilibrium potentials.
The results have been obtained in joint works with Denis Bonheure, Pietro d'Avenia and Wolfgang Reichel.
|21/03/18||Seminario||16:00||17:00||1201 Dal Passo||Wojciech Dybalski||TUM Munich||Infravacuum representations and velocity superselection in non-relativistic QED|
It is well established that in QED plane-wave configurations of the electron corresponding to different velocities induce inequivalent representations of the algebra of the electromagnetic field. This phenomenon of velocity superselection is one of the standard features of the infraparticle picture of the electron, which
relies on mild fluctuations of the electromagnetic field at spacelike infinity. As these fluctuations are large in the complementary infravacuum description of the electron, it has long been conjectured that velocity superselection, and other aspects of the infraparticle problem, can be cured in this approach. We consider two implementations of the infravacuum picture in a Pauli-Fierz model of QED. In the first one, which relies on a
decomposition of the electron into the bare electron and a cloud of soft photons, we prove the absence of velocity superselection. In the second one, which does not rely on such a decomposition, we show that velocity superselection persists, but can be eliminated by suitably inverting the representations. In the language of superselection theory,
we exhibit an unusual situation, where a family of distinct sectors has one and the same conjugate sector. (Joint work with Daniela Cadamuro).
|20/03/18||Seminario||14:30||15:30||1201 Dal Passo||Mikaela Iacobelli||Durham University||Recent results on quasineutral limit for Vlasov-Poisson via Wasserstein stability estimates|
The Vlasov-Poisson system is a kinetic equation that models collisionless plasma. A plasma has a characteristic scale called the Debye length, which is typically much shorter than the scale of observation. In this case the plasma is called 'quasineutral'. This motivates studying the limit in which the ratio between the Debye length and the observation scale tends to zero. Under this scaling, the formal limit of the Vlasov-Poisson system is the Kinetic Isothermal Euler system.
The Vlasov-Poisson system itself can formally be derived as the limit of a system of ODEs describing the dynamics of a system of N interacting particles, as the number of particles approaches infinity. The rigorous justification of this mean field limit remains a fundamental open problem.
In this talk we present the rigorous justification of the quasineutral limit for very small but rough perturbations of analytic initial data for the Vlasov-Poisson equation in dimensions 1, 2, and 3. Also, we discuss a recent result in which we derive the Kinetic Isothermal Euler system from a regularised particle model. Our approach uses a combined mean field and quasineutral limit.
|16/03/18||Seminario||15:30||16:30||1101 D'Antoni||Kirill ZAYNULLIN||University of Ottawa||Equivariant motives and Sheaves on moment graphs
Goresky, Kottwitz and MacPherson showed that the equivariant
cohomology of varieties equipped with an action of a torus T can be
described using the so called moment graph, hence, translating computations in equivariant cohomology into a combinatorial problem. Braden and MacPherson proved that the information contained in this moment graph is sufficient to compute the equivariant intersection cohomology of the variety. In order to do this, they introduced the notion of a sheaf on moment graph whose space of sections (stalks) describes the (local) intersection cohomology. These results motivated
a series of paper by Fiebig, where he developed and axiomatized sheaves of moment graphs theory and exploited Braden-MacPherson’s construction to attack representation theoretical problems.
In the talk we explain how to extend this theory of sheaves on moment
graphs to an arbitrary algebraic oriented equivariant cohomology h
in the sense of Levine-Morel (e.g. to K-theory or algebraic
cobordism). Moreover, we show that in the case of a total flag variety X the space of global sections of the respective h-sheaf also describes an endomorphism ring of the equivariant h-motive of X.
This is a very recent joint work with Rostislav Devyatov and Martina Lanini.