25/05/18  Seminario  15:00  16:00  1101 D'Antoni  Ernesto SPINELLI  “Sapienza” Università di Roma  Codimension growth and minimal varieties
In characteristic zero an effective way of measuring the polynomial identities satisfied by an algebra is provided by the sequence of its codimensions introduced by Regev. In this talk we review some features of the codimension growth of PI algebras, including the deep contribution of Giambruno and Zaicev on the existence of the PIexponent, and discuss some recent developments in the framework of group graded algebras. In particular, a characterisation of minimal supervarieties of fixed superexponent will be given. The last result is part of a joint work with O.M. Di Vincenzo and V. da Silva. 
22/05/18  Seminario  14:00  15:00  1201 Dal Passo  Filippo Giuliani  Università degli Studi "Roma Tre"  On the integrability and quasiperiodic dynamics of the dispersive DegasperisProcesi equation
The DegasperisProcesi equation
$$
u_t + c_0 u_x + gamma u_{xxx} alpha^2 u_{xxt} = left( c_2 (u^2_x+uu_{xx})  frac{2c_3}{alpha^2}u^2
ight)_x
$$
has been extensively studied by many authors, especially in its dispersionless form, since it presents interesting phenomena such as breaking waves and existence of peakonlike solutions. DegasperisHolmHone proved the integrability of this equation and they provided an iterative method to compute infinite conserved quantities.
Since the DegasperisProcesi equation is a quasilinear equation the presence of dispersive terms depends on the chosen frame. In absence of dispersive terms there are no constants of motion even controlling the $H^1$norm.
We show that, in the dispersive case, we can construct infinitely many constants of motion which are analytic and control the Sobolev norms in a neighborhood of the origin.
Moreover, thanks to the analysis of the algebraic structure of the quadratic parts of these conserved quantities we show that the (formal) Birkhoff normal form is actionpreserving (integrable) at any order. This fact is used to prove the first existence result of quasiperiodic solutions for the DegasperisProcesi equation on the circle.
These results have been obtained in collaboration with R. Feola, S. Pasquali and M. Procesi. 
21/05/18  Seminario  14:30  15:30  1101 D'Antoni  Andrew Zimmer  William & Mary University  Smoothly bounded domains covering finite volume manifolds
In this talk we will discuss the following
result: if a bounded domain with C^2 boundary covers a
manifold which has finite volume with respect to either the
Bergman volume, the K\"ahlerEinstein volume, or the
KobayashiEisenman volume, then the domain is biholomorphic
to the unit ball. The proof uses a variety of tools from Riemannian geometry and several complex variables including
the squeezing function, Busemann functions, estimates on
invariant distances, and a version of E. Cartan's fixed point
theorem. 
18/05/18  Seminario  15:00  16:00  1101 D'Antoni  Herve' Gaussier  Universita' di Grenoble  Local and Global Properties of strongly pseudoconvex domains.
I will try to explain how the geometry
of such domains imposes curvature estimates of invariant
metrics and I will discuss global equivalence problems. This
is a joint work with H.Seshadri and results obtained by
S.Gontard.

16/05/18  Seminario  16:00  17:00  1201 Dal Passo  Jacopo Bassi  SISSA  C*algebras associated to horocycle flows
Murray and von Neumann introduced the notion of crossed product to give examples of different types of factors. Since then many von Neumann algebras and C*algebras with interesting properties have been constructed following this pattern. We will give an example of a class of C*algebras to which the classification result by Elliott, Gong, Lin and Niu of 2015 cannot be applied and see some of their properties. 
15/05/18  Seminario  14:30  15:30  1201 Dal Passo  Philippe Souplet  Université Paris XIII  Reactiondiffusion systems with dissipation of mass: old and new results.
We consider positivitypreserving reactiondiffusion systems of the form
$$partial_t u_id_iDelta d_i=f_i(u),qquad u=(u_1,dots,u_m),$$
under the Neumann boundary conditions, with the structure condition $sum f_ile 0$, which guarantees that the total mass is nonincreasing in time.
Such systems are often encountered in applications, for instance in models of reversible chemistry.
Whereas global existence and boundedness of solutions is easy in the equidiffusive case $d_iequiv d$,
the question becomes quite involved in the case when the $d_i>0$ are different
(a case which is indeed relevant in models of chemical reactions),
and there has been an abundant mathematical literature on this question in the past 30 years.
Various sufficient conditions on the nonlinearities $f_i$ for global existence are known, as well as examples of finite time blowup for certain systems. The latter is a special case of the socalled diffusion induced blowup phenomenon.
We will discuss old and new results on this subject.

08/05/18  Seminario  14:30  15:30  1201 Dal Passo  Adriano Pisante  Sapienza, Università di Roma  Large deviations for the stochastic AllenCahn approximation of the mean curvature flow
We consider the sharp interface limit for the AllenCahn equation on the three dimensional torus with deterministic initial condition and deterministic or stochastic forcing terms. In the deterministic case, we discuss the convergence of solutions to the mean curvature flow, possibly with a forcing term, in the spirit of the pioneering work of Tom Ilmanen (JDG '93). In addition we analyze the convergence of the corresponding action functionals to a limiting functional described in terms of varifolds. In the second part I will comment on related results for the stochastic case, describing how this limiting functional enters in the large deviation asymptotics for the laws of the corresponding processes in the joint sharp interface and small noise limit. 
24/04/18  Seminario  14:30  15:30  1201 Dal Passo  Fabio Camilli  Sapienza, Università di Roma  Timefractional 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 HamiltonJacobiBellman and FokkerPlanck equations with timefractional derivatives.
We first discuss separately the wellposedness 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 BlankKellerLiverani, BaladiTsujii and other dynamicists and their microlocal interpretation by FaureSjoestrand.
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 DyatlovGuillarmou, DangRiviere and Hadfield.
The talk will be nontechnical 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. 