05/06/18  Seminario  14:30  15:30  1201 Dal Passo  Gabriele Grillo  Politecnico di Milano  On some nonlinear diffusions on manifolds
I shall discuss recent results on the porous medium and fast diffusion equations on negatively curved manifolds. Among the main problems considered I mention detailed asymptotics of positive solutions, that depend in a crucial way on curvature assumptions. Uniqueness of solutions in suitable classes is another critical issue, and I shall discuss how in the fast diffusion case this turns out to be related to parabolicity, a purely linear concept. 
31/05/18  Seminario  13:30  15:00  1201 Dal Passo  Oleg Davydov  University of Giessen  Local Approximation with Polynomials and Kernels
Many numerical algorithms for data fitting and numerical PDEs require local approximation of unknown function values or
derivatives from the data at arbitrary locations in R^d.
I will present recent results (joint work with Robert Schaback) on the error bounds for both polynomial and kernelbased methods of local approximation and numerical differentiation, and their applications 
25/05/18  Seminario  16:30  17:30  1101 D'Antoni  Giovanni CERULLI IRELLI  “Sapienza” Università di Roma  Cellular decomposition of quiver Grassmannians
I will report on a joint project with F. Esposito, H. Franzen and M. Reineke – cf. arXiv:1804.07736. Quiver Grassmannians are projective varieties parametrizing subrepresentations of quiver representations of a fixed dimension vector. The geometry of such projective varieties can be studied via the representation theory of quivers (or of finite dimensional algebras). Quiver Grassmannians appeared in the theory of cluster algebras. As a consequence of the positivity conjecture of Fomin and Zelevinsky, the Euler characteristic of quiver Grassmannians associated with rigid quiver representations must be positive; this fact was proved by Nakajima.
We explore the geometry of quiver Grassmannians associated with rigid quiver representations: we show that they have property (S) meaning that: (1) there is no odd cohomology, (2) the cycle map is an isomorphism, (3) the Chow ring admits explicit generators defined over any field. As a consequence, we deduce that they have polynomial point count. If we restrict to quivers which are of finite or affine type (i.e. orientation of simplylaced extended Dynkin diagrams) we can prove much more: in this case, every quiver Grassmannian associated with an indecomposable representation (not necessarily rigid) admits a cellular decomposition. 
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. 