Alberto Boscaggin, Università di Torino, Periodic solutions to perturbed Kepler problems, Tuesday, May 22, 2018, time 15:15, Aula seminari 3° piano
Abstract:Abstract:
As well known (by third Kepler’s law) the Kepler problem has many periodic solutions with minimal period T (for any given T > 0). We will try to understand how many of them survive after a T-periodic external perturbation preserving the Newtonian structure of the equation. In doing this, we will be naturally led to the concept of generalized solution and to the theory of regularization of collisions in Celestial Mechanics. Joint work with Rafael Ortega (Granada) and Lei Zhao (Augsburg).

Carlo Mantegazza, Università degli Studi di Napoli Federico II, Evolution by curvature of networks in the plane, Wednesday, May 16, 2018, time 15:15, Aula seminari piano 3
Abstract:Abstract:
We will present the state-of-the-art of the problem of the motion by curvature of a network of curves in the plane, discussing existence, uniqueness, singularity formation and asymptotic behavior of the flow.

Alessandro Savo, Università La Sapienza Roma, Heat content asymptotics of bounded domains, Tuesday, May 08, 2018, time 15:15, Aula Seminari 3° piano
Abstract:Abstract:
For a bounded domain in a Riemannian manifold, we consider the solution of the heat equation with unit initial data and Dirichlet boundary conditions. Integrating the solution with respect to the space variable one obtains the function of time known in the literature as the "heat content" of the given domain. In this talk we show how the geometry of the boundary affects heat diffusion by examining the small time behavior of the heat content. In particular, we study a three term asymptotic expansion for polyhedral Euclidean domains, and give a recursive algorithm for the calculation of the entire asymptotic series when the boundary is smooth.

Adriano Pisante, Università degli Studi di ROMA "La Sapienza" , Large deviations for the stochastic Allen-Cahn approximation of the mean curvature flow, Thursday, May 03, 2018, time 15:15, Aula seminari 3° piano
Abstract:Abstract:
We consider the sharp interface limit for the Allen-Cahn 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.

Zindine Djadli, Université Grenoble Alpes, A review on some fourth order problems on manifolds, Tuesday, April 24, 2018, time 15:15, Sala del Consiglio 7° piano
Abstract:Abstract:
I will review some recent works on some non linear problem on manifolds, mostly in conformal geometry. This seminar is organized within the PRIN 2015 Research project «Variational methods, with applications to problems in mathematical physics and geometry» Grant Registration 2015KB9WPT_010, funded by MIUR – Project coordinator Prof. Gianmaria Verzini

Tobias Weth, Goethe-Universitat Frankfurt, Serrin's overdetermined problem on the sphere, Monday, April 23, 2018, time 16:00, Aula 6° piano
Abstract:Abstract:
In this talk, I will discuss Serrin's overdetermined boundary value problem \begin{equation*} -\Delta\, u=1 \quad \text{ in $\Omega$},\qquad u=0, \; \partial_\eta u=\textrm{const} \quad \text{on $\partial \Omega$} \end{equation*} in subdomains $\Omega$ of the round unit sphere $S^N \subset {\mathbb R}^{N+1}$, where $\Delta$ denotes the Laplace-Beltrami operator on $S^N$. We call a subdomain $\Omega$ of $S^N$ a Serrin domain if it admits a solution of this overdetermined problem. In our main result, we construct Serrin domains in $S^N$, $N \ge 2$ which bifurcate from symmetric straight tubular neighborhoods of the equator. By this we complement recent rigidity results for Serrin domains on the sphere. This is joint work with M.M.Fall and I.A.Minlend (AIMS Senegal). This seminar is organized within the PRIN 2015 Research project «Variational methods, with applications to problems in mathematical physics and geometry» Grant Registration 2015KB9WPT_010, funded by MIUR – Project coordinator Prof. Gianmaria Verzini