### Seminari

### Prossimi Seminari

**Dealing with unreliable computing platforms at extreme scale**

Luc Giraud, INRIA (Inria Bordeaux – Sud-Ouest)

mercoledì 23 gennaio 2019 alle ore 14:00, Aula Consiglio VII Piano – Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO**Poroelasticity: Discretizations and fast solvers based on geometric multigrid methods**

Francisco José Gaspar Lorenz, Department of Applied Mathematics -Zaragoza University – Spain

giovedì 31 gennaio 2019 alle ore 14:00, Sala Consiglio VII Piano – Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO**Application of Polyconvexity and multivariable convexity of energy potentials in nonlinear solid mechanics**

Javier Bonet, University of Greenwich

giovedì 14 febbraio 2019 alle ore 14:00, Aula Consiglio VII Piano – Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO

### Seminari Passati

**Computer, simulazioni ed esperimenti: all’alba di un nuovo metodo sperimentale?**

Viola Schiaffonati, Politecnico di Milano

mercoledì 9 maggio 2018 alle ore 12:15, Politecnico di Milano Campus Bonardi Edificio14 aula B21**Heat content asymptotics of bounded domains**

Alessandro Savo, Università La Sapienza Roma

martedì 8 maggio 2018 alle ore 15:15, Aula Seminari 3° pianoABSTRACTFor 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.**Statistical inference for price staleness**

Giulia Livieri, Scuola Normale Superiore

martedì 8 maggio 2018 alle ore 13:15 precise, Aula Seminari del Sesto Piano**Large deviations for the stochastic Allen-Cahn approximation of the mean curvature flow**

Adriano Pisante, Università degli Studi di ROMA “La Sapienza”

giovedì 3 maggio 2018 alle ore 15:15, Aula seminari 3° pianoABSTRACTWe 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.**Computing disconnected bifurcation diagrams of partial differential equations**

Patrick Farrell, Mathematical Institute, Oxford

giovedì 26 aprile 2018 alle ore 14:00, Aula Consiglio VII Piano – Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANOABSTRACTComputing the distinct solutions $u$ of an equation $f(u, \lambda) = 0$ as a parameter $\lambda \in \mathbb{R}$ is varied is a central task in applied mathematics and engineering. The solutions are captured in a bifurcation diagram, plotting (some functional of) $u$ as a function of $\lambda$. In this talk I will present a new algorithm, deflated continuation, for this task. Deflated continuation has three advantages. First, it is capable of computing disconnected bifurcation diagrams; previous algorithms only aimed to compute that part of the bifurcation diagram continuously connected to the initial data.

Second, its implementation is extremely simple: it only requires a minor modification to any existing Newton-based solver. Third, it can scale to very large discretisations if a good preconditioner is available. Among other problems, we will apply this to a famous singularly perturbed ODE, Carrier’s problem. The computations reveal a striking and beautiful bifurcation diagram, with an infinite sequence of alternating pitchfork and fold bifurcations as the singular perturbation parameter tends to zero. The analysis yields a novel and complete taxonomy of the solutions to the problem. We will also apply it to discover previously unknown solutions to equations arising in liquid crystals and quantum mechanics.

This seminar is organized within the Research project MFAG 17412 «Mathematical insights of glioblastoma growth: a mechano-biology approach for patientspecific clinical tools» funded by the Italian Association for Cancer Research (AIRC), Project coordinator Prof. Pasquale Ciarletta

Contact: pasquale.ciarletta@polimi.it**A review on some fourth order problems on manifolds**

Zindine Djadli, Université Grenoble Alpes

martedì 24 aprile 2018 alle ore 15:15, Sala del Consiglio 7° pianoABSTRACTI will review some recent works on some non linear problem on manifolds, mostly in conformal geometry.**Serrin’s overdetermined problem on the sphere**

Tobias Weth, Goethe-Universitat Frankfurt

lunedì 23 aprile 2018 alle ore 16:00, Aula 6° pianoABSTRACTIn 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).**Ricostruire l’invisibile…fantasmi permettendo**

Paolo Dulio, Politecnico di Milano

mercoledì 18 aprile 2018 alle ore 12:15, Politecnico di Milano Campus Bonardi Edificio14 aula B21