### Seminari

### Prossimi Seminari

**Computational Prediction of Blood Damage**

Marek Behr, Chair for Computational Analysis of Technical Systems Faculty of Mechanical Engineering, RWTH Aachen

lunedì 1 ottobre 2018 alle ore 14:00, Aula Consiglio VII Piano – Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO**Caputo Evolution Equations with time-nonlocal initial condition**

Lorenzo Toniazzi, University of Warwick

martedì 9 ottobre 2018 alle ore 15:15, Aula Seminari 3° piano**Statistical modeling and monitoring of product and process quality in Additive Manufacturing: opportunities and challenges**

Bianca Maria Colosimo, Dipartimento di Meccanica, Politecnico di Milano

giovedì 11 ottobre 2018 alle ore 14:00, Aula Consiglio VII Piano – Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO**Elastic waves in soft tissues: inverse analysis, experiments, simulations, validation**

Michel Destrade, Chair of Applied Mathematics at NUI Galway

giovedì 18 ottobre 2018 alle ore 14:00, Aula Consiglio VII Piano – Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO**An overview of some mathematical and computational problems in Network Science**

Michele Benzi, Scuola Normale Superiore, Pisa

giovedì 22 novembre 2018 alle ore 14:00, Aula Consiglio VII Piano – Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO**BIRATIONAL EQUIVALENCE OF ALGEBRAIC VARIETIES**

Shigefumi Mori, Kyoto University Institute of Advanced Study

lunedì 26 novembre 2018 alle ore 16:30, Aula Chisini, Diparimento di Matematica, Via C. Saldini 50

### Seminari Passati

**Development of a HPC library for the parallel implementation of p-adaptive discontinuous finite element methods applied to geophysical flows.**

Stella Paronuzzi Ticco, OGS Trieste and Laboratorio MOX Milano

giovedì 10 maggio 2018 alle ore 10:30, Aula Seminari ‘Saleri’ VI Piano MOX-Dipartimento di Matematica, Politecnico di Milano – Edificio 14ABSTRACTDiscontinuous finite element methods have been gaining in popularity for large scale geophysical applications. They are also a natural environment to take advantage of adaptive approaches in which the degree of the approximating polynomials is chosen locally and dynamically, in order to minimize memory occupation and computational cost. However, this poses major challenges to the parallel efficiency of the resulting methods, since a greater effort to achieve optimal load balancing is required. At present, no general HPC infrastructure for efficient and natively adaptive implementation of DG methods on massively parallel is available.The purpose of this joint research with G. Tumolo of ICTP Trieste is to move towards the development of such a tool especially tailored for the simulation of fluid dynamics problems in climate dynamics, oceanography and volcanology.

contact: luca.bonaventura@polimi.it**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).