### 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

**A Panoramic View of Valuation Adjustments**

Marco Francischello, Imperial College

martedì 22 maggio 2018 alle ore 12:15 precise, Aula Seminari Terzo Piano**Maximally writhed real algebraic knots and links**

Grigory Mikhalkin, Université de Genève

giovedì 17 maggio 2018 alle ore 17:00 precise, Sala di Rappresentanza, Università di Milano, Via C. Saldini 50, MilanoABSTRACTThe Alexander-Briggs tabulation of knots in R^3 (started almost

a century ago, and considered as one of the most traditional ones

in classical Knot Theory) is based on the minimal number of crossings

for a knot diagram. From the point of view of Real Algebraic Geometry

it is more natural to consider knots in RP^3 rather than R^3, and use

a different number also serving as a measure of complexity of a knot:

the minimal degree of a real algebraic curve representing this knot.

As it was noticed by Oleg Viro about 20 years ago, the writhe of a knot

diagram becomes an invariant of a knot in the real algebraic set-up,

and corresponds to a Vassiliev invariant of degree 1. In the talk we’ll

survey these notions, and consider the knots with the maximal possible

writhe for its degree. Surprisingly, it turns out that there is a unique

maximally writhed knot in RP^3 for every degree d. Furthermore, this

real algebraic knot type has a number of characteristic properties, from

the minimal number of diagram crossing points (equal to d(d-3)/2) to

the minimal number of transverse intersections with a plane (equal to

d-2). Based on a series of joint works with Stepan Orevkov.

**Modellazione paziente specifica in emodialisi**

Maria Laura Costantino, Politecnico di Milano

mercoledì 16 maggio 2018 alle ore 12:15, Politecnico di Milano Campus Bonardi Edificio14 aula B21**Evolution by curvature of networks in the plane**

Carlo Mantegazza, Università degli Studi di Napoli Federico II

mercoledì 16 maggio 2018 alle ore 15:15, Aula seminari piano 3ABSTRACTWe 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.**Numerical Wiener-Hopf factorization method for option pricing under Lévy models**

Oleg Kudryavtsev, Rostov Branch of Russian Customs Academy

martedì 15 maggio 2018 alle ore 12:15 precise, Aula Seminari Terzo Piano**Recent progress on rationality problems**

Arnaud Beauville, Université de Nice

lunedì 14 maggio 2018 alle ore 15:30, Sala di Rappresentanza, Università di Milano, Via C. Saldini 50, MilanoABSTRACTWe say that an algebraic variety is unirational if it can be parametrized by rational functions, rational if moreover the parametrization can be chosen to be one-to-one. A very classical problem, called nowadays the Luroth problem, asks whether a unirational variety is necessarily rational. This holds for curves (Luroth, 1875) and for surfaces (Castelnuovo, 1894); after various unsuccessful attempts, it was shown in 1971 that the answer is quite negative in dimension 3: there are many examples of unirational varieties which are not rational. Up to 3 years ago the known examples in dimension >3 were quite particular, but a new idea of Claire Voisin has significantly improved the situation. I will survey the colorful history of the problem, then explain Voisin’s idea, and how it leads to a number of new results.

**Preconditioning and stabilization of poromechanics problem with CutFem approximation**

Daniele Cerroni, MOX- Politecnico di Milano

venerdì 11 maggio 2018 alle ore 11:30, Aula Seminari ‘Saleri’ VI Piano MOX-Dipartimento di Matematica, Politecnico di Milano – Edificio 14ABSTRACTWe investigate the conditioning of a computational model for poroelasticity in the case of a moving domain boundary. We approximate the problem by means of a numerical scheme which does not require that the computational mesh conforms with the moving boundary (CutFem approximation) and, we use a Nitsche’s method to apply boundary condition onto this region. The ill conditioning driven by the approximation with CutFem is combined with the naturally ill conditioning due to the saddle point nature of the poroelastic problem. The latter problem can be addressed with a splitting iterative scheme that decouple the solution of the mechanics problem from the solution of the pressure equation.

In this work we investigate the conditioning of the two sub-problems in the case of tiny intersection produced by the CutFem approximation. In particular we explore the possibility of adding a stabilization term into the pressure equation and use a propoer preconditioner for the displacement equation.

Contact: paolo.zunino@polimi.it

**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