### 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

**Periodic solutions to perturbed Kepler problems**

Alberto Boscaggin, Università di Torino

martedì 22 maggio 2018 alle ore 15:15, Aula seminari 3° pianoABSTRACTAs 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).**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