### Welcome to the group “Mathematics in Computational Science and Engineering (MATHICSE-Group)

The group of Mathematics in Computational Science and Engineering includes the Chair of Computational

Mathematics and Numerical Analysis (ANMC), the Chair of Modelling and Scientific Computing (CMCS), the Chair of Numerical Algorithms and High Performance Computing (ANCHP), the Chair of Scientific Computing and Uncertainty Quantification (CSQI), the Chair of Computational Mathematics and Simulation Science (MCSS), the Chair of Numerical Modelling and Simulation (MNS) and the group of Professor

M. Picasso (GR-PI).

### Mission

Promote at the highest scientific level the research and education on mathematical modeling, numerical modeling, algorithmic development and simulation, as well as their application in nature, environment, life, society, science and engineering. Establish and lead research programs in Computational Science and Engineering within the Institute of Mathematics and interact with existing projects in the CSE area across the EPFL Campus.

### EVENTS

### Seminars of the month

## Applications of Partition Functions

The goal of this workshop is to discuss the wide set of practical and theoretical applications of the computability of partition functions and address the challenges that arise.

## Periodic orbits and topological restriction homology

I will talk about a project to import trace methods, usually reserved for algebraic K-theory computations, into the study of periodic orbits of continuous dynamical systems (and vice-versa). Our main result so far is that a certain fixed-point invariant built using equivariant spectra can be ``unwound'' into a more classical invariant that detects periodic orbits. As a simple consequence, periodic-point problems (i.e. finding a homotopy of a continuous map that removes its n-periodic orbits) can be reduced to equivariant fixed-point problems. This answers a conjecture of Klein and Williams, and allows us to interpret their invariant as a class in topological restriction homology (TR), coinciding with a class defined earlier in the thesis of Iwashita and separately by Luck. This is joint work with Kate Ponto.

By: Cary Malkiewich

## Stochastic Processes in Domains with Boundaries and Some of Their Financial Applications

In this talk we consider two connected problems:

First, we study the classical problem of the first passage hitting density of an Ornstein-Uhlenbeck process. We give two complementary (forward and backward) formulations of this problem and provide semi-analytical solutions for both. The corresponding problems are comparable in complexity. By using the method of heat potentials, we show how to reduce these problems to linear Volterra integral equations of the second kind. For small values of t we solve these equations analytically by using Abel equation approximation; for larger t we solve them numerically. We also provide a comparison with other known methods for finding the hitting density of interest, and argue that our method has considerable advantages and provides additional valuable insights.

Second, we study the non-linear diffusion equation associated with a particle system where the common drift depends on the rate of absorption of particles at a boundary. We provide an interpretation as a structural credit risk model with default contagion in a large interconnected banking system. Using the method of heat potentials, we derive a coupled system of Volterra integral equations for the transition density and for the loss through absorption. An approximation by expansion is given for a small interaction parameter. We also present a numerical solution algorithm and conduct computational tests.

By: Alexander LIPTON, SilaMoney, MIT & EPFL

**NEWS**

Prof. **Annalisa Buffa** awarded the ERG Adcanced Grant CHANGE, “New CHallenges for (adaptive) PDE solvers: the interplay of ANalysis and Geometry”. Host Institution: Ecole Polytechnique Federale de Lausanne (EPFL). Addition Beneficiaries: Consiglio Nazionale Della Ricerche Istituto di Matematica Applicata e Technologie Informatiche “E. Magenes” (CNR-IMATI); Universitat Linz Johannes Kepler University (JKU-LINZ); Oesterreichische Akademie des Wissenschaften Johann Radon Institute for Computational and Applied Mathematics (RICAM)

**ECCOMAS Award for the best PhD Thesis in 2016 to Dr D. Guignard (GR-PI & CSQI, EPFL)**

Dr. Diane Guignard, member of the Chair of Scientific Computing and Uncertainty Quantification and the Group Picasso, Institute of Mathematics, EPFL, has been awarded the ECCOMAS Award for for one of the two best PhD Theses in 2016, for her PhD Thesis entitled “A posteriori error estimation for partial differential equations with random input data” (EPFL thesis #7260, 2016). The European Community on Computational Methods in Applied Sciences (ECCOMAS) attributes the award to highlight outstanding achievements of two young persons at the start of their scientific careers; the awards will be handed over at the ECCOMAS Young Investigator Conference – YIC 2017, Milan, Italy, September 13 – 15.

Many congratulations to Diane!

**Highlight on the Master in CSE**

**ECCOMAS Award for the best PhD Thesis in 2015 to Dr. F. Negri (CMCS, EPFL)**

Dr. Federico Negri, member of the Chair of Modelling and Scientific Computing, MATHICSE, SB, EPFL, has been awarded the ECCOMAS Award for one of the two best PhD Theses in 2015. The European Community on Computational Methods in Applied Sciences (ECCOMAS) attributes the award to highlight outstanding achievements of two young persons at the start of their scientific careers; the award will be handed over at the ECCOMAS 2016 Conference in Crete, Greece, June 5 – 10.

The thesis of Dr. Negri, titled “Efficient Reduction Techniques for the Simulation and Optimization of Parametrized Systems: Analysis and Applications” (EPFL thesis #6810, 2015) and developed under the supervision of Prof. A. Quarteroni and Prof. G. Rozza, has been awarded the prize for its outstanding contributions in developing an efficient Reduced Basis method for the high fidelity solution of computationally-intensive problems described by Partial Differential Equations, with application to blood flows, mass transport, and control.

Many congratulations to Federico!