## Distinguished PDE Lecture Series

The Distinguished PDE Lecture Series is intended to spread powerful new ideas and
substantial contributions in Partial Differential Equations and related fields.
Outstanding scientists present the latest developments of their research and make
their current mathematical ideas accessible also to non-specialists.

### 2017

**Alfio Quarteroni**, Ecole Polytechnique Federale de Lausanne, Switzerland
(ERC Advanced Grant 2008, ERC Proof of Concept 2012 and 2015)

*Mathematical and numerical modeling of multiphysics problems, with application
to the cardiocirculatory system*

Cardiovascular diseases unfortunately represent one of the leading causes of death in
Western countries. Mathematical models allow the description of the blood motion in the
human circulatory system, as well as the interplay between electrical, mechanical and
fluid-dynamical processes occurring in the heart. This is a classical environment where
multiphysics processes have to be addressed.
Appropriate numerical strategies can be devised to allow for an effective description
of the fluid in large and medium size arteries, the analysis of physiological and
pathological conditions, and the simulation, control and shape optimization of assisted
devices or surgical prostheses.
This presentation will address some of these issues and a few representative
applications of clinical interest.

June 06, 2017, 16:00h. Getreidemarkt 9, 11th floor, TUtheSky
### 2016

**Eduard Feireisl**, Charles University, Prague, Czech Republic
(ERC Advanced Grant 2012)

*Stability issues for compressible fluid flow*

We present several stability results concerning smooth solutions of the compressible
Euler and Navier-Stokes system in the class of measure-valued solutions. We show that
strong and measure-valued solutions of these systems coincide as soon as the
strong solution exists. The question if any measure-valued solution can be generated
by a sequence of weak solutions will be also addressed.

May 31, 2016, 16:00h. Getreidemarkt 9, 11th floor, TUtheSky
### 2015

**Martin Hairer**, University of Warwick, United Kingdom (Fields Medal 2014)

*Modelling a random rubber band*

A rubber band constrained to remain on a manifold
evolves by trying to shorten its length, eventually settling
on some minimal closed geodesic, or collapsing entirely.
It is natural to try to consider a noisy version of such a
model where each segment of the band gets pulled
in random directions. Trying to build such a model turns
out to be surprisingly difficult and generates a number of
nice geometric insights, as well as some beautiful algebraic
and analytical objects.

June 17, 2015, 16:00h. Getreidemarkt 9, 11th floor, TUtheSky
### 2014

**Roland Donninger**, Universität Bonn, Germany (Sofja Kovalevskaja Award 2014)

*Self-similar blowup in nonlinear wave equations*

I discuss some recent progress in the study of stable self-
similar blowup in energy-supercritical wave equations. In
particular, I present a proof for the stability of the so-
called ODE blowup for the energy-supercritical focusing
wave equation without symmetry assumptions. This talk
is based on joint work with Birgit Schörkhuber.

December 16, 2014, 14:00h. Wiedner Hauptstr. 8-10, green area, SEM 101C