# Fakultätskolloquium im Sommersemester 2018

**Termin:** Das Kolloquium findet in loser Folge mittwochs statt, mit jeweils zwei Vorträgen von 14:30 – 15:30 Uhr und von 16:00 – 17:00 Uhr im Hörsaal 3 (MI 00.06.011).

In der Pause ist für Getränke und Brez'n in der Magistrale gesorgt.

**Ansprechpartner:** Felix Krahmer, Robert König.

Vorträge im vergangenen Semester:

Wintersemester 17/18.

## Vorträge im Sommersemester 2018

#### Amir Beck — The Gradient Method: Past and Present

The gradient method is probably one of the oldest optimization algorithms going back as early as 1847 with the initial work of Cauchy. Surprisingly, it is still the basis for many of the most relevant algorithms nowadays that are capable of solving very large-scale problems arising from many diverse fields of applications such as image processing and data science. This talk will explore the evolution of the method from the 19th century to this date.

#### Stefan Weltge — A Barrier to P=NP Proofs

The P-vs-NP problem describes one of the most famous open questions in mathematics and theoretical computer science. The media are reporting
regularly about proof attempts, all of them being later shown to contain
flaws. Some of these approaches where based on small-size linear
programs that were designed to solve problems such as the traveling
salesman problem efficiently. Fortunately, a few years ago, in a
breakthrough result researchers were able to show that no such linear
programs can exist and hence that all such attempts must fail, answering
a 20-year old conjecture. In this lecture, I would like to present a
quite simple approach to obtain such a strong result. Besides an
elementary proof, we will hear about (i) the review of all reviews, (ii)
why having kids can boost your career, and (iii) a nice interplay of
theoretical computer science, geometry, and combinatorics.

#### Filippo Santambrogio — Crowd motion and evolution PDE with density constraints

I will explain a general model to deal with the evolution of a population density ρ which is advected by a velocity field u, but is subject to a non-overcrowding constraint ρ≤1. This model (rather, a meta-model) mainly refers to the motion of a crowd of pedestrians, but can be adapted to many different situations according to how u is given or depends on ρ. Since in general u will not preserve the density constraint, the main assumption is that motion will be advected by the projection of u onto the cone of feasible velocities. This takes its inspiration from granular contact models, when the crowd is described by a collection of particles. I will present the equations, the main ideas to prove existence of solutions (in particular, using tools from optimal transport and gradient flows), and to simulate them. We will see how this continuous PDE model provides results which are stinkingly qualitatively similar to the simulations obtained by granular models, but could require a much smaller complexity.
The talk summarizes joint works with several colleagues in Orsay as well as numerical methods developed both by us and by the INRIA team MOKAPLAN, and will try not to be exhaustive but just focus on the main features of the theory.

#### Barbara Gentz — Synchronization in the noisy Kuramoto model of oscillators

Synchronization is a collective phenomenon observed, for instance, in fireflies, in a clapping audience or in the pacemaker cells in the cardiac pacemaker. Mathematical models for this type of synchronization are based on systems of coupled oscillators. We will start by reviewing the Kuramoto model, introduced by Yoshiki Kuramoto in 1975. It has been successfully analyzed, including many generalizations. In particular, the emergence of synchronization in the Kuramoto model is well understood by now, while much less is known about the effect of noise on sychronization of Kuramoto oscillators. We will address the questions of emergence and of persistence of synchronziation in the presence of random perturbations for an arbitrary

*finite* number of non-identical oscillators. The main results and ideas will be explained in the special case of two oscillators which is particularly easy to study since the model can be reduced to a stochastic version of the Adler equation in this case.