# Mathematical Physics

### Large coupling asymptotics for the Lyapunov exponent of quasi-periodic Schrödinger operators with analytic potentials

Christoph Marx
In this talk we will quantify the coupling asymptotics for the Lyapunov exponent (LE) of a one-frequency quasi-periodic Schrödinger operator with analytic potential sampling function. By proving an asymptotic formula for the LE valid for all...

### Reinforced random walks and statistical physics

Pierre Tarres
We explain how the Edge-reinforced random walk, introduced by Coppersmith and Diaconis in 1986, is related to several models in statistical physics, namely the supersymmetric hyperbolic sigma model studied by Disertori, Spencer and Zirnbauer (2010)...

### Free dynamics of a tracer particle in a Fermi sea

The talk is about the dynamics of a tracer particle coupled strongly to a dense non-interacting electron gas in two dimensions. I will present a recent result that shows that for high densities the tracer particle moves freely for very long times.

### Universality in numerical computations with random data. Analytical results.

Percy Deift
This is joint work with Tom Trogdon. Here the author shows how to prove universality rigorously for certain numerical algorithms of the type described in the first lecture. The proofs rely on recent state of the art results from random matrix theory...

### Universality in numerical computations with random data. Case studies.

Percy Deift
This is joint work with Govind Menon, Sheehan Olver and Thomas Trogdon. The speaker will present evidence for universality in numerical computations with random data. Given a (possibly stochastic) numerical algorithm with random input data, the time...

### Derivation of the Vlasov equation

Peter Pickl
The rigorous derivation of the Vlasov equation from Newtonian mechanics of $N$ Coulomb-interacting particles is still an open problem. In the talk I will present recent results, where an $N$-dependent cutoff is used to make the derivation possible...

Clement Hongler

### Quantum Beauty

Does the world embody beautiful ideas? This is a question that people have thought about for a long time. Pythagoras and Plato intuited that the world should embody beautiful ideas; Newton and Maxwell demonstrated how the world could embody...

### The Universal Relation Between Exponents in First-Passage Percolation

Sourav Chatterjee

It has been conjectured in numerous physics papers that in ordinary first-passage percolation on integer lattices, the fluctuation exponent \chi and the wandering exponent \xi are related through the universal relation \chi=2\xi -1, irrespective of...