# Geometric and Algebraic Combinatorics

**Lecturer:**Bernd Sturmfels**Date:**October, 29 – November 2 and November 16**Room:**tba**Language:**English**Target audience:**PhD students**Prerequisites:**Mathematical maturity of an advanced graduate student. Interest in combinatorics.**Remarks:**For details check https://math.berkeley.edu/˜bernd/nov18.html

## Abstract:

The problem of the generation of random dynamical systems by stochastic partial diﬀerential equations (SPDE) is one of the open problems in the application of dynamical systems theory to SPDE. Despite its fundamental nature, most results are restricted to ”simple” random perturbations of aﬃne-linear structure. However, as we will see in this course, applications like scaling limits of particle systems with interaction and branching and non-equilibrium statistical mechanics, lead to porous media equations perturbed by nonlinear multiplicative or nonlinear conservative noise. We will ﬁrst convince ourselves that established methods such as the variational approach to SPDE cannot be applied to these equations, let alone prove the generation of random dynamical systems. Then, based on entropy and kinetic theory we will prove their well-posedness. This will lead to a strong notion of uniqueness, so-called path-by-path uniqueness, based on rough path theory which in turn proves the generation of a corresponding random dynamical system and opens the way to a qualitative analysis of the (stochastic) ﬂow of the solutions.

## Regular Lectures (Winter 2018/2019)

**Condition: the geometry of numerical algorithms**- Paul Breiding
- Tuesday, 09:00 - 10:00, MPI MiS G3 10, till January 30

**Information, Physics and Computation**- Pau Vilimelis Aceituno
- Wednesday, 13:00 - 14:30, MPI MiS A3 02

**Introduction to Random Algebraic Geometry**- Antonio Lerario
- Tuesday, 09:00 - 10:00, MPI MiS G3 10, from February 6 to March 27

**Random dynamical systems and stochastic porous media equations with nonlinear noise**- Benjamin Gess
- Monday, 16:15 - 17:45, MPI MiS A3 01

**Artiﬁcial Neural Networks and Machine Learning: Theoretical Foundations**- Nihat Ay
- Thursday, 11:15 - 12:45, MPI MiS A3 01
- First Lecture: November, 15th

**Geometric and topological methods for the analysis of data in biology, neurobiology and other fields**- Jürgen Jost
- Friday, 13:30 - 15:00, MPI MiS A3 01
- First Lecture: October, 26th

**Important abstract mathematical concepts (algebraic structures, category theory, (pre)sheaves and schemes)**- Jürgen Jost
- Monday, 13:30 - 15:00, MPI MiS A3 01
- First Lecture: November, 12th

**Singular stochastic PDEs**- Nicolas Perkowski
- Wednesday, 11:15 - 12:45, MPI MiS A3 01

**Seminar on inverse spectral theory**- Angkana Rüland
- Thursdays, 9:15 - 10:45, Leipzig University, SG 3-14

**Introduction into regularity structures**- Felix Otto
- Wednesday, 09:10 - 11:00, MPI MiS A3 01

**Toric Varieties**- Mateusz Michalek
- Friday, 11:00 - 12:30, MPI MiS G3 10

**Morse Theory and Closed Geodesics**- Hans-Bert Rademacher
- Wednesday, 13:15 - 14:45, Leipzig University, SG 3-10

**An introduction to Information Geometry and Mathematical Population Genetics**- Tat Dat Tran
- Friday, 15:15 - 16:45, MPI MiS A3 02

**Reading Seminar: Representation theory - The basics**- Joscha Diehl
- first meeting: Tuesday 16.10.2018 at 11:00h, F3 Section

**Reading Seminar: Geometric Measure Theory**- Renan Assimos Martins, Kostas Zemas
- Monday, 15:00 - 17:00, MPI MiS A3 02

**Geometric and Algebraic Combinatorics**- Bernd Sturmfels
- October, 29 – November 2 and November 16

**IMPRS-Ringvorlesung**- Nihat Ay, Christiane Görgen, Guido Montúfar, André Uschmajew, Stefan Hollands
- Tuesday, 10:00 - 12:00 (tba), MPI MiS G3 10