Past

TBA

Descent theory is the art of gluing local data together to global data. Beside of being an invaluable tool for the working geometer, the descent philosophy has changed our perception of space and topology. In this talk I will introduce the audience to the basic results of scheme and descent theory and explain how those can be applied to concrete examples.

Standard quantum logic, as intitiated by Birkhoff and von Neumann, suffers from severe problems which relate quite directly to interpretational issues in the foundations of quantum theory. In this talk, I will present some aspects of the so-called topos approach to quantum theory, as initiated by Isham and Butterfield, which aims at a mathematical reformulation of quantum theory and provides a new, well-behaved form of quantum logic that is based upon the internal logic of a certain (pre)sheaf topos.

TBA

We shall explain how to give substance to an old dream of Tits, to invent exotic new zeta functions, and discover the skeleton of algebraic varieties (toric manifolds and tropical geometry).

We shall explain how to give substance to an old dream of Tits, to invent exotic new zeta functions, and discover the skeleton of algebraic varieties (toric manifolds and tropical geometry).

The Green-Griffiths conjecture from 1979 says that every projective algebraic variety $X$ of general type contains a certain proper algebraic subvariety $Y$ such that all nonconstant entire holomorphic curves in $X$ must lie inside $Y$. In this talk we explain that for projective hypersurfaces of degree $d>dim(X)^6$ this is the consequence of a positivity conjecture in global singularity theory.

A graph is $\chi$-bounded with a function $f$ is for all induced subgraph H of G, we have $\chi(H) \le f(\omega(H))$.  Here, $\chi(H)$ denotes the chromatic number of $H$, and $\omega(H)$ the size of a largest clique in $H$. We will survey several results saying that excluding various kinds of induced subgraphs implies $\chi$-boundedness. More precisely, let $L$ be a set of graphs. If a $C$ is the class of all graphs that do not any induced subgraph isomorphic to a member of $L$, is it true that there is a function $f$ that $\chi$-bounds all graphs from $C$? For some lists $L$, the answer is yes, for others, it is no.  

A decomposition theorems is a theorem saying that all graphs from a given class are either "basic" (very simple), or can be partitioned into parts with interesting relationship. We will discuss whether proving decomposition theorems is an efficient method to prove $\chi$-boundedness. 

The main aim is to incorporate the nonlinear term into non-Markovian Master equations for a continuous time random walk (CTRW) with non-exponential waiting time distributions. We derive new nonlinear evolution equations for the mesoscopic density of reacting particles corresponding to CTRW with arbitrary jump and waiting time distributions. We apply these equations to the problem of front propagation in the reaction-transport systems of KPP-type.

We find an explicit expression for the speed of a propagating front in the case of subdiffusive transport.

TBA

We shall report on the use of algebraic geometry for the calculation of Feynman amplitudes (work of Bloch, Brown, Esnault and Kreimer). Or how to combine Grothendieck's motives with high energy physics in an unexpected way, radically distinct from string theory.

TBA

Heike Gramberg - Flagellar beating in trypanosomes

Robert Whittaker - High-Frequency Self-Excited Oscillations in 3D Collapsible Tube Flows