The celebrated Gan-Gross-Prasad conjectures aim to describe the branching behavior of representations of classical groups, i.e., the decomposition of irreducible representations when restricted to a lower rank subgroup.
The Mass Transport Principle is a useful technique that was introduced to the study of automorphism-invariant percolations by Häggström in 1997. The technique is a sort of mass conservation principle, that allows us to relate random properties (such as the random degree of a vertex) to geometric properties of the graph.
I will introduce the principle and the class of unimodular graphs on which it holds, as well as a few of its applications.
I will discuss the inverse Monge-Ampere flow and its applications to the existence, and non-existence, of Kahler-Einstein metrics. To motivate this discussion I will first describe the classical theory of the Donaldson heat flow on a Riemann surface, and its relationship with the Harder-Narasimhan filtration of an unstable vector bundle.
I will discuss a family of random processes in discrete time related to products of random matrices (product matrix processes). Such processes are formed by singular values of random matrix products, and the number of factors in a random matrix product plays a role of a discrete time. I will explain that in certain cases product matrix processes are discrete-time determinantal point processes, whose correlation kernels can be expressed in terms of double contour integrals. This enables to investigate determinantal processes for products of ra ndom matrices in
Manchester Building (Hall 2), Hebrew University Jerusalem
A major difficulty in finding polynomial patterns in primes is the need to understand their distribution properties at short scales. We describe how for some polynomial configurations one can overcome this problem by concatenating short scale behavior in "many directions" to long scale behavior for which tools from additive combinatorics are available.