# School of Mathematics

## Graph Sparsification by Edge-Connectivity and Random Spanning Trees

A "sparsifier" of a graph is a weighted subgraph for which every cut has approximately the same value as the original graph, up to a factor of (1 +/- eps). Sparsifiers were first studied by Benczur and Karger (1996). They have wide-ranging applications, including fast network flow algorithms, fast linear system solvers, etc. Batson, Spielman and Srivastava (2009) showed that sparsifiers with O(n/eps^2) edges exist, and they can be computed in time poly(n,eps).

## QUESTION SESSION ON GRASSMANNIANS, POLYTOPES AND QUANTUM FIELD THEORY

## Overconvergent Igusa Tower and Overconvergent Modular Forms

**GALOIS REPRESENTATIONS AND AUTOMORPHIC FORMS SEMINAR**

Note: *(joint work with O. Brinon and A. Mokrane)*

## Automorphic Cohomology II (Carayol's work and an Application)

## Infinite Generaton of Non-Cocompact Lattices on Right-Angled Buildings

SPECIAL LECTURE

## "We know that God exists because mathematics is consistent and we know that the devil exists because we cannot prove the consist

**MATHEMATICAL CONVERSATIONS**

"We know that God exists because mathematics is consistent and we know that the devil exists because we cannot prove the consistency." -- Andre Weil

## Improved Bounds for the Randomized Decision Tree Complexity of Recursive Majority

Recursive Majority-of-three (3-Maj) is a deceptively simple problem in the study of randomized decision tree complexity. The precise complexity of this problem is unknown, while that of the similarly defined Recursive NAND tree is completely understood.