School of Mathematics
Atiyah's Connectivity, Morse Theory and Solution Sets
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).
Overconvergent Igusa Tower and Overconvergent Modular Forms
GALOIS REPRESENTATIONS AND AUTOMORPHIC FORMS SEMINAR
Note: (joint work with O. Brinon and A. Mokrane)
QUESTION SESSION ON GRASSMANNIANS, POLYTOPES AND QUANTUM FIELD THEORY
Infinite Generaton of Non-Cocompact Lattices on Right-Angled Buildings
SPECIAL LECTURE
Let Gamma be a non-cocompact lattice on a right-angled building X. Examples of such X include products of trees, or Bourdon's building I_{p,q}, which has apartments hyperbolic planes tesselated by right-angled p-gons and all vertex links the complete bipartite graph K_{q,q}. We prove that if Gamma has a strict fundamental domain then Gamma is not finitely generated. The proof uses a topological criterion for finite generation and the separation properties of subcomplexes of X called tree-walls. This is joint work with Kevin Wortman (Utah).
Automorphic Cohomology II (Carayol's work and an Application)
"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
Symplectic Dynamics of Integrable Hamiltonian Systems
I will start with a review the basic notions of Hamiltonian/symplectic vector field and of Hamiltonian/symplectic group action, and the classical structure theorems of Kostant, Atiyah, Guillemin-Sternberg and Delzant on Hamiltonian torus actions. Then I will state a structure theorem for general symplectic torus actions, and give an idea of its proof.
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.