The notion of exactly (or approximately) representing certain combinatorial properties of a graph $G$ on a simpler graph is ubiquitous in combinatorial optimization. In this talk, I will introduce the notion of vertex sparsification. Here we are given a graph $G = (V, E)$ and a set of terminals $K \subset V$ and our goal is to find one single graph $H = (K, E_H)$ on just the terminal set so that $H$ approximately preserves the minimum cut between every bi-partition of the terminals.
The Davenport-Heilbronn function (introduced by Titchmarsh) is a linear combination of the two L-functions with a complex character mod 5, with a functional equation of L-function type but for which the analogue of the Riemann hypothesis fails. In this lecture, we study the Moebius inversion for functions of this type and show how its behavior is related to the distribution of zeros in the half-plane of absolute convergence. Work in collaboration with Amit Ghosh.
I will first discuss the orientability of the moduli spaces of J-holomorphic maps with Lagrangian boundary conditions. It is known that these spaces are not always orientable and I will explain what the obstruction depends on. Then, in the presence of an anti-symplectic involution on the target, I will give a construction of open Gromov-Witten disk invariants. This is a generalization to higher dimensions of the works of Cho and Solomon, and is related to the invariants defined by Welschinger
Current educational policy discussions frequently invoke “equality” as the reigning ideal. But how clear a view do we have of what we mean by this? What exactly are we trying to achieve? In this lecture, Danielle Allen, UPS Foundation Professor in the School of Social Science, revisits the question of how to understand the ideal of equality in the context of educational policy.
The world is running out of available water supplies, and the potential for conflict will be severe. In this lecture, Maude Barlow, Chair of the Council of Canadians and Chair of Food and Water Watch, sets out the nature and cause of the crisis and offers a three-part solution to achieve a water-secure world.