School of Mathematics

A natural problem in the study of local systems on complex varieties is to characterize those that arise in a family of varieties. We refer to such local systems as motivic. Simpson conjectured that for a reductive group G, rigid G-local systems...

Consider a point mass traveling in a polygon. It travels in a straight line, with constant speed, until it hits a side, at which point it obeys the rules of elastic collision. What can we say about this? When all the angles of the polygon are...

In this work, we develop a new method for proving lower bounds for static data structures in the classical cellprobe model of Yao. Our methods give the strongest known lower bounds for any explicit problem in this model (quadratically stronger for...

I will talk about the well known relation between cocycles and covers.  Then, I will discuss the relation of cocycle expansion to approximate covers, and finally how these show up in low-soundness PCP agreement tests.

What is the cost of a task if we have to perform it many times? Can we achieve economies of scale? Such "direct-sum problems" play a central role in many areas of mathematics, physics and computer science. Protagonistic problems of this kind are...

Given a Hamiltonian H∈C∞(S1×M), what is the relationship between the dynamics of the isotopy generated by H and the various Floer-theoretic invariants associated to H? In this talk I will discuss how — in the case where M is a closed surface —one...

We will go in-depth into the proof that for all functions t(n) greater than or equal to n, every multitape Turing machine running in time t can be simulated in space only O(tlogt‾‾‾‾‾√). We will attempt to be completely self-contained. To that end...

The field of unlikely Intersections presents a robust paradigm for problems in which several subjects intermingle: arithmetic, o-minimality, and hodge theory. The goal of this talk will be to introduce some of those connections. My aim is to...

A linear extension of P is a linear ordering compatible with the poset relations. Let p(x less than y) be the probability that x

precedes y in a uniformly random linear extension, and let δ(x,y)=min(p(x less than y),p(y less than x)) and δ(P) be the...