# Past Events

We will discuss the clean composition calculus of Guillemin and Duistermaat.

The joints problem asks to determine the maximum number of joints N lines can form, where a joint in a d-dimensional space is a point on d lines in linearly independent directions. Recently, Ting-Wei Chao and I determined the maximum exactly for k choose d-1 lines in d-dimensional space, …

Given a set of integers, we wish to know how many primes there are in the set. Modern tools allow us to obtain an asymptotic for the number of primes, or at least a lower bound of the expected order, assuming certain strength Type-I information (the distribution of the sequence in…

Perhaps the most elegant mathematical definition of privacy of data is called "differential privacy". I will describe a somewhat more general framework, which leads to some fun questions at the interface of probability and metric geometry. This talk is based on joint work with March Boedihardjo…

Following Kronheimer and Mrowka’s approach, we show that Khovanov homology detects the unknot and the projective unknot in RP^3. I’ll explain the idea of the proof. Time permitting, I’ll discuss potential further detection results.

Abstract: This talk discusses a problem introduced by Yau on estimating the size of nodal sets of eigenfunction in terms of the eigenvalue. We show that one can obtain improved polynomial upper bounds when the Riemannian manifold has a Gevrey or quasianalytic regularity. Yau's upper bound…

I will sketch why the critical point for percolation on an infinite transitive graph G only depends on the geometry of G on small scales (except in the degenerate case when G is one-dimensional). This is based on joint work with Hutchcroft and was…

Abstract: Every Anosov flow on a closed oriented three-manifold gives rise to a four-dimensional

Liouville domain, whose Liouville homotopy class depends only on the homotopy class of the

Anosov flow. The goal of this talk is to explain this construction and discuss geometric…

Abstract: We define the K-theoretical virtual fundamental cycle of an almost complex global

Kuranishi atlas, as an element in the (analytic) orbifold K-homology of the base space of the

atlas, and verify that it defines the same K-theoretical Gromov-Witten invariants as in Abouzaid…