seminars:topsem

## Geometry and Topology Seminar

We meet Thursdays at 2:50–3:50 pm in WH-100E followed by refreshments served from 4:00–4:25 pm in WH-102. This semester's organizer is Jonathan Williams.

Some seminar speakers will also give a colloquium talk at 4:30 pm on the same day as the seminar talk. This seminar is partly funded as one of Dean's Speaker Series in Harpur College (College of Arts and Sciences) at Binghamton University.

The seminar has an announcement mailing list open to all. There is also a Google calendar with the seminar schedule (also in iCal).

# Spring 2018

• Special date and time: May 1, 1:15pm in WH-100E (joint with combinatorics)
Speaker: Boris Bukh (Carnegie Mellon)
Title: Topological Version of Pach's Overlap Theorem

Abstract: Consider the collection of all the simplices spanned by some n-point set in $\mathbb{R}^d$. There are several results showing that simplices defined in this way must overlap very much. In this talk I focus on the generalization of these results to 'curvy' simplices.

Specifically, Pach showed that every $d+1$ sets of points $Q_1, \ldots, Q_{d+1}$ in $\mathbb{R}^d$ contain linearly-sized subsets $P_i\subset Q_i$ such that all the transversal simplices that they span intersect. In joint work with Alfredo Hubard, we show, by means of an example, that a topological extension of Pach's theorem does not hold with subsets of size $C(\log n)^{1/(d-1)}$. We show that this is tight in dimension 2, for all surfaces other than $S^2$. Surprisingly, the optimal bound for $S^2$ is $(\log n)^{1/2}$. This improves upon results of Bárány, Meshulam, Nevo, and Tancer.

• May 3
Speaker: Jamie Conway (UC Berkeley)
Title: Classifying Contact Structures on Hyperbolic 3-Manifolds

Abstract: Two of the basic questions in contact topology are which manifolds admit tight contact structures, and on those that do, can we classify such structures. In dimension 3, these questions have been answered for large classes of manifolds, but notably not on any hyperbolic manifolds. In this talk, I will discuss a new classification result on an infinite family of hyperbolic 3-manifolds arising from Dehn surgery on the figure-eight knot. This is joint work with Hyunki Min.