Distinguished Lectures in Topology and Geometry

The lectures are held several times per semester, usually on Mondays at 4 pm in Smith hall, room 204 (Rutgers-Newark campus), preceded by tea at 3:30 pm.

Upcoming lecture: March 4th, 2024

Speaker: Professor Jennifer Schultens from the University of California, Davis

Website: https://www.math.ucdavis.edu/~jcs/
Wikipedia page: https://en.wikipedia.org/wiki/Jennifer_Schultens

Title: Surfaces in Seifert fibered spaces

Abstract: Curve complexes and surface complexes come in several varieties. They have been studied by geometric group theorists and employed by low-dimensional topologists. The unique structure of Seifert fibered spaces allows us to describe certain surface complexes in terms of certain curve complexes.

Recent (past) lectures:

Speaker: Professor Efstratia Kalfagianni from Michigan State University

Website: https://users.math.msu.edu/users/kalfagia/
Wikipedia page: https://en.wikipedia.org/wiki/Efstratia_Kalfagianni

Title: Knot crossing numbers and Jones polynomials

Abstract: The crossing number of a knot is the smallest number of “double points” (crossings) over all planar projections of the knot. Crossing numbers are hard to compute and their behavior under basic topological operations is poorly understood. In this talk I will discuss how the knot Jones polynomial and its relative the colored Jones polynomial can be used to determine the crossing numbers for large families of knots. The talk is partly based on joint work with Christine Lee.

Speaker: Professor Shelly Harvey from Rice University

Website: https://math.rice.edu/~shelly/
Wikipedia page: https://en.wikipedia.org/wiki/Shelly_Harvey

Title: Linking in 4-dimensions
Abstract: Knots and links play an essential role in classifying 3- and 4-dimensional manifolds (in both the smooth and topological category). Where knots/links up to isotopy is the correct equivalence relation on knots/links to understand 3-manifolds. In this talk, we will be concerned with knots/links up to concordance – the correct equivalence relation to understand 4-manifolds. After a review of concordance, we will discuss new work (with C. Leidy, C. Davis, and J.H. Park) towards an understanding of links up to what could be called algebraic concordance. While the classification of knots up to algebraic concordance has been well understood since the 60’s, we still know little about links. This talk will be accessible to a wide audience. In particular, I will not assume any knowledge of knot theory or low-dimensional topology.

Organizers: Kyle Hayden, John Loftin and Anastasiia Tsvietkova. Funded by NSF CAREER DMS-2142487 grant.