TSVP Talk: "Symmetries of Knots and Khovanov's Homology" by Kristen Hendricks

Title: Symmetries of Knots and Khovanov's Homology

Speaker: Kristen Hendricks, Rutgers University

Abstract: A knot is an embedding of a circle into standard three-dimensional space. Knots are special objects in topology because they are very concrete and tractable, but they have deep connections to
three- and four-dimensional geometry, which is generally much harder to visualize and understand. One aspect of knot theory that is currently enjoying a lot of attention is knots with symmetries, which is to say knots which are preserved by some reflection or rotation of three-dimensional space.
Khovanov homology is an invariant of knots which was introduced around 2000. It has a deceptively simple construction, easy to describe on a blackboard, but encodes a wealth of geometric information. However, it turns out to be difficult to extract any good statements about knot symmetry from Khovanov homology in its original form. We discuss various ways one might upgrade such a theory geometrically to better understand its behavior in the presence of symmetry.

Profile: Kristen Hendricks is a professor at Rutgers University working in low-dimensional and symplectic topology. Most of her research is on equivariant versions of various Floer-theoretic invariants of knots and three-manifolds. She obtained her PhD from Columbia in 2013, after which she was a postdoc at UCLA and an assistant professor at Michigan State before moving to Rutgers in 2019.

Language: English

Target audience: General audience/everyone at OIST and beyond.
Freely accessible to all OIST members and guests without registration.

This talk will also be broadcast online via Zoom:
Meeting ID: 993 1216 5065
Passcode: 603487

※ Please note that this event may be recorded and the videos uploaded. In addition, photos may be taken during the event. These are intended for publication online (the OIST website, social media, etc.)※