Mina Aganagic, Ph.D.University of California, Berkeley
Presidential Lectures are free public colloquia centered on four main themes: Biology, Physics, Mathematics and Computer Science, and Neuroscience and Autism Science. These curated, high-level scientific talks feature leading scientists and mathematicians and are intended to foster discourse and drive discovery among the broader NYC-area research community. We invite those interested in the topic to join us for this weekly lecture series.
Quantum invariants of knots (also known as Chern-Simons knot invariants) have many applications in mathematics and physics. For example, Khovanov showed in 1999 that the simplest such invariant, the Jones polynomial, arises as the Euler characteristic of a homology theory. The knot categorification problem is to find a general construction of knot homology groups and to explain their meaning: What are they homologies of?
Mirror symmetry is another important strand in the interaction between mathematics and physics. Homological mirror symmetry, formulated by Kontsevich in 1994, naturally produces hosts of homological invariants. Sometimes, it can be made manifest, and then its striking mathematical power comes to the fore. Typically, though, it leads to invariants that have no particular interest outside of the problem at hand.
In this lecture, Mina Aganagic will present how she recently showed there is a vast new family of mirror pairs of manifolds, for which homological mirror symmetry can be made manifest. They do lead to interesting invariants. In particular, they solve the knot categorification problem.
To attend this in-person event, you will need to register in advance and provide:
Acceptable proof of vaccination (vaccine card/certificate, a copy or photo of vaccine card/certificate or electronic NYS Excelsior Pass or NJ Docket Pass)
Eventbrite ticket confirmation email with QR code
Simons Foundation Health Screening Questionnaire approval email
Entrance will not be granted without this documentation.
On-site registration will not be permitted. Walk-in entry will be denied.