【SeminarDAY1】Khovanov Homology and Its Application to Low-Dimensional Topology

Speaker: Dr. Taketo Sano （RIKEN)

I am happy to announce that we will have Sano-san (Riken) to come over in 2 weeks and deliver a series of introductory lectures on Khovanov Homology and Its Application to Low-Dimensional Topology

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Abstract: Knot homology theories revolutionized the study of knots and links, much like (simplicial or singular) homology theory revolutionized the study of topological spaces. One of the major knot homology theories, Khovanov homology, was introduced by M. Khovanov in 2000 as a "categorification of the Jones polynomial." One notable feature of Khovanov homology is its ability to detect the unknot, a feature not known to be possessed by the Jones polynomial. Recently, it has found notable applications in low-dimensional topology, including the detection of exotic surfaces in the 4-ball.

I will conduct a three-day seminar starting with the basics of Khovanov homology and progressing to my own research. The outline is as follows:

Day 1: Jones polynomial and its categorification.

Zoom Link

https://oist.zoom.us/j/97832302984?pwd=FTtlizpBpWFXaxw8RvnNOcH40AkWu8.1

Meeting ID: 978 3230 2984
Passcode: 367484

Recording of the Seminar Day 1

https://oist.zoom.us/rec/share/ZwpFvfA7uB80gL5hzzNj_iOnUFWts6AAzS9T3TPs5qe90Wnyo6YsOIBPR4zVZxjM.wxtjXo5ttvZXHb67

パスコード： JO5@^L2v

Day 2: Numerical invariants from Khovanov homology and their applications.

Day 3: Recent developments of Khovanov homology and its applications to low-dimensional topology.

On the final day, I plan to give a brief introduction to my recent work,

"Involutive Khovanov Homology and Equivariant Knots"

https://arxiv.org/abs/2404.08568

The talk is aimed at anyone interested in these topics. No specific knowledge of knot theory is assumed. Basic understanding of algebraic topology and category theory, such as  concepts of homology and chain complexes, categories and functors, is expected.

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