Knot Homology Theories
Roland van der Veen and some of his MSc and PhD students have a reading group on Knot Homology Theories. We plan to study mainly Khovanov homology and knot Floer homology. Of course, any other topological or knot-theoretical discussion is welcome!
We plan to meet on Tuesdays at 15:00. Everyone is welcome to join! For more information about the seminar please see the description below or contact Jorge.
Schedule
Upcoming talks
Tuesday 15 December 2020, 15:00 - 16:00 via this link (final meeting)
Jeffrey Weenink: Traces and skein modules.
Past talks
Tuesday 8 December 2020, 15:00 - 16:00 via this link
Kevin van Helder: Gradings and a TQFT. Kevin's slides.
Tuesday 1 December 2020, 15:00 - 16:00 via this link
Jeffrey Weenink: Planar diagrams and tangle compositions. Jeffrey's notes.
Tuesday 24 November 2020, 15:00 - 16:00 via this link
Aarnout Los: Invariance under the Reidemeister move R2. Aarnout's drawings.
Tuesday 17 November 2020, 15:00 - 16:00 via this link
Jorge Becerra: Khovanov homology à la Bar-Natan. Jorge's notes.
Tuesday 10 November 2020, 15:00 - 16:00 via this link
Jeffrey Weenink: Functoriality of Khovanov homology. Jeffrey's notes.
Tuesday 3 November 2020, 15:00 - 16:00 via this link
Oscar Koster: A long exact sequence for Khovanov homology.
Tuesday 27 October 2020, 15:00 - 16:00 via this link
Jorge Becerra: Isotopy invariance of Khovanov homology II. Jorge's notes.
Tuesday 20 October 2020, 15:00 - 16:00 via this link
Jorge Becerra: Isotopy invariance of Khovanov homology I. Jorge's notes and Mathematica notebook.
Tuesday 13 October 2020, 15:00 - 16:00 via this link
Tuesday 6 October 2020, 15:00 - 16:00 via this link
Jeffrey Weenink: The Khovanov chain complex of cobordisms
*Monday* 28 September 2020, 13:00 - 14:00 in room 5161.0253
Description
References
Our two main references will be
Ozsváth, P. & Szabó, Z. - Heegaard Floer Homology and Knot Theory (Chapters 1 and 2)
Turner, P. - Five Lectures on Khovanov Homology. Errata.
Some other complementary references are
Bar-Natan, D. - On Khovanov’s categorification of the Jones polynomial.
Hom, J. - Heegaard-Floer homology
Khovanov, M. - A categorification of the Jones polynomial
Kock, J - Frobenius algebras and 2D topological quantum field theories
Manolescu, C. - An introduction to knot Floer homology.
Depending on the interest of the audience, some more advanced topics may include
Bar-Natan, D. - Khovanov's homology for tangles and cobordisms.
Ozsváth, P. & Szabó, Z. - On the Heegaard Floer homology of branched double-covers
Piccirillo, L. - The Conway knot is not slice
Rasmussen, J. - Knot Polynomials and Knot Homologies
Turner, P. - A hitchhiker's guide to Khovanov homology