## Seminars and Colloquia by Series

Monday, November 5, 2018 - 14:00 , Location: Skiles 006 , Min Hoon Kim , Korea Institute for Advanced Study , Organizer: Jennifer Hom
Monday, October 29, 2018 - 14:30 , Location: Boyd , TBA , TBA , Organizer: Caitlin Leverson
Monday, October 15, 2018 - 14:00 , Location: Skile 006 , Lev Tovstopyat-Nelip , Boston College , Organizer: John Etnyre
Monday, October 8, 2018 - 14:00 , Location: Skile 006 , None , None , Organizer: John Etnyre
Monday, October 1, 2018 - 15:30 , Location: TBA , TBA , TBA , Organizer: Caitlin Leverson
Monday, October 1, 2018 - 14:00 , Location: Skiles 006 , Lenny Ng , Duke University , Organizer: Caitlin Leverson
Monday, September 24, 2018 - 14:00 , Location: Skiles 006 , Miriam Kuzbary , Rice University , Organizer: Jennifer Hom
Monday, September 3, 2018 - 14:00 , Location: Skile 006 , None , None , Organizer: John Etnyre
Monday, August 27, 2018 - 14:30 , Location: Boyd , Akram Alishahi and Artem Kotelskiy , Columbia and Indiana University , Organizer: Caitlin Leverson
(Akram Alishahi)Unknotting number is one of the simplest, yet mysterious, knot invariants. For example, it is not known whether it is additive under connected sum or not. In this talk, we will construct lower bounds for the unknotting number using two homological knot invariants: knot Floer homology, and (variants of) Khovanov homology. Unlike most lower bounds for the unknotting number, these invariants are not lower bound for the slice genus and they only vanish for the unknot. Parallely, we will discuss connections between knot Floer homology and (variants of) Khovanov homology. One main conjecture relating knot Floer homology and Khovanov homology is that there is a spectral sequence from Khovanov homology to knot Floer homology. If time permits, we will sketch an algebraically defined knot invariant, for which there is a spectral sequence from Khovanov homology converging to it. The construction is inspired by counting holomorphic discs, so we expect it to recover the knot Floer homology. This talk is based on joint works with Eaman Eftekhary and Nathan Dowlin. (Artem Kotelskiy) We will describe a geometric interpretation of Khovanov homology as Lagrangian Floer homology of two immersed curves in the 4-punctured 2-dimensional sphere. The main ingredient is a construction which associates an immersed curve to a 4-ended tangle. This curve is a geometric way to represent Khovanov (or Bar-Natan) invariant for a tangle. We will show that for a rational tangle the curve coincides with the representation variety of the tangle complement.  The construction is inspired by a result of [Hedden, Herald, Hogancamp, Kirk], which embeds 4-ended reduced Khovanov arc algebra (or, equivalently, Bar-Natan dotted cobordism algebra) into the Fukaya category of the 4-punctured sphere. The main tool we will use is a category of peculiar modules, introduced by Zibrowius, which is a model for the Fukaya category of a 2-sphere with 4 discs removed. This is joint work with Claudius Zibrowius and Liam Watson.
Friday, July 20, 2018 - 13:00 , Location: Skiles 006 , Kashyap Rajeevsarathy , IISER Bhopal , Organizer: Dan Margalit
Let Mod(Sg) denote the mapping class group of the closed orientable surface Sg of genus g ≥ 2. Given a finite subgroup H < Mod(Sg), let Fix(H) denote the set of fixed points induced by the action of H on the Teichmuller space Teich(Sg). In this talk, we give an explicit description of Fix(H), when H is cyclic, thereby providing a complete solution to the Modular Nielsen Realization Problem for this case. Among other applications of these realizations, we derive an intriguing correlation between finite order maps and the filling systems of surfaces. Finally, we will briefly discuss some examples of realizations of two-generator finite abelian actions.