Homological Link Invariants from Floer Theory


LePage, E. (2023). Homological Link Invariants from Floer Theory. Perimeter Institute. https://pirsa.org/23050138


LePage, Elise. Homological Link Invariants from Floer Theory. Perimeter Institute, May. 11, 2023, https://pirsa.org/23050138


          @misc{ pirsa_23050138,
            doi = {10.48660/23050138},
            url = {https://pirsa.org/23050138},
            author = {LePage, Elise},
            keywords = {Mathematical physics},
            language = {en},
            title = {Homological Link Invariants from Floer Theory},
            publisher = {Perimeter Institute},
            year = {2023},
            month = {may},
            note = {PIRSA:23050138 see, \url{https://pirsa.org}}

Elise LePage University of California, Berkeley


In recent work, Aganagic proposed a categorification of quantum link invariants based on a category of A-branes, which is solvable explicitly. The theory is a generalization of Heegaard-Floer theory from gl(1|1) to arbitrary Lie algebras. I will describe in the detail the two simplest cases: the su(2) theory, categorifying the Jones polynomial, and the gl(1|1) theory, categorifying the Alexander polynomial. I will give an explicit algorithm for computing link homologies in these cases. I will also briefly describe the generalization to other simple Lie algebras and to Lie superalgebras of type gl(m|n). This talk is based on work to appear with Mina Aganagic and Miroslav Rapcak.

Zoom Link: TBD