Survey of Homology of Yang-Baxter operators

Speaker(s)

Józef Przytycki

Affiliation

George Washington University

Language of the talk

English

Date

June 11, 2025, 10:15 a.m.

Room

room 4070

Seminar

Seminar Algebraic Topology

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The homology of Yang-Baxter operators were discovered/constructed by Victoria Lebed and the speaker in Spring of 2012. They generalize
homology of racks,  quandles, and set theoretic Yang-Baxter operators. A proper visualization of precubic modules gives
the decisive hint into successful definition.
In the first part of my talk I will discuss the background of Yang-Baxter homology. In the second part, I will discuss how the homology
of HOMFLYPT Yang-Baxter operator can be (partially) computed by using a cascade of filtrations and their splittings. We speculate that
Yang-Baxter homology is related to Khovanov homology (they both generalize Jones and HOMFLYPT polynomials) and can be used to analyze
phase transition for some physical processes

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