Survey of Homology of Yang-Baxter operators
- Prelegent(ci)
- Józef Przytycki
- Afiliacja
- George Washington University
- Język referatu
- angielski
- Termin
- 11 czerwca 2025 10:15
- Pokój
- p. 4070
- Seminarium
- Seminarium „Topologia algebraiczna”
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