30 November 2020, 18:30 - (UTC+3)
Title : Comparing a new homology theory for trivalent graphs with Khovanov homology for virtual links
Speaker : Scott Baldridge
Organization : Knots and representation theory (by Zoom)
Abstract: In this lecture, I will show how to categorify the 2-factor polynomial to get a homology theory of trivalent ribbon graphs with perfect matchings. The 2-factor polynomial is useful in graph theory because it counts certain 3-edge colorings of a graph. I will then introduce the notion of a graphene, which is an equivalence class of ribbon graphs that behaves like a virtual link. Finally, I will compare the homology theory to Khovanov homology of virtual links using graphenes and show that, while the two share many similarities, they are different theories.
The work on graphenes is joint with Lou Kauffman and Will Rushworth.
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Meeting ID: 818 6674 5751
02 December 2020, 10:30 - (UTC+3)
Title: On the different flavours of Lawrence-Bigelow representations
Speaker: Martin Palmer (IMAR, Romania)
Organization : Seminar in Moscow and Beijing by zoom
Abstract : The family of Lawrence-Bigelow representations of the braid groups are of central importance in the study of the braid groups themselves, as well as their connections with quantum invariants of knots and links. They are an example of a wider class of homological representations of mapping class groups of surfaces, arising from twisted homology of configuration spaces. These homological representations come in many different flavours, depending on the kind of homology theory used, whether we forget part of the boundary or consider homology relative to part of the boundary, and whether we consider twisted homology or instead the homology of an associated covering space.
We will describe these different constructions of homological representations, and then explain the fundamental relationships between them in terms of non-degenerate pairings, embeddings and isomorphisms. In many cases, the representations are free (as modules), and we will also describe, pictorially, explicit bases for these representations.
This represents joint work with Cristina Anghel and is based on http://arxiv.org/abs/2011.02388.
The seminar will be held during 15:30--17:00 (Beijing time) on Zoom.
Meeting ID: 831 5020 0580
03 December 2020, 17:30 - (UTC+3)
Organization: Mathematical colloquium in BMSTU