Bauman University host a scientific seminar on the combinatorial enhancements of Homfly and Kauffman skein invariants. It will take place in Conference Hall of Bauman University (Moscow, Rubtsovskaya nab., 2/18). The Seminar leader is Professor Vasily Olegovich Manturov.
May, 11, Thursday:
15:00 - 18:00 Sofia Lambropoulou and Louis Kauffman «New Invariants of Links and Their State Sum Models»
Abstaract: We introduce new 4-variable invariants of links, H[R], K[Q] and D[T], based on the invariants of knots, R, Q and T, denoting the regular isotopy version of the Homflypt polynomial, the Kauffman polynomial and the Dubrovnik polynomial. The new invariants are obtained by abstracting the skein relation of the corresponding invariant and making a new skein algorithm comprising two computational levels: first producing unlinked knotted components, then evaluating the resulting knots. We provide skein theoretic proofs of the well-definedness and topological properties of these invariants. State sum models are formulated and relationships with statistical mechanics models are articulated. Finally, we discuss physical situations where this course of action is taken naturally. The new invariants in this paper were revealed through generalizing the skein theoretic definition of the invariants Θd related to the Yokonuma-Hecke algebras and their 3-variable generalization Θ for classical links, which generalizes the Homflypt polynomial as well as the Gauss linking number.
18.00-19.30 Manturov V.O. «Braids, groups G_{n}^{k}, the problems of identity and contingency, permutohedra and fundamental groups of configuration spaces»
May, 12, Friday:
15:00 - 16:30 Zhiqing Yang «Knot invariant with multiple skein relations»
Abstract: Given any oriented link diagram, one can construct knot invariants using skein relations. Usually such a skein relation contains three or four terms. The author introduces several new ways to smooth a crossings, and uses a system of skein equations to construct link invariant. This invariant can also be modified by writhe to get a more powerful invariant. The modified invariant is a generalization of both the HOMFLYPT polynomial and the two-variable Kauffman polynomial. Using the diamond lemma, a simplified version of the modified invariant is given. It is easy to compute
http://www.fn.bmstu.ru/en/research-fs-en/personalities-fs-en/item/530-v-manturov-en
We invite you to participate!
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