I will talk about the computational problem of knot recognition: given two knots, can one smoothly transform one into the other? I will show the method of arc coloring, which provides a large class of invariants of various strengths. For example, coloring can be used to obtain a certificate of unknottedness which can be verified in polynomial time. In the end, I will talk about the underlying algebraic structures, so called quandles, and their relation to the theory of permutation groups.
A combinatorial approach to knot recognition
Sep. 05, 2017 2pm (MATH 350)
Lie Theory
Farid Aliniaeifard (CU)
X
In 1911, Schur defined the Schur's Q functions in the studies of projective representations of symmetric groups. They showed great importance in many different contexts including representation of Lie superalgebras and certain cohomology classes, etc. Naturally, Stembridge generalized Schur's Q functions to peak algebra. It later appears that the Q functions and peak algebra are odd Hopf subalgebras of symmetric functions and quasi-symmetric functions respectively. In this talk, we will precisely give a definition of odd Hopf subalgebra for any combinatorial Hopf algebra. Then, we will provide a strategy to find the odd Hopf subalgebra of any combinatorial Hopf algebra.
The odd Hopf subalgebra of a combinatorial Hopf algebra
Sep. 05, 2017 3pm (MATH 350)
Topology
Agnès Beaudry (CU Boulder) Computations with the Adams Spectral Sequence
A combinatorial approach to knot recognition