Topology Seminar (Introductory Talk): Introduction to Skein Algebras and Character Varieties

Seminar | September 5 | 2-3 p.m. | 736 Evans Hall | Note change in location

 Semeon Artamonov, University of California, Berkeley

 Department of Mathematics

To each oriented surface one can associate two algebras: commutative coordinate ring of the character variety of the fundamental group and noncommutative skein algebra. Both algebras enjoy the action of the mapping class group of the surface by automorphisms. In my introductory talk I will define both algebras mentioned above and show how they are related to each other. I will then describe a one-parameter deformation of the skein algebra of torus known as the Spherical Double Affine Hecke Algebra (DAHA) and review some applications to the theory of symmetric polynomials.