Algebraický seminář
Josef Svoboda (Caltech): Inverted Habiro series and its residues
Abstract: Quantum algebra provides an important source of invariants of knots and 3-manifolds. Using Verma modules of the algebra $U_q(sl_2)$, Park defined a knot invariant and observed that it can be written in a very peculiar form, which he called inverted Habiro series. I will describe a commutative ring $\Lambda$ that contains these series and explain how $\Lambda$ could arise as the center of some form of $U_q(sl_2)$. Then I will show how $q$-series identities of Euler, Hecke--Rogers and Ramanujan follow from the study of residues of the inverted Habiro series for the simplest knots.
September 29 - TBA
The Algebra Seminar was founded by Vladimir Korinek in the early 1950's and continued by Karel Drbohlav until 1981. The seminar resumed its activities in 1990 under the guidance of Jaroslav Jezek and Tomas Kepka. Since 1994, the seminar is headed by Jan Trlifaj.
Presently, the seminar is supported by GACR. It serves primarily as a platform for presentation of recent research of the visitors to the Department of Algebra as well as members of the Department and their students.
