| Date | Topic | Date | Topic |
|---|---|---|---|
| 1/23 | Kauffman bracket and Jones polynomial, TQFT origin of skein relations | 1/25 | 2d TQFTs and Frobenius algebras, Temperley-Lieb algebroid $\mathrm{TL}$ |
| 1/30 | Jones-Wenzl projectors, Temperley-Lieb-Jones algebroid | 2/1 | monoidal, braided, and ribbon categories |
| 2/6 | pivotality of ribbon categories, dimensions and traces, category of colored ribbon graphs | 2/8 | Reshetikhin-Turaev (RT) functor |
| 2/13 | algebras and coalgebras, convolution algebras, restricted dual of an algebra | 2/15 | bialgebras and Hopf algebras |
| 2/20 | braided and cobraided bialgebras, ribbon Hopf algebras | 2/22 | twisted products and coproducts, quantum double |
| 2/27 | Hopf pairing and generalized quantum double | 2/29 | quantized universal enveloping algebras $U_q(\mathfrak{sl}_N)$, modular categories |
| 3/5 | Witten-Reshetikhin-Turaev (WRT) invariants | 3/7 | Witten-Reshetikhin-Turaev (WRT) invariants (cont.) |
| 3/12 | No class (Spring recess) | 3/14 | No class (Spring recess) |
| 3/19 | Class canceled | 3/21 | Class canceled |
| 3/26 | skein modules and character varieties | 3/28 | Class canceled |
| 4/2 | quantum Teichmuller space, 2d quantum trace map | 4/4 | stated skein algebras of surfaces, splitting map, bigons and $O_q(SL_N)$-comodule structures |
| 4/9 | Hochschild cohomology, reduced stated skein algebras, stated skein modules of 3-manifolds |
4/11 | 3d quantum trace map, modified dimensions and renormalized RT invariants, Akutsu-Deguchi-Otsuki (ADO) invariants |
| 4/16 | ideals and modified traces, unrolled quantum group $\overline{U}_q^H(\mathfrak{sl}_2)$, $G$-grading, realization of an additive abelian group $Z$ in a ribbon category | 4/18 | relative $G$-modular categories, Costantino-Geer-Patureau (CGP) invariants, admissible skein modules |
| 4/23 | BPS $q$-series $\widehat{Z}$ |