Surface cluster algebras and their bases

In this talk, we first provide a gentle introduction to (quantum) cluster algebras and skein algebras associated with surfaces. Then we focus on three most important classes of bases—bangles, bands, and bracelets—presenting their combinatorial structures and algebraic properties. We demonstrate how surface cutting techniques significantly simplify the study of these bases. Finally, we present some recent progress on the basis elements.

For information about the Richard P. Stanley Seminar in Combinatorics, visit https://math.mit.edu/combin/