Qingtao Chen, Zürich
"New developments in knot theory: Congruent skein relations, Cyclotomic expansion and Volume Conjecture"
I will first briefly review the history of Labastida-Marino-Ooguri-Vafa Conjecture. Then I will explain in detail how we obtain these congruent skein relations for (reformulated) colored HOMFLY-PT invariants from the idea of framed LMOV conjecture. I will also discuss the congruent skein relations of colored Jones polynomials and SU(n) invariants. Finally I will report a recent discovery of Volume Conjectures and cyclotomic expansion for SU(n) invariants. This is a joint work with K. Liu, P. Peng and S. Zhu. If time permits, I will talk about Volume Conjectures for Reshetikhin-Turaev and Turaev-Viro invariants, which is joint work with Tian Yang.