Program
Quantum Invariants of Knots and 3-Manifolds
Student No.:50
Time:Tue/Thu 10:10-12:00, 2015-08-25 ~ 2015-09-17
Instructor:Tian Yang  [Stanford University]
Place:Conference Room 1, Floor 1, Jin Chun Yuan West Building
Starting Date:2015-8-25
Ending Date:2015-9-17
 

Description:

This is an introduction to quantum invariants of 3-manifolds and its relationship with hyperbolic geometry.

In this series of lectures, I will introduce various invariants of 3-manifolds defined using skein theory and representation theory of quantum groups, including the colored Jones polynomials, Witten-Reshetikhin-Tureav invariants and Turaev-Viro invariants. The relationship between them and their relationship with hyperbolic geometry will also be mentioned.

 

 

Prerequisite:

Prof. Feng Luo’s course on quantum calculus is highly recommended, but not required.

 

 

Reference:

Kirillov, A. N.; Reshetikhin, N. Yu., Representations of the algebra Uq(sl(2)), q- orthogonal polynomials and invariants of links. Infinite-dimensional Lie algebras and groups (Luminy-Marseille, 1988), 285–339, Adv. Ser. Math. Phys., 7, World Sci. Publ., Teaneck, NJ, 1989.

Reshetikhin, N. Yu.; Turaev, V. G., Ribbon graphs and their invariants derived from quantum groups. Comm. Math. Phys. 127 (1990), no. 1, 1–26.

Reshetikhin, N.; Turaev, V. G., Invariants of 3-manifolds via link polynomials and quantum groups. Invent. Math. 103 (1991), no. 3, 547–597.

Turaev, V. G.; Viro, O. Ya., State sum invariants of 3-manifolds and quantum 6j- symbols. Topology 31 (1992), no. 4, 865–902.

Roberts, Justin, Skein theory and Turaev-Viro invariants. Topology 34 (1995), no. 4, 771–787.

Murakami, Hitoshi; Murakami, Jun, The colored Jones polynomials and the simplicial volume of a knot. Acta Math. 186 (2001), no. 1, 85–104.

Costantino, Francesco, 6j-symbols, hyperbolic structures and the volume conjec- ture. Geom. Topol. 11 (2007), 18311854.