|Quantum Invariants of Knots and 3-Manifolds|
|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|
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.
Prof. Feng Luo’s course on quantum calculus is highly recommended, but not required.
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.
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.