From quantum topology to classical geometry
This course studies quantum invariants of knot and 3-manifolds from the perspective of their classical limit. It will focus on the question: How does classical three-dimensional geometry emerge from quantum topology? The course will begin with the introduction of several quantum invariants of knot and 3-manifolds appeared in the 90s. Then we see how the classical (hyperbolic) geometry naturally emerges from the asymptotic analysis of these invariants. The course will also discuss some recent developments on some state-integral models.
Lecturer
Date
8th September ~ 30th December, 2026
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Tuesday | 14:20 - 16:55 | A14-101 | ZOOM B | 462 110 5973 | BIMSA |
Prerequisite
Mathematical Analysis, Complex Analysis, Linear Algebra, Undergraduate Topology
Syllabus
Week 1-6: Quantum invariants: Kauffman Bracket, Jones Polynomial, Reshetikhin-Turaev Invariants, Quantum 6-j symbols, Turaev-Viro Invariants.
Week 7-10: 3-dimensional Hyperbolic Geometry: Ideal tetrahedra, Gluing Equations, Character varieties, Hyperbolic Dehn Surgery, Neumman-Zagier functional
Week 11-16: The Classical Limit: Volume Conjecture, Saddle Point Analysis, Quantum Dilogrithm, b-6j symbols, State-integral models, Reidemeister Torsion, Quantum Modularity
Week 7-10: 3-dimensional Hyperbolic Geometry: Ideal tetrahedra, Gluing Equations, Character varieties, Hyperbolic Dehn Surgery, Neumman-Zagier functional
Week 11-16: The Classical Limit: Volume Conjecture, Saddle Point Analysis, Quantum Dilogrithm, b-6j symbols, State-integral models, Reidemeister Torsion, Quantum Modularity
Audience
Graduate
, Postdoc
, Researcher
Video Public
Yes
Notes Public
Yes
Language
Chinese