Quantum Topology at generic q (part 3)

Abstract: This is the third of a 4-lecture miniseries.

Quantum topology is a blend of topology and quantum algebra, where topological invariants of knots and 3-manifolds are constructed from basic building blocks of algebraic origin. The latter, in turn, can come from symmetries of solvable lattice models, from vertex operator algebras, from quantum field theories, and from various constructions in geometric representation theory, thus providing "algebraic bridges" between these different areas of mathematics and physics. Many invariants of 3-manifolds --- e.g. the Rokhlin invariant, Witten-Reshetikhin-Turaev invariants and their non-semisimple generalizations (ADO and CGP invariants) --- arise in this way and involve quantum groups at roots of unity. Constructing q-series invariants associated with quantum groups at generic q requires qualitatively new techniques. The main goal of these lectures is to offer a slow introduction and a practical guide to these techniques, illustrated by many examples and, hopefully, led by many questions and suggestions from the audience.

algebraic geometrysymplectic geometry

Audience: researchers in the topic

M-seminar