# Topological Quantum Field Theory Seminar

## Planned sessions

### Cyclotomic expansions of the $gl_N$ knot invariants

Newton’s interpolation is a method to reconstruct a function from its values at different points. In the talk I will explain how one can use this method to construct an explicit basis for the center of quantum $gl_N$ and to show that the universal $gl_N$ knot invariant expands in this basis. This will lead us to an explicit construction of the so-called unified invariants for integral homology 3-spheres, that dominate all Witten-Reshetikhin-Turaev invariants. This is a joint work with Eugene Gorsky, that generalizes famous results of Habiro for $sl_2$.

### Multiple zeta values in deformation quantization

In 1997, Kontsevich gave a universal solution to the deformation quantization problem in mathematical physics: starting from any Poisson manifold (the classical phase space), it produces a noncommutative algebra of quantum observables by deforming the ordinary multiplication of functions. His formula is a Feynman expansion whose Feynman integrals give periods of the moduli space of marked holomorphic disks. I will describe joint work with Peter Banks and Erik Panzer, in which we prove that Kontsevich's integrals evaluate to integer-linear combinations of multiple zeta values, building on Francis Brown's theory of polylogarithms on the moduli space of genus zero curves.