Events

Metric ribbon graphs (MRG) are graphs embedded into surfaces equipped with positive edge lengths. Functions counting MRG's with given boundary lengths are a priori piecewise polynomials, but in some cases become honest polynomials.

I will first present one such case -- Kontsevich's polynomials counting trivalent MRG's (from his proof of Witten's conjecture about intersection numbers on the moduli spaces of curves), and explain how they are used to study hyperbolic and flat surfaces.

Given a finite group $G$ a 4-cocycle $\pi \in \mathrm{H}^4(G,U(1))$, the 4D Dijkgraaf–Witten model provides an exactly solvable gauge theory with applications in high-energy physics and topological phases of matter. The topological defects in this model form a braided fusion 2-category $\mathscr{Z}(\mathbf{2Vect}^\pi_G)$, the Drinfeld center of $\pi$-twisted $G$-crossed finite semisimple linear categories.

Geometric quantization on symplectic manifolds plays an important role in representation theory and mathematical physics, and is deeply related to symplectic and differential geometry. A crucial problem is to understand the relationships among geometric quantizations associated with different polarizations. In this talk, we will discuss the existence of mixed polarizations and degeneration of Kähler polarizations associated to imaginary-time flow.