On a random matrix proof of a bipartite Harer-Zagier formula
A talk in the Seminar Zufallsmatrizen series by
Hai An Mai
| Abstract: | The celebrated work of Harer and Zagier (1986) on the Euler characteristic of moduli spaces of curves lead to an interesting combinatorial problem: counting the ways in which an orientable surface of a given genus can be obtained by pairing the edges of a polygon. Using techniques from Hermitian Random Matrix Theory, they derived explicit formulas for these numbers. I will introduce a generalized problem, concerning bipartite pairings between a kM-gon and k smaller M-gons. I will then present key concepts behind the proof of this generalized Harer-Zagier formula, which relies on the decomposition of powers of Ginibre eigenvalues as a superposition of smaller independent point processes. Finally, I will discuss a further generalization of the formula to polygons of different sizes. This talk is based on joint work with Guillaume Dubach. Within the CRC this talk is associated to the project(s): C6 |