## Algebra

•  Leonid Chekov, MSU
•  Topological Recursion
•  03/22/2017
•  3:00 PM - 3:50 PM
•  C304 Wells Hall

I begin with solving the loop equations in matrix models. The TR allows constructing in a very algorithmic way all correlation functions $W_s^{(g)}(x_1,\dots,x_s)$ of a model on the base of the spectral curve $\Sigma(x,y)=0$ obtained as a solution of a master loop equation in the planar approximation; the variable $y$ is identified with $W_1^{(0)}$. We are then able to construct all $W_s^{(g)}$ out of this, not very abundant, set of data supplied with the two-point correlation function $W_2^{(0)}(x_1,x_2)dx_1dx_2$, which is a universal Bergmann 2-differential on the spectral curve. We are also able to construct terms of the free energy $F^g$ using the Ch.-Eynard integration formula applied to $W_1^{(g)}$. Finally, I will describe a Feynman-like diagrammatic technique for evaluation all $W_s^{(g)}$.

## Contact

Department of Mathematics
Michigan State University
C212 Wells Hall
East Lansing, MI 48824

Phone: (517) 353-0844
Fax: (517) 432-1562

College of Natural Science