# Motohico Mulase

**Regular Faculty****Complex geometry**

Ph.D., 1985, Kyoto University**Refereed publications:** Via Math Reviews

**Web Page: ** http://www.math.ucdavis.edu/~mulase/

Email: mulase@math.ucdavis.edu

Office: MSB 3103

### Research

The research expertise of Motohico Mulase lies in the interplay of many areas of mathematics, such as algebraic geometry of moduli spaces or Riemann surfaces and vector bundles, nonlinear integrable systems such as KP and KdV equations, Gromov-Witten theory, and topological string theory. His research accomplishments include a solution to the Schottky problem (a characterization of Jacobian varieties) in terms of KP equations**[1]**, establishing the solvability of soliton equations

**[2]**, a proof of the Bouchard-Marino conjecture on Hurwitz numbers

**[3,4]**, and the discovery of the virtual Poincare polynomials of the moduli space of pointed smooth curves

**[5]**.

### Selected publications

**[1]**M. Mulase. "Cohomological structure in soliton equations and Jacobian varieties,"

*Journal of Differential Geometry*,

**19**(2):403-430, (1984). Full Text.

**[2]** M. Mulase. "Solvability of the super KP equation and a generalization of the Birkhoff decomposition," *Inventiones Mathematicae*, **92**:1-46, (1988). Full Text.

**[3]** Mulase, M., and N. Zhang. "Polynomial recursion formula for linear Hodge integrals," *Communications in Number Theory and Physics*, **4**:267-294, (2010). Full Text.

**[4]** Eynard, E., Mulase, M., and B. Safnuk. "The Laplace transform of the cut-and-join equation and the Bouchard-Marino conjecture on Hurwitz numbers," *Publications of the Research Institute for Mathematical Sciences*, **47**:629-670, (2011). Full Text.

**[5]** Mulase, M., and M. Penkava. "Topological recursion for the Poincare polynomial of the combinatorial moduli space of curves," to appear in *Advances in Mathematics*, (2012). Full Text.

### Honors and Awards

- Hironaka Foundation Fellowship (Harvard), 1982-83
- Member, MSRI, Berkeley, 1982-84
- Member, IAS, Princeton, 1988-89
- Member, Max Planck Institute for Mathematics, Bonn, 1991-92, 2011
- RIMS International Project Research Professor, Kyoto University, 2007-08
- UC Davis Academic Senate Distinguished Teaching Award, 2009

*Last updated: 2012-04-19*