# Motohico Mulase

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

Email: mulase@math.ucdavis.edu

Office: MSB 3103

Current Courses: MAT 21B, MAT 108

Office Hours: W 2:00p-5:00p

Additional Information: Distinguished Professor of Mathematics

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### Research

The research expertise of Motohico Mulase lies in the interplay of many areas of mathematics, such as algebraic geometry of moduli spaces of Riemann surfaces and Higgs bundles, nonlinear integrable systems such as KP and KdV equations, Gromov-Witten theory, and topological recursion. His research accomplishments include a solution to the Schottky problem (a characterization of Jacobian varieties) in terms of KP equations (Novikov conjecture) **[1]**, establishing the solvability of soliton equations and supersymmetric generalizations **[2]**, discovery of the equivalence between Strebel differentials and Grothendieck's dessins d'enfants **[3], **a proof of the Bouchard-Mariño conjecture on Hurwitz numbers **[4]**, and a solution to the conjecture of Gaiotto** **on conformal limit and opers of Beilinson and Drinfeld **[5]**.

### Selected publications

- M. Mulase. "Cohomological structure in soliton equations and Jacobian varieties,"
*Journal of Differential Geometry*,**19**(2):403-430, (1984). Full Text - M. Mulase. "Solvability of the super KP equation and a generalization of the Birkhoff decomposition,"
*Inventiones Mathematicae*,**92**:1-46, (1988). Full Text. - M. Mulase and M. Penkava. "Ribbon Graphs, Quadratic Differentials on Riemann Surfaces, and Algebraic Curves Defined over
**Q**,"*Asian Journal of Mathematics*,**2**:875-920, (1998). Full Text. - B. Eynard, M. Mulase, and B. Safnuk. "The Laplace transform of the cut-and-join equation and the Bouchard-Mariño conjecture on Hurwitz numbers,"
*Publications of the Research Institute for Mathematical Sciences*,**47**:629-670, (2011). Full Text. - O. Dumitrescu, L. Fredrickson, G. Kydonakis, R. Mazzeo, M. Mulase and A. Neitzke. "From the Hitchin section to opers through nonabelian Hodge,"
*Journal of Differential Geometry*,**117**(2), 223--253 (2021). Full Text.

### Honors and Awards

- Member, MSRI, Berkeley, 1982-84
- Member, IAS, Princeton, 1988-89
- Member, Max-Planck-Institut für Mathematik, Bonn, 1991-92, 2011, 2013, 2014, 2015, 2016, 2019, 2022, 2023
- RIMS International Project Research Professor, Kyoto University, 2008, 2024
- UC Davis Academic Senate Distinguished Teaching Award, 2009
- Member, Institut des Hautes Études Scientifiques, Bures-sur-Yvette, 2013
- Visiting Senior Scientist, Kavli Institute for the Physics and Mathematics of the Universe, the University of Tokyo, 2013-
- UC Davis Distinguished Professor, 2019

*Last updated: 2024-08-15*