Selected Publications of Motohico Mulase


Quantum Curves, Hitchin Moduli Spaces, Opers, Gromov-Witten Invariants, TQFT, Topological Recursion (Eynard-Orantin Theory), Hurwitz Numbers, and Witten-Kontsevich Theory:

Hitchin's Integrable Systems, Geometric Langlands Duality, and Characterization of Prym Varieties:

Ribbon Graphs, Grothendieck's Dessins d'Enfants, Belyi Morphisms, Strebel Differentials, and Orbifold Structure of the Moduli Space of Riemann Surfaces:

Matrix Models, Matrix Duality, Topological Expansion of Matrix Integrals, and their Generalizations with Applications to Geometry of Moduli Spaces

Surveys on the KP Theory, Sato Grassmannians, and their Applications to the Schottky Problem and Matrix Integrals:

A Solution to the Schottky Problem in terms of KP Equations, and its Supersymmetric Generalizations:

Solvability and Complete Integrability of KP equations, Birkhoff Decomposition of the Group of Pseudo-Differential Operators, and Supersymmetric Generalizations:

Sato Grassmannian, Commutative Rings of Differential Operators, Moduli of Vector Bundles on Algebraic Curves, and their Supersymmetric Generalizations:

Instantons:


Unpublished Lecture Notes:

Combinatorial Structure of the Moduli Space of Riemann Surfaces and the KP Equations, (1997)

Lectures on the Combinatorial Structure of the Moduli Spaces of Riemann Surfaces and Feynman Diagram Expansion of Matrix Integrals, (2001)