Interplay between opers, quantum curves, WKB analysis, and Higgs bundles, with Olivia Dumitrescu, SIGMA 17, 036, 53 pages (2021)
From the Hitchin section to opers through nonabelian Hodge, with Olivia Dumitrescu, Laura Fredrickson, Georgios Kydonakis, Rafe Mazzeo, and Andrew Neitzke, Journal of Differential Geometry 117 (2), 223--253 (2021)
Mirror curve of orbifold Hurwitz numbers, with Olivia Dumitrescu, Revue Roumaine de Mathématiques Pures et Appliquées, 66 > (2), 307--328 (2021)
Topological Recursion and its Influence in Analysis, Geometry, and Topology, Book edited with Chiu-Chu Melissa Liu, Proceedings of Symposia in Pure Mathematics 100, 549 pps, American Mathematical Society (2018) [ISBN: 978-1-4704-3541-7]
An invitation to 2D TQFT and quantization of Hitchin spectral curves (Revised Version), with Olivia Dumitrescu, Banach Center Publications 114, 85--144 (2018) [DOI: 10.4064/bc114-3]
Edge contraction on dual ribbon graphs and 2D TQFT, with Olivia Dumitrescu, Journal of Algebra 494, 1--27 (2018)
Quantization of spectral curves for meromorphic Higgs bundles through topological recursion (the 2017 revised version for publication), with Olivia Dumitrescu, Proceedings of Symposia in Pure Mathematics 100, 179--230, American Mathematical Society (2018)
Lectures on the topological recursion for Higgs bundles and quantum curves, with Olivia Dumitrescu, in The Geometry, Topology and Physics of Moduli Spaces of Higgs Bundles, Richard Wentworth and Graeme Wilkin, Editors, Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore Vol 36, 103--198 (2018) [ISBN: 978-981-3229-08-2]
Quantum curves for simple Hurwitz numbers of an arbitrary base curve, with Xiaojun Liu and Adam Sorkin, Proceedings of Symposia in Pure Mathematics 100, 533--549, American Mathematical Society (2018)
An invitation to 2D TQFT and quantization of Hitchin spectral curves (Enlarged Japanese Edition), with Olivia Dumitrescu, in Proceedings of the 15th Oka Symposium (2017)
Quantum spectral curve for the Gromov-Witten theory of the complex projective line, with Petr Dunin-Barkowski, Paul Norbury, Alexandr Popolitov, and Sergey Shadrin, Journal für die reine und angewandte Mathematik 2017-726, 267--289 (2017)
Recursions and asymptotics of intersection numbers, with Kefeng Liu and Hao Xu, International Journal of Mathematics 27, (2016) [ preliminary preprint ]
Edge-contraction on dual ribbon graphs, 2D TQFT, and the mirror of orbifold Hurwitz numbers, with Olivia Dumitrescu, arXiv:1508.05922 (2015)
Spectral curves and the Schrödinger equations for the Eynard-Orantin recursion, with Piotr Sułkowski, Advances in Theoretical and Mathematical Physics 19, No. 5, 955--1015 (2015)
Quantum curves for Hitchin fibrations and the Eynard-Orantin theory, with Olivia Dumitrescu, Letters in Mathematical Physics 104, 635--671 (2014)
Mirror symmetry for orbifold Hurwitz numbers, with Vincent Bouchard, Daniel Hernández Serrano, and Xiaojun Liu, Journal of Differential Geometry 98, 375--423 (2014)
The spectral curve and the Schrödinger equation of double Hurwitz numbers and higher spin structures, with Sergey Shadrin and Loek Spitz, Communications in Number Theory and Physics 7, no. 1, 125--143 (2013)
The Laplace transform, mirror symmetry, and the topological recursion of Eynard-Orantin, arXiv:1210.2106 math.QA (2012), in Geometric Methods in Physics, Trends in Mathematics. Kielanowski, Odesskii, Odzijewicz, Schlichenmaier, and Voronov, Eds., 127--142, Birkhäuser Basel, 2013.
The spectral curve of the Eynard-Orantin recursion via the Laplace transform, with Olivia Dumitrescu, Brad Safnuk and Adam Sorkin, in Algebraic and Geometric Aspects of Integrable Systems and Random Matrices, Dzhamay, Maruno and Pierce, Eds. Contemporary Mathematics 593, 263--315 (2013)
Topological recursion for the Poincaré polynomial of the combinatorial moduli space of curves, with Michael Penkava, Advances in Mathematics 230, 1322--1339 (2012)
The Kontsevich constants for the volume of the moduli of curves and topological recursion, with Kevin Chapman and Brad Safnuk, Communications in Number Theory and Physics 5, 643--698 (2011)
The Laplace transform of the cut-and-join equation and the Bouchard-Marino conjecture on Hurwitz numbers, with Bertrand Eynard and Brad Safnuk, Publications of the Research Institute for Mathematical Sciences 47, 629--670 (2011)
A matrix model for simple Hurwitz numbers, and topological recursion, with Gaëtan Borot, Bertrand Eynard, and Brad Safnuk, Journal of Geometry and Physics 61, 522--540 (2011)
Polynomial recursion formula for linear Hodge integrals, with Naizhen Zhang, Communications in Number Theory and Physics 4, 267--294 (2010)
Mirzakhani's Recursion Relations, Virasoro Constraints and the KdV Hierarchy with Brad Safnuk, Indian Journal of Mathematics 50, 189--228 (2008)
A Child's Point of View (in Japanese, Kodomo no me), an expository book chapter on the Witten-Kontsevich theory, mirror symmetry, and the Gromov-Witten theory. Invited contribution. In "Kono Suugagusha ni Deaete Yokatta (The Great Moments of Meeting Mathematicians)," By Kazuhiko Aomoto, Takashi Ono, Mitsuyoshi Kato, Yasuyuki Kawahigashi, Shoshichi Kobayashi, Koichiro Harada, Motohico Mulase, et al. Sugagu-Shobo, 2011.
New developments in Witten-Kontsevich theory (in Japanese), Surikagaku (Mathematical Sciences) 543, 8--14 (September 2008)
Hitchin integrable systems, deformations of spectral curves, and KP-type equations, with Andrew R. Hodge, Advanced Studies in Pure Mathematics 59, 31--77 (2010)
Geometry of character varieties of surface groups, Research Institute for Mathematical Sciences Kokyuroku 1605, 1--21 (2008)
Prym varieties and integrable systems, with Yingchen Li, Communications in Analysis and Geometry 5, 279--332 (1997)
The Hitchin systems and the KP equations, with Yingchen Li, International Journal of Mathematics 7, 227--244 (1996)
Ribbon Graphs, Quadratic Differentials on Riemann Surfaces, and Algebraic Curves Defined over Q-bar, with Michael Penkava, The Asian Journal of Mathematics 2 (4), 875--920 (1998)
Periods of Strebel Differentials and Algebraic Curves defined over the Field of Algebraic Numbers, with Michael Penkava, The Asian Journal of Mathematics 6 (4), 743--748 (2002)
Non-commutative matrix integrals and representation varieties of surface groups in a finite group, with Josephine T. Yu, Annales de l'Institut Fourier 55, 1001--1036 (2005)
A generating function of the number of homomorphisms from a surface group into a finite group, with Josephine T. Yu, Preprint math.QA/0209008.
Duality of Orthogonal and Symplectic Matrix Integrals and Quaternionic Feynman Graphs, with Andrew Waldron, Communications in Mathematical Physics 240, 553--586 (2003)
Lectures on the Asymptotic Expansion of a Hermitian Matrix Integral, in Springer Lecture Notes in Physics 502, H. Aratyn et al., Editors, 91--134 (1998)
Asymptotic analysis of a Hermitian matrix integral, International Journal of Mathematics 6, 881-892 (1995)
Algebraic theory of the KP equations, in Perspectives in Mathematical Physics, R. Penner and S.-T. Yau, Editors, International Press Company, 157--223 (1994)
Matrix integrals and integrable systems, in Topology, geometry and field theory, K. Fukaya et. al., Editors, World Scientific, 111--127 (1994)
KP equations, strings and the Schottky problem, in Algebraic Analysis, M. Kashiwara et. al., Editors, vol.II, Academic Press, 473--492 (1988)
Cohomological structure in soliton equations and Jacobian varieties, Journal of Differential Geometry 19, 403--430 (1984)
Algebraic geometry of soliton equations, Proceedings of the Japan Academy 59 (A), 285--288 (1983)
A new super KP system and a characterization of the Jacobians of arbitrary algebraic super curves, Journal of Differential Geometry 34, 651--680 (1991)
Super Krichever functor, with J. Rabin, International Journal of Mathematics 2, 741--760 (1991)
Solvability of the super KP equation and a generalization of the Birkhoff decomposition, Inventiones Mathematicae 92, 1--46 (1988)
Complete integrability of the Kadomtsev-Petviashvili equation, Advances in Mathematics 54, 57--66 (1984)
Category of vector bundles on algebraic curves and infinite dimensional Grassmannians, International Journal of Mathematics 1, 293--342 (1990)
Geometric classification of Z2-commutative algebras of super differential operators, Marcel Dekker Lecture Notes in Pure and Applied Mathematics 145, Einstein Metrics and Yang-Mills Connections, 161--180 (1993)
Normalization of the Krichever Data, Contemporary Mathematics 136, Curves, Jacobians, and Abelian Varieties, 297--304 (1992)
Geometric classification of commutative algebras of ordinary differential operators, Differential Geometric Methods in Theoretical Physics, NATO Advanced Sciences Institutes Series 245 B, 13--27 (1990)
A correspondence between an infinite Grassmannian and arbitrary vector bundles on algebraic curves, Proceedings of Symposia in Pure Mathematics 49, 39--50 (1989)
Poles of instantons and jumping lines of algebraic vector bundles on P^3, Proceedings of the Japan Academy 55 (A), 185--189 (1979)
Combinatorial Structure of the Moduli Space of Riemann Surfaces and the KP Equations, (1997)