In progress
Co-editor: Advances in Complex Lagrangians, Integrable systems and Quantization - with L. Schaposnik, J. Sawon and M. Mulase
Google Scholar profile. Mathscinet.
Visits: RIMS kyoto summer 2024.
Research directions
Hitchin systems: Quantum curves, Moduli of Opers, Conformal limits.
Enumerative geometry: Topological recursion, Relations to Gromov-Witten theory.
Algebraic geometry: Birational geometry, Degeneration theory, Toric geometry.
UNC Reading seminar 2021-2022 with my graduate students on introductive topics in enumerative geometry:
Fall: Hitchin theory/ Introduction to Gauge Theory,
Spring: Mirzakhani's work on WP volume/ Kontsevich's count of curves, WK intersection numbers
Organization (In person)
2023 - Complex Lagrangians, Mirror Symmetry, and Quantization, with M. Mulase, L. Schaposnik, J. A. Cruz Morales, E. Garcia Failde.
BIRS Banff Canada, October
2022 - Quantization of Complex Symplectic Varieties, mini-workshop in Oberwolfach, Germany.
2019 - Geometry, Integrability and Moduli with Gaetan Borot, Steven Rayan and Don Zagier,
MPIM Bonn in the honor of Motohico Mulase.
2018 - Geometry and Physics of Quantum Curves with R. Donagi, M. Gualtieri and M. Mulase,
BIRS, Banff International Research Station, Canada, September
Osaka City University Advanced Mathematics Institute Japan, November
Short Courses on Higgs bundles, with Marcus Sperling,
Leibniz Universität Hannover, Germany
AIM Conference AIM workshop Quantum curves, Hitchin systems, and the Eynard-Orantin theory, M. Mulase, S. Shadrin and P. Sulkowski
American Institute of Mathematics, Palo Alto, US.
Leibniz Universität Hannover, Germany
Visiting
Simons Center for Geometry and Physics, during the semester program Geometry and Physics of Hitchin Systems 2019 (one month)
Institut Henri Poincare IHP, France, March (one month) during the semester program Combinatorics and Interactions 2017
Institut Henri Poincare IHP, France, June-July (1 week) during the semester program Program on the Mathematics of String Theory.
Osaka City University Advanced Mathematical Institute, Japan, (2 weeks)
Research in Pair Grants
Trento, January, Centro Internazionale per la Ricerca Matematica, (1 month)
Mini-courses (In Person)
2013 Complex Lagrangians, Integrable systems and Quantization, Oxford University, mini-course (organized by Laura Schaposnik, M. Yang, C. Mahadeo) June
2019 - Simons Center for Geometry and Physics, March
2018 - Mirror Symmetry and Related Topics, University of Miami, January2018.
2018 - Geometries and Physics of the Gauge Theories at infinity, Elk Ridge Resort, Prince Albert National Park, Saskatchewan, Canada.
2018 - Tuebingen school on topological recursion 2018, Tuebingen, Germany, August 2018,
Osaka City University Advanced Mathematics Institute, (Japan) Enumerative geometry, quantization of Higgs bundles and 2D TQFT
Perimeter Institute, Waterloo, (Canada) , Video: here
Topological recursion for Higgs bundles and Cohomological Field Theory, Advances in Perturbation Theory and Feynmann Amplitudes, May.
Kobe Summer School: Graduate Course, Kobe University (7.5 hours) A mathematical theory of quantum curves, August.
Kobe Summer School: Undergraduate Course, Kobe University Interplay between differential equations, integrable systems, and algebraic geometry, (4.5 hours), July.
Summer School, National University of Singapore IMS: Lecture Notes (2 hours) The Geometry, Topology and Physics of Moduli Spaces of Higgs Bundles, Quantization of spectral curves of Higgs bundles via a B-model topological recursion
Formation
Phd Adviser: Rick Miranda.
Member at Max Planck Institute for Mathematics, Bonn.
Postdoctoral Fellow (Algebraic Geometry) at GRK Analysis, Geometry and String Theory (Graduiertenkolleg 1463), Leibniz Universitaet Hannover.
Krener Assistant Professor (postdoctoral fellow) at University of California, Davis.
Grants
June 2022 - May 2025 NSF FRG
Sept 2021 - Aug 2026 "Geometry and Physics of Quantum Curves and Higgs bundles" Simons Foundation, Collaboration Grant 855897.
June 2018 - May 2022 ''Enumerative geometry of Hitchin systems and TQFT'', National Science Foundation, DMS - 1802082 and 2041740
Sept 2017 - August 2022 "Holomorphic Quantization of Hitchin Spectral Curves'' Simons Foundation, Collaboration Grant 524545
2015 - 2016 Max Planck Institute for Mathematics, Postdoctoral
Visitors (CMU)
Mihai Fulger, University of Connecticut
Nathan Priddis, Brigham Young University
Nikita Nikolaev, University of Geneva
Motohico Mulase, University of California, Davis
Steven Rayan, University of Saskatchewan
Matthew Woolf, UIC