Clair Xinle Dai
Clair Xinle Dai
Email: xd214@math.rutgers.edu
Address: Hill Center 510, Department of Mathematics,
110 Frelinghuysen Road, Piscataway, NJ 08854-8019, USA
I am a Hill Assistant Professor in the Department of Mathematics at Rutgers University - New Brunswick. I received my Ph.D. in Mathematics from Harvard University. I was fortunate to be advised by Denis Auroux and Peter Kronheimer. My main research interests are symplectic geometry, mirror symmetry, and low-dimensional topology.
Publications and Preprints:
Homological Mirror Symmetry of Symmetric Products of Surfaces (in preparation)
Sectorial decomposition of symmetric product of surfaces arXiv:2511.16584
Talks and Presentations:
Geometry and Topology Seminar, Rutgers University, 2026
AMS Fall Eastern Sectional Meeting, George Washington University, 2026
Workshop on Lagrangian Floer Theory and Applications, Harvard CMSA, 2026
AMS Spring Eastern Sectional Meeting, Boston College, 2026
Groups, Geometry, and Topology Seminar, University of Illinois Urbana-Champaign, 2026
Minnesota Symplectic Geometry Seminar, University of Minnesota, 2026
Seoul National University Symplectic Geometry Seminar, Seoul National University, 2025
PU/IAS Symplectic Seminar, Princeton University, 2025
Stanford Symplectic Seminar, Stanford University, 2025
Rutgers Symplectic Summer School, Rutgers University, 2025
New structures in Low-Dimensional Topology Simons Collaboration Annual Meeting (poster session), 2025
AMS Spring Western Sectional Meeting, California Polytechnic State University, San Luis Obispo, 2025
AMS Spring Southeastern Sectional Meeting, Clemson University, 2025
UMass Geometry and Topology Seminar, 2025
Shanghai Institute for Mathematics and Interdisciplinary Sciences, Fudan University, January 2025
Academy of Mathematics and Systems Science of China, Morningside Center of Mathematics, Symplectic Geometry and Mathematical Physics Seminar, 2024
University of Angers Student Seminar, 2024
Tech Topology Conference, 2024
Columbia Geometric Topology Seminar, 2024
Harvard Gauge Theory Seminar, 2024
New England Algebraic Topology and Mathematical Physics Seminar, 2024
Boston University Geometry and Physics Seminar, 2024
Boston College Algebraic Geometry Seminar, 2024
Conference on New Structures in Low-Dimensional Topology in Budapest, 2024
Stony Brook Symplectic Geometry Seminar, 2024
MIT Symplectic Geometry Seminar, 2024
Jane Street Graduate Research Fellowship Workshop (poster session), 2024
Mid-Atlantic Topology Conference (poster session), Northeastern University, 2024
AMS–AWM Special Session: Women and Gender Minorities in Symplectic and Contact Geometry at Joint Mathematics Meetings, January 2024
Kylerec Workshop on Homological Mirror Symmetry, 2023
MIT Juvitop Seminar, 2023
Geometric Topology Grad and Postdoc Seminar, 2023
MSRI/Simons Laufer Mathematical Sciences Institute Graduate Student Seminar, 2022
Symplectic Reading Seminar, MIT, 2022
University of Cambridge Part III Seminar Series, 2019
Algebraic Combinatorics Seminar, University of Waterloo, 2019
Park City Mathematics Institute, presentation of research under Professor Rafe Mazzeo, 2018
Diversity in Math Summer School, University of British Columbia, 2018
Geometric Working Seminar, University of Waterloo, 2017
Canadian Undergraduate Mathematics Conference, University of Victoria, 2016
Geometric Working Seminar, University of Waterloo, 2016
Awards and Honors:
Bok Center Certificate of Distinction in Teaching, Harvard University
Women and Mathematics Program Graduate Ambassadorship Grant
Early Career AMS-NSF-Simons-ICM Travel Grant
Cambridge Trust Scholarship, Cambridge Trust
Sheila Edmonds Bursary, Cambridge University
Newnham College Scholarship, Cambridge University
Combinatorics Undergraduate Research Award, University of Waterloo
Mike Vangoch Memorial Scholarship, University of Waterloo
Pure Mathematics Department Silver Award, University of Waterloo
EPFL Scholarship of Excellence
David Johnston International Experience Award, University of Waterloo
President’s International Experience Award, University of Waterloo
Pure Math Department Undergraduate Research Award, University of Waterloo
President’s Research Award, University of Waterloo
Pure Math Undergraduate Research Award, University of Waterloo
Faculty of Mathematics Senate Scholarship, University of Waterloo
International Student Entrance Scholarship, University of Waterloo
President’s Scholarship of Distinction, University of Waterloo
Seminars and Workshops:
I co-organized the Kylerec Workshop on Link Spectral Invariants and Weyl Laws (2026).
I co-organized the AMS-AWM Special Session for Women and Gender Minorities in Symplectic and Contact Geometry and Topology (2026).
I am a co-organizer of Harvard Gauge Theory and Topology Seminar.
I have been co-organizing a symplectic geometry and topology workshop KYLEREC workshop (2022, 2023, 2024, and 2025).
I co-organized Graduate Student Topology and Geometry Conference 2023.
I co-organized Harvard Real Representation for Minorities in Math (support group for all underrepresented groups within the Harvard math department).
I am co-organizing the Directed Reading Program at Harvard from 2021.
I am co-organizing a weekly Zoom seminar Geometric Topology Grad and Postdoc Seminar (GT GAPS) from 2023.
In the 2021-2022, I co-organized the Trivial Notions seminar with Grant Barkley.
Mentoring:
At Rutgers University, I currently mentor one undergraduate on a senior thesis and another through an honors contract course.
I help organize the Directed Reading Program at Harvard from 2021 to 2025.
I mentored 12 undergraduate students at Harvard reading projects on algebraic topology, real analysis, complex analysis, symplectic geometry, complex geometry, knot theory, mirror symmetry and enumerative geometry.
Teaching:
In Fall 2026, I am an instructor for Math 354: Linear Optimization at Rutgers University.
In Spring 2026, I was a teaching fellow for Math 25b: Theoretical linear algebra and real analysis II.
In Fall 2025, I was a teaching fellow for Math 25a: Theoretical linear algebra and real analysis I.
In Fall 2025, I was a course assistant for Math 254z: Applications of Khovanov homology in low-dimensional topology.
In Spring 2025, I was a course assistant for Math 213b: Riemann surfaces (taught by Yum-Tong Siu).
In Fall 2024, I was a teaching fellow for Math 22a: Vector calculus and linear algebra I.
In Fall 2024, I was a course assistant for Math 230: Differential geometry (taught by Dan Freed).
In Spring 2024, I am a graduate course assistant for MATH 231BR: Advanced algebraic topology.
In Fall 2023, I was a teaching fellow for Math 22a: Vector calculus and linear algebra I.
In Fall 2023, I was a graduate course assistant for Math 262a: Quantum theory from the geometric viewpoint (taught by Dan Freed).
In Spring 2023, I was a teaching fellow for Math 22b: Vector calculus and linear algebra II.
In Spring 2023, I was a graduate course assistant for Math 113: Complex analysis.
In Summer 2022, I was teaching a tutorial on Symplectic and contact geometry.
In Spring 2022, I was a graduate Course assistant for MATH 213BR: Riemann surfaces (taught by Yum-Tong Siu).
In Fall 2022, I was a coach for Math 21a: Multivariable calculus.
Expository Writing:
Cambridge Part III essay - Dirac operators and Seiberg-Witten theory
Minor thesis - The Grothendieck-Riemann-Roch theorem