Xinle (Clair) Dai 戴欣玏
Xinle (Clair) Dai 戴欣玏
Email: xdai@math.harvard.edu
Address: Science Center 421g, 1 Oxford St, Cambridge, MA 02138
I am a PhD student in the Department of Mathematics at Harvard University, where I am fortunate to be advised by Denis Auroux and Peter Kronheimer. My main research interests are symplectic geometry, mirror symmetry, and low-dimensional topology.
I am on the job market this fall and expect to graduate in May 2026!
I spent the Fall 2022 semester at University of California, Berkeley, hosted by Michael Hutchings and I was a visiting scholar at Peking University, Beijing International Center for Mathematical Research from 2020-2021, hosted by Yi Xie.
Before that, I spent one year in the UK, sponsored by a Cambridge Trust scholarship, completing master's degree at Cambridge University. I graduated from the University of Waterloo in 2019.
Here is a list of my publications and preprints:
Homological Mirror Symmetry of Symmetric Products of Surfaces (in preparation)
Sectorial decomposition of symmetric product of surfaces (draft available upon request)
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
Talks given:
University of Minnesota Symplectic Geometry Seminar, 2026
Stanford Symplectic Seminar, Stanford University, November 2025
PU/IAS Symplectic Seminar, Princeton University, September 2025
Rutgers Symplectic Summer School, Rutgers University, August 2025
AMS Spring Western Sectional Meeting, California State University, May 2025
UMass Geometry and Topology Seminar, May 2025
Simons Collaboration on New Structures in Low-Dimensional Topology Annual Meeting (poster session), March 2025
AMS Spring Southeastern Sectional Meeting, Clemson University, March 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, December 2024
University of Angers Student Seminar, December 2024
Tech Topology Conference, December 2024
Columbia Geometric Topology Seminar, November 2024
Harvard Gauge Theory Seminar, November 2024
New England Algebraic Topology and Mathematical Physics Seminar, November 2024
Boston University Geometry and Physics Seminar, October 2024
Boston College Algebraic Geometry Seminar, September 2024
Conference on New Structures in Low-Dimensional Topology, Budapest, July 2024
Stony Brook Symplectic Geometry Seminar, April 2024
MIT Symplectic Geometry Seminar, April 2024
Jane Street Graduate Research Fellowship Workshop (poster session), April 2024
Mid-Atlantic Topology Conference, Northeastern University (poster session), April 2024
AMS–AWM Special Session: Women and Gender Minorities in Symplectic and Contact Geometry at Joint Mathematics Meetings, January 2024
MIT Juvitop Seminar, March 2023
Geometric Topology Graduate and Postdoc Seminar, January 2023
MSRI Gauge Theory Graduate Seminar, December 2022
MIT Reading Seminar on Ganatra-Pardon-Shende I and II, April 2022
Seminars and Workshops:
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:
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 Spring 2025, I will be a teaching fellow for Math 25b: Theoretical linear algebra and real analysis II.
In Fall 2025, I am a teaching fellow for Math 25a: Theoretical linear algebra and real analysis I.
In Fall 2025, I am 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