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Photo by Dashen Yan, 2024.
About
About
My name is Shuhao Li. I'm a fifth-year Ph.D. student in math at Stony Brook. My advisor is Mark McLean.
Email: [My first name].[My last name]@stonybrook.edu
Office: Math Tower 2-106
Research Interest
Research Interest
I am interested in the area of symplectic geometry and particularly its interaction with geometric and algebraic topology. I have been using tools from homotopy algebra, applied to algebraic structures from Gromov-Witten theory, Floer theory, and string topology, to study foundational problems in symplectic geometry like the topology of Lagrangians in Euclidean spaces. I am also broadly interested in topics in geometric topology, e.g. cobordism theory, surgery theory, perturbative Chern-Simons theory, and more generally invariants from topological quantum field theories.
Papers
Papers
Open-closed string topology and Maslov-Zero Lagrangian Embeddings. In preparation.
Organizations and services
Organizations and services
Symplectic Geometry, Gauge Theory, and Low-Dimensional Topology Seminar (Fall 2025): co-organizer
Student Symplectic Seminar (Fall 2024): Symplectic topology of cotangent bundles (co-organized with Frank Zheng)
Student Symplectic Seminar (Fall 2022): Weinstein domains and their symplectic invariants (co-organized with Sam Auyeung).
I have been participating in the Stony Brook Directed Reading Program, and have supervised 4 students across several semesters, on topics ranging from general relativity and game theory to surgery theory on exotic spheres.
Notes from expository talks
Notes from expository talks
Spectra, unoriented bordism, and the Steenrod problem. Student symplectic seminar (Spring 2025)
Introduction to the nearby Lagrangian conjecture. Student symplectic seminar (Fall 2024)
Cohomology of Grassmannians without Schubert Calculus. Topology Student Seminar (Fall 2022)
An introduction to Weinstein manifolds. Student symplectic seminar (Fall 2022)
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