Wenyuan Li

李文远

I am a (postdoctoral) Assistant Professor (RTPC) in Mathematics at University of Southern California. Here is my CV.

I obtained my PhD degree at Northwestern University in Spring 2023 under the supervision of Professor Emmy Murphy and Professor Eric Zaslow. I obtained my Bachelor's degree at Peking University in China.

Email: wenyuanli1995.math at outlook.com or wenyuanli2023 at u.northwestern.edu (My USC Email will no longer be in use starting from the middle of May.)

Office: KAP 424A, USC.

Research

My research interest is symplectic and contact topology. Roughly speaking, symplectic geometry is the geometry of generalized phase spaces in Hamiltonian mechanics, encoding both the position and the momentum of the objects. The word 'symplectic' is made up by H. Weyl by translating 'complex' into Greek.

More specifically, my research interest is in algebraic and categorical invariants in symplectic and contact topology coming from microlocal sheaf theory, pseudo-holomorphic curves and generating families, with their connections to cluster algebras, mirror symmetry, noncommutative geometry, algebraic K-theory and persistence modules. I am also interested in the flexibility side of symplectic and contact topology involving h-principles.

Papers and Preprints

• 14. S^1-action on the Hochschild homology of the Tamarkin category, joint with Bingyu Zhang, in preparation.
• 13. Microsheaf composition of Lagrangian correspondences, joint with David Nadler and Vivek Shende, 105pp, arXiv.
• 12. C^0-rigidity of Legendrians and coisotropics via sheaf quantization, joint with Tomohiro Asano, Yuichi Ike and Christopher Kuo, 45pp, arXiv.
• 11. Decompositions of augmentation varieties via weaves and rulings, joint with Johan Asplund, Orsola Capovilla-Searle, James Hughes, Caitlin Leverson and Angela Wu, 88pp, arXiv.
• 10. Positive microlocal holonomies are globally regular, joint with Roger Casals, 34pp, Comm. Amer. Math Soc. 6 (2026), 492-535, journal, arXiv.
• 9. Relative Calabi-Yau structure on microlocalization, joint with Christopher Kuo, 50pp, arXiv.
• 8. Duality and kernels in microlocal geometry, joint with Christopher Kuo, Int. Math. Res. Not. 2025, no.6, 1-34, journal, arXiv.
• 7. Lagrangian cobordism and shadow distance in Tamarkin category, joint with Tomohiro Asano and Yuichi Ike, Sel. Math. New Ser. 31, 45 (2025), journal, arXiv.
• 6. Existence of generating families on Lagrangian cobordisms, Math. Ann. 390, (2024): 5471–5494, journal, arXiv.
• 5. Lagrangian cobordism functor in microlocal sheaf theory II, J. Sympl. Geom. 23 no.3 (2025): 599-672, journal, arXiv.
• 4. Spherical adjunction and Serre functor from microlocalization, joint with Christopher Kuo, 62pp, arXiv.
• 3. Conjugate fillings and Legendrian weaves, joint with Roger Casals, 100pp, arXiv.
• 2. Lagrangian cobordism functor in microlocal sheaf theory I, J. Topol. 16.3 (2023): 1113-1166, journal, arXiv.
• 1. Estimating Reeb chords using microlocal sheaf theory, 39pp, to appear in Algebr. Geom. Topol., journal, arXiv.

Research Notes

• 2. Sheaf quantization of geometrically bounded exact Lagrangians, pdf. The mathematical content is essentially extracted from Lagrangian cobordism functor in microlocal sheaf theory II Section 3.3 and my thesis Some functoriality results for microlocal sheaves over Legendrians and Lagrangians Section 4.2-4.3.
• 1. Functoriality of sheaf categories over Weinstein manifolds, pdf. The mathematical content is essentially extracted from Lagrangian cobordism functor in microlocal sheaf theory I Section 3.2.

Notes

• 2. h-principle in symplectic geometry
• 1. Sheaf theory in symplectic geometry (This note needs to be updated.)

Slides

• 8. BIRS Workshop - Regular functions on the moduli of Lagrangian fillings
• 7. AMS Fall 2024 Western Sectional Meeting - Relative Calabi-Yau structure on microlocal sheaves
• 6. INU 15th International Symposium on National Sciences - Generating families on Lagrangian cobordisms
• 5. PKU Algebra & Geometry Mini Forum - Duality and spherical adjunction from microlocalization
• 4. TJU Geometry & Topology Seminar - Conjugate fillings and Legendrian weaves
• 3. Uppsala Symplectic Geometry Seminar - Lagrangian cobordism functor in sheaf theory
• 2. Symplectic Zoominar - Estimating Reeb chords using microlocal sheaf theory
• 1. Kylerec Student Seminar - An introduction to loose Legendrian submanifolds

Teaching

Instructor

• MATH 425a, Foundational Concepts of Modern Analysis, Spring 2026, USC, Syllabus, Lecture notes
• MATH 225, Linear Algebra and Differential Equations, Fall 2025, USC
• MATH 535a, Differential Topology, Spring 2025, USC, Syllabus, Lecture notes
• MATH 225, Linear Algebra and Differential Equations, Fall 2024, USC
• MATH 126g, Calculus II, Spring 2023, USC
• MATH 126g, Calculus II, Fall 2023, USC
• GRE Sub preparation, Causeway Postbaccalaureate Certificate Program, Summer 2022, Northwestern

External links

• USC Math Department
• USC Geometry & Topology Seminar
• Joint Los Angeles Topology Seminar
• Caltech/USC Algebra & Geometry Seminar
• Northwestern Math Department