Wenyuan Li

李文远

I am a (postdoctoral) Assistant Professor (RTPC) in Mathematics at University of Southern California starting from Fall 2023, working with Professor Harold Williams. 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: wenyuan.li at usc.edu

Office: KAP 424A, USC.

Research

My research interest is symplectic/contact topology. It originates from the study of 'phase spaces' in classical mechanics, where one considers the space encoding both the location and the momentum of the particles. The word 'symplectic' is borrowed from ancient Greek which means 'complex' (I learned this from Professor Ivan Smith's ICM talk).

More specifically, my research interest is in symplectic/contact invariants coming from microlocal sheaf theory, especially invariants of Legendrian and Lagrangian submanifolds and its relation to invariants coming from pseudo-holomorphic curves or generating families. I am also trying to understand their connections between symplectic geometry and cluster algebras, mirror symmetry, noncommutative geometry and persistence modules.

I am interested in the flexibility side of symplectic/contact topology (in higher dimensions) involving h-principles as well.

Papers and Preprints

• 7. Lagrangian cobordism and shadow distance in Tamarkin category, joint with Tomohiro Asano and Yuichi Ike, arXiv:2312.14429.
• 6. Existence of generating families on Lagrangian cobordisms, arXiv:2308.05727.
• 5. Lagrangian cobordism functor in microlocal sheaf theory II, arXiv:2308.05089.
• 4. Duality and spherical adjunction from microlocalization, joint with Christopher Kuo, arXiv:2210.06643.
• 3. Conjugate fillings and Legendrian weaves, joint with Roger Casals, arXiv:2210.02039.
• 2. Lagrangian cobordism functor in microlocal sheaf theory I, Journal of Topology 16.3 (2023): 1113-1166, arXiv:2108.10914.
• 1. Estimating Reeb chords using microlocal sheaf theory, arXiv:2106.04079.

Research Notes

• 1. Functoriality of sheaf categories over Weinstein manifolds, pdf. The mathematical content is essentially extracted from Lagrangian cobordism functor in microlocal sheaf theory Section 3.2.

Notes

• 2. h-principle in symplectic geometry
• 1. Sheaf theory in symplectic geometry

Slides

• 6. Incheon National University 15th International Symposium on National Sciences - Generating families on Lagrangian cobordisms
• 5. Peking University Algebra & Geometry Mini Forum - Duality and spherical adjunction from microlocalization
• 4. Tianjin University 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 126g, Calculus II, Spring 2023, USC
• MATH 126g, Calculus II, Fall 2023, USC
• GRE Sub preparation, Causeway Postbaccalaureate Certificate Program, Summer 2022, Northwestern

Teaching Assistant

• MATH 300-BR, Foundations of Higher Mathematics, 2022, Northwestern
• MATH 290-1--3, Linear Algebra and Multi Variable Calculus, 2020--2021, Northwestern
• MATH 330-1--3, Abstract Algebra, 2020--2021, Northwestern
• MATH 220-1, Single Variable Calculus, 2019, Northwestern
• MATH 230-1, Multi Variable Calculus, 2020, Northwestern

External links

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