Shaoyun Bai

Photo by Fanying Chen

I am a Ritt Assistant Professor at Columbia University. My research focuses on symplectic topology, though my research projects are related to or inspired by nearby fields, including low-dimensional topology, algebraic geometry, algebraic topology, and dynamics. Here is my CV.

I spent Spring 2023 at the Simons Center for Geometry and Physics as a short-term visitor. Prior to that, I was a postdoctoral member of the MSRI program "Floer Homotopy Theory" in Fall 2022, mentored by Mohammed Abouzaid. There is a short biography of me on Page 15 of MSRI's Emissary Newsletter. Before that, I received my Ph.D. from Princeton University in Spring 2022 under the supervision of John Pardon.

This website will be under a Columbia URL soon, and I gratefully acknowledge Princeton's math department to allow me to use the current URL until today!

Email: sb4841 [at] columbia [dot] edu

Papers

• Hofer-Zehnder conjecture for toric manifolds (With Guangbo Xu), arXiv:2309.07991.
• Arnold conjecture over integers (With Guangbo Xu), arXiv:2209.08599.
• An integral Euler cycle in normally complex orbifolds and Z-valued Gromov-Witten type invariants (With Guangbo Xu), arXiv:2201.02688.
• On the Rouquier dimension of wrapped Fukaya categories and a conjecture of Orlov (With Laurent Côté), Compos. Math. 159 (2023), no. 3, 437--487. Published Version.
• Bifurcations of embedded curves and towards an extension of Taubes' Gromov invariant to Calabi-Yau 3-folds (With Mohan Swaminathan), arXiv:2106.01206.
• A symplectic formula for generalized Casson invariants, arXiv:2102.03665.
• Equivariant Cerf theory and perturbative SU(n) Casson invariants (With Boyu Zhang), arXiv:2009.01118.

Slides and Videos from Previous Talks

• Floer Homotopical Methods in Low Dimensional and Symplectic Topology, MSRI, November 2022, video.
• Floer Homotopy Theory Program Formal Seminar, MSRI, September 2022, video.
• Real and Complex Geometry Seminar, Tel Aviv, April 2022, slides.
• Recent developments in Lagrangian Floer theory, SCGP, March 2022, video.
• Symplectic Geometry Seminar, Stanford University, November 2021, slides.
• Western Hemisphere Virtual Symplectic Seminar, September 2021, slides, video.
• Sympletic Zoominar (CRM-Montréal, Princeton/IAS, Tel Aviv and Paris), March 2021, slides, video.
• Topology Seminar, Stanford University, November 2020, slides.

Public Service

I am co-organizing Columbia Symplectic Geometry and Gauge Theory Seminar.

I am maintaining the AIM problem list on Floer theory of symmetric products and Hilbert schemes.