Sheel Ganatra

I am a Professor and Interim Department Chair of Mathematics at the University of Southern California, working on symplectic topology.

In 2023-2024 I was on sabbatical, supported by a Simons Fellowship. I gratefully acknowledge the support of the National Science Foundation through Awards DMS-1907635, DMS-2002137 and CAREER DMS-2048055.

More details can be found in my CV (last updated 11/2024).

Email: sheel (dot) ganatra (at) usc (dot) edu

Research

Much of my recent work concerns structural aspects of Fukaya categories and Floer theory, using methods of homological algebra and non-commutative geometry, with applications to mirror symmetry and string topology.

Papers

• S. Ganatra, M. Maydanskiy, Legendrian Surgery Formulae and P. Seidel's Conjecture, appendix to Bourgeois, Ekholm, and Eliashberg's Effect of Legendrian Surgery, Geometry & Topology 16 (2012), no. 1, 301-389. ArXiv link: arXiv:0911.0026,
• Eliashberg, S. Ganatra, O. Lazarev, Flexible Lagrangians, International Mathematics Research Notices 2020 (2020), 2408-2435. ArXiv link: arXiv:1510.01287.
• Ganatra, J. Pardon, V. Shende, Covariantly functorial wrapped Floer theory on Liouville sectors, Publications mathématiques de l’IHÉS 131 (2020), 73-200. ArXiv link: arXiv:1706.03152.
• Abouzaid, S. Ganatra, H. Iritani, N. Sheridan, The Gamma and Strominger-Yau-Zaslow conjectures: a tropical approach to periods, Geometry & Topology 24 (2020), no. 5, 2547-2602. ArXiv link: arXiv:1809.02177.
• Ganatra, D. Pomerleano, Symplectic cohomology rings of affine varieties in the topological limit, Geometric and Functional Analysis 30 (2020), no. 2, 334-456. ArXiv link: arXiv:1811.03609.
• Ganatra, D. Pomerleano, A log PSS morphism with applications to Lagrangian embeddings, Journal of Topology 14 (2021), 291-368. ArXiv link: arXiv:1611.06849.
• Ganatra, Cyclic homology, S^1-equivariant Floer cohomology, and Calabi-Yau structures, Geometry & Topology 27 (2023), no. 9, 3461-3584. ArXiv link: arXiv:1912.13510.
• Ganatra, J. Pardon, V. Shende, Sectorial descent for wrapped Fukaya categories, Journal of the American Mathematical Society 37 (2024), 499-635. ArXiv link: arXiv:1809.03427.
• Ganatra, J. Pardon, V. Shende, Microlocal Morse theory of wrapped Fukaya categories, Annals of Mathematics 199 (2024), 943-1042. ArXiv link: arXiv:1809.08807.
• Ganatra, K. Siegel, On the embedding complexity of Liouville manifolds, Journal of Differential Geometry 127 (2024), no. 3, 1019-1082. ArXiv link: arXiv:2012.04627.
• Ganatra, Symplectic cohomology and duality for the wrapped Fukaya category, preprint (2013), 166 pages, arXiv:1304.7312. My Ph.D. thesis. A slightly more up to date version is available here.
• Ganatra, T. Perutz, N. Sheridan, Mirror symmetry: from categories to curve counts, preprint (2015), 37 pages, arXiv:1510.03839.
• Ganatra, Automatically generating Fukaya categories and computing quantum cohomology, preprint (2019), 27 pages, arXiv:1605.07702.
• Ganatra, Categorical non-properness in wrapped Floer theory, preprint (2021), 19 pages, arXiv:2104.06516.
• Ganatra, Y. Gao, S. Venkatesh, Rabinowitz Fukaya categories and the categorical formal punctured neighborhood of infinity, preprint (2022), 82 pages, arXiv:2212.14863.
• Ganatra, A. Hanlon, J. Hicks, D. Pomerleano, N. Sheridan, Integrality of mirror maps and arithmetic homological mirror symmetry for Greene--Plesser mirrors, preprint (2023), 30 pages, arXiv:2312.01949.
• Ganatra, A. Hanlon, J. Hicks, D. Pomerleano, N. Sheridan, Homological mirror symmetry for Batyrev mirror pairs, preprint (2024), 86 pages, arXiv:2406.05272.

Teaching

• Math 641 (USC, Spring 2023)
• Math 229 (USC, Spring 2023)
• Math 599 (USC, Fall 2022)
• Math 535a (USC, Spring 2022)
• Math 226r (USC, Fall 2021)
• Math 641 (USC, Spring 2021)
• Math 641 (USC, Fall 2020)
• Math 125g (USC, Fall 2020)
• Math 520 (USC, Spring 2020)
• Math 535b (USC, Spring 2020)
• Math 535b (USC, Spring 2019)
• Math 535a (USC, Spring 2018)
• Math 440 (USC, Fall 2017)
• Math 535a (USC, Spring 2017)
• Math 51 (Stanford, Summer 2016)
• Math 257b (Stanford, Spring 2016)
• Math 171 (Stanford, Spring 2016)
• Math 51(Stanford, Winter 2015)
• Math 113 (Stanford, Spring 2013)
• Math 215B (Stanford, Winter 2013)
• Math 51 (Stanford, Fall 2012)

Links

• Western Hemisphere Virtual Symplectic Seminar (WHVSS)
• USC's Topology Seminar
• From Sept. 29-Oct. 2 2020, I co-organized a virtual workshop, Floer-theoretic and algebro-geometric aspects of SYZ mirror symmetry.
• In June 2019, I served as a mentor of the Kylerec 2019 (graduate student) workshop.
• In January 2016, I served on the resident scientific committee of a graduate student workshop on Lefschetz Fibrations: Rigidity and Flexibility, held in New Orleans.
• From 2009-2013, I co-organized the Talbot Workshop. In 2010 and 2011 I co-organized the MIT Geometry Workshop.
• Here are some notes from conferences and seminars, which I am currently organizing and formatting (some older notes are currently down, and will be re-posted soon). Please feel free to contact me if you have any questions or would like clarification.

Contact

Email: sheel (dot) ganatra (at) usc (dot) edu