Sheel Ganatra

e-mail: sheel (dot) ganatra (at) usc \\dot\\ edu

I am an Associate Professor at the University of Southern California working on symplectic topology. 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.

In 2023-2024 I am on sabbatical, supported by a Simons Fellowship. I also 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 12/2023).

Papers

S. Ganatra, M. Maydanskiy, Legendrian Surgery Formulae and P. Seidel's Conjecture, appendix to Bourgeois, Ekholm, and Eliashberg's Effect of Legendrian Surgery, Geom. Topol. 16 (2012), no. 1, 301-389. ArXiv link: arXiv:0911.0026,

Y. Eliashberg, S. Ganatra, O. Lazarev, Flexible Lagrangians, Int. Math. Res. Not. 2020 (2020), 2408-2435. ArXiv link: arXiv:1510.01287.

S. Ganatra, J. Pardon, V. Shende, Covariantly functorial wrapped Floer theory on Liouville sectors, Publ. Math. IHES 131 (2020), 73-200. ArXiv link: arXiv:1706.03152.

M. Abouzaid, S. Ganatra, H. Iritani, N. Sheridan, The Gamma and Strominger-Yau-Zaslow conjectures: a tropical approach to periods, Geom. Topol. 24 (2020), no. 5, 2547-2602. ArXiv link: arXiv:1809.02177.

S. Ganatra, D. Pomerleano, Symplectic cohomology rings of affine varieties in the topological limit, GAFA 30 (2020), no. 2, 334-456. ArXiv link: arXiv:1811.03609.

S. Ganatra, D. Pomerleano, A log PSS morphism with applications to Lagrangian embeddings, J. Topol. 14 (2021), 291-368. ArXiv link: arXiv:1611.06849.

S. Ganatra, Cyclic homology, S^1-equivariant Floer cohomology, and Calabi-Yau structures, Geom. Topol. 27 (2023), no. 9, 3461--3584. ArXiv link: arXiv:1912.13510.

S. Ganatra, K. Siegel, On the embedding complexity of Liouville manifolds, to appear in J. Differ. Geom. (2021), 52 pages, arXiv:2012.04627.

S. Ganatra, J. Pardon, V. Shende, Sectorial descent for wrapped Fukaya categories, to appear in J. Amer. Math. Soc. (2023), 145 pages, arXiv:1809.03427.

S. Ganatra, J. Pardon, V. Shende, Microlocal Morse theory of wrapped Fukaya categories, to appear in Ann. of Math. (2023), 87 pages, arXiv:1809.08807.

S. 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.

S. Ganatra, T. Perutz, N. Sheridan, Mirror symmetry: from categories to curve counts, preprint (2015), 37 pages, arXiv:1510.03839.

S. Ganatra, Automatically generating Fukaya categories and computing quantum cohomology, preprint (2019), 27 pages, arXiv:1605.07702.

S. Ganatra, Categorical non-properness in wrapped Floer theory, preprint (2021), 19 pages, arXiv:2104.06516.

S. Ganatra, Y. Gao, S. Venkatesh, Rabinowitz Fukaya categories and the categorical formal punctured neighborhood of infinity, preprint (2022), 82 pages, arXiv:2212.14863.

S. 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.

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)

Other Links

• I co-organize the 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.