Research Articles:
37. Canonical orientations in Heegaard Floer theory (with Mohammed Abouzaid), preprint (2025)
36. Real Heegaard Floer homology (with Gary Guth), preprint (2025)
35. Searching for ribbons with machine learning (with S. Gukov, J. Halverson and F. Ruehle), Machine Learning: Science and Technology, Vol. 6 (2025), 025065
34. A Rasmussen invariant for links in ℝP3 (with M. Willis), Transactions of the American Mathematical Society, Vol. 12 (2025), 789-830
33. Heegaard Floer homology and integer surgeries on links (with P. Ozsváth), Geometry & Topology, Vol. 29 (2025), 2783-3062
32. Grid diagrams and Heegaard Floer invariants (with P. Ozsváth and D. Thurston), Annals of Mathematics, Vol. 201 (2025), 1-78
31. Skein lasagna modules and handle decompositions (with K. Walker and P. Wedrich), Advances in Mathematics, Vol. 425 (2023), Paper No. 109071
30. A knot Floer stable homotopy type (with S. Sarkar), preprint (2021)
29. From zero surgeries to candidates for exotic definite four-manifolds (with L. Piccirillo), Journal of the London Mathematical Society, Vol. 108 (2023), 2001-2036
28. Relative genus bounds in indefinite four-manifolds (with M. Marengon and L. Piccirillo), Mathematische Annalen, Vol. 390 (2024), 1481-1506
27. Skein lasagna modules for 2-handlebodies (with I. Neithalath), Journal für die reine und angewandte Mathematik, Vol. 788 (2022), 37-76 (with Errata)
26. A generalization of Rasmussen's invariant, with applications to surfaces in some four-manifolds (with M. Marengon, S. Sarkar and M. Willis), Duke Mathematical Journal, Vol. 172 (2023), 231-311.
25. A two-variable series for knot complements (with S. Gukov), Quantum Topology, Vol. 12 (2021), 1-109
24. A sheaf-theoretic SL(2,C) Floer homology for knots (with L. Côté), Proceedings of the London Mathematical Society, Vol. 119 (2019), 1336-1387
23. The Knight Move Conjecture is false (with M. Marengon), Proceedings of the American Mathematical Society, Vol. 148 (2020), 435-439
22. A sheaf-theoretic model for SL(2,C) Floer homology (with M. Abouzaid), Journal of the European Mathematical Society, Vol. 22 (2020), 3641-3695
21. Involutive Heegaard Floer homology and plumbed three-manifolds (with I. Dai), Journal of the Institute of Mathematics of Jussieu, Vol. 18 (2019), 1115-1155
20. A connected sum formula for involutive Heegaard Floer homology (with K. Hendricks and I. Zemke), Selecta Mathematica, Vol. 24 (2018), 1183-1245
19. Floer homology and covering spaces (with T. Lidman), Geometry & Topology, Vol. 22 (2018), 2817-2838
18. Involutive Heegaard Floer homology (with K. Hendricks), Duke Mathematical Journal, Vol. 166 (2017), 1211-1299 (with Errata)
17. On the intersection forms of spin four-manifolds with boundary, Mathematische Annalen, Vol. 359 (2014), 695-728
16. A generalized asynchronous computability theorem (with E. Gafni and P. Kuznetsov), in Proceedings of the 2014 ACM Symposium on Principles of Distributed Computing (PODC '14), ACM, New York (2014), 222-231
15. Pin(2)-equivariant Seiberg-Witten Floer homology and the Triangulation Conjecture, Journal of the American Mathematical Society, Vol. 29 (2016), 147-176 (with Erratum)
14. An untwisted cube of resolutions for knot Floer homology, Quantum Topology, Vol. 5 (2014), 185-223
13. On the algebra of cornered Floer homology (with C. Douglas), Journal of Topology, Vol. 7 (2014), 1-68
12. Floer homology on the extended moduli space (with C. Woodward), in Perspectives in Analysis, Geometry and Topology, Progress in Mathematics Vol. 296, Birkhauser/Springer, New York (2012), 283-329
11. On the Khovanov and knot Floer homologies of quasi-alternating links (with P. Ozsváth), in Proceedings of the Gökova Geometry-Topology Conference 2007, Gökova (2008), 60-81
10. Combinatorial cobordism maps in hat Heegaard Floer theory (with R. Lipshitz and J. Wang), Duke Mathematical Journal, Vol. 145 (2008), 207-247
9. On combinatorial link Floer homology (with P. Ozsváth, D. Thurston and Z. Szabó), Geometry & Topology, Vol. 12 (2007), 2339-2412 (with Errata)
8. An unoriented skein exact triangle for knot Floer homology, Mathematical Research Letters, Vol. 14 (2007), 839-852 (with Erratum)
7. A combinatorial description of knot Floer homology (with P. Ozsváth and S. Sarkar), Annals of Mathematics, Vol. 169 (2009), 633-660
6. Link homology theories from symplectic geometry, Advances in Mathematics, Vol. 211 (2007), 363-416 (with Erratum)
5. A concordance invariant from the Floer homology of double branched covers (with B. Owens), International Mathematics Research Notices, Vol. 2007, doi:10.1093/imrn/rnm077
4. Nilpotent slices, Hilbert schemes, and the Jones polynomial, Duke Mathematical Journal, Vol. 132 (2006), 311-369
3. A gluing theorem for the relative Bauer-Furuta invariants, Journal of Differential Geometry, Vol. 76 (2007), 117-153 (with Errata)
2. Periodic Floer pro-spectra from the Seiberg-Witten equations (with P. Kronheimer), unpublished manuscript (2003)
1. Seiberg-Witten-Floer stable homotopy type of three-manifolds with b_1=0, Geometry & Topology, Vol. 7 (2003), 889-932 (with Errata)
Research Monographs:
2. The equivalence of two Seiberg-Witten Floer homologies (with T. Lidman), Astérisque, Vol. 399 (2018)
1. Cornered Heegaard Floer homology (with C. Douglas and R. Lipshitz), Memoirs of the American Mathematical Society, Vol. 262 (2019), no. 1266
Expository Articles:
11. From knots to four-manifolds, in Proceedings of the International Congress of Mathematicians, Philadelphia (2026)
10. New knot invariants from BPS states (with S. Gukov), in Proceedings of the 2025 ICBS, to appear
9. Triangulations and Floer homology, in Proceedings of the 2024 ICBS, to appear
8. Four-dimensional topology, in Literature and History of Mathematical Science, CMSA Series in Mathematics, Vol. 3 (2024), 415-438
7. Homology cobordism and triangulations, in Proceedings of the International Congress of Mathematicians, Rio de Janeiro (2018), Vol. 2, 1175-1192
6. Lectures on the triangulation conjecture, in Proceedings of the Gökova Geometry / Topology Conference 2015, Gökova (2016), 1-38
5. Floer theory and its topological applications, Japanese Journal of Mathematics, Vol. 10 (2015), 105-133
4. Triangulations of manifolds, Notices of the International Congress of Chinese Mathematicians, Vol. 2 (2014), no.2, 21-23
3. An introduction to knot Floer homology, in Physics and mathematics of link homology, Contemp. Math., Vol. 680, AMS (2016), 99-135 (with Errata)
2. The Conley index, gauge theory, and triangulations, Journal of Fixed Point Theory and Applications, Vol. 13 (2013), 431-457
1. Grid diagrams in Heegaard Floer theory, in European Congress of Mathematics, Krakow, 2-7 July, 2012, European Mathematical Society (2013), 643-657
Contributions:
3. K3: A New Problem List in Low-Dimensional Topology (edited by Inanc Baykur, Daniel Ruberman, Robion Kirby), to be published by the American Mathematical Society. I proposed and scribed some problems, and acted as associate editor for Chapter 4
2. Humanity's Last Exam (by Long Phan et al.); published as A benchmark of expert-level academic questions to assess AI capabilities (by Center for AI Safety, Scale AI & HLE Contributors Consortium), Nature, Vol. 649 (2026), 1139-1146. I contributed a problem in low-dimensional topology
1. Quantum Field Theory and Manifold Invariants, IAS/Park City Mathematics Series, Vol. 28, 2021 (book co-edited with Dan Freed, Sergei Gukov, Constantin Teleman, and Ulrike Tillman). It includes an introduction to topological quantum field theories.
Textbook:
1. An Introduction to Topology and Geometry, to be published by Princeton University Press