Johan Asplund
Department of Mathematics
Stony Brook University
100 Nicolls Road
Stony Brook, NY 11794, USA
firstname.lastname[at]stonybrook.edu
CV
I am a James H. Simons Instructor at Stony Brook University. Previously I was a Postdoctoral Research Fellow at Columbia University mentored by Mohammed Abouzaid, funded by Knut and Alice Wallenberg Foundation.
I received my PhD in Mathematics from Uppsala University in 2021 under supervision of Tobias Ekholm.
Research
I am working in the fields of symplectic and contact geometry. My work is focused on Floer theory and symplectic field theory, and I am also interested in interactions and applications to neighboring fields such as string topology and low-dimensional topology.
Photo by Gustav Hammarhjelm 2021.
Papers and preprints
- Homotopy rigidity of nearby Lagrangian cocores. In preparation.
with Y. Deshmukh and A. Pieloch.
[video] - Decompositions of augmentation varieties via weaves and rulings. In preparation.
with O. Capovilla-Searle, J. Hughes, C. Leverson, W. Li, and A. Wu.
- Persistence of unknottedness of clean Lagrangian intersections. Preprint, 2025.
with Y. Li.
[arXiv:2501.09110] - Spectral equivalence of nearby Lagrangians. Preprint, 2024.
with Y. Deshmukh and A. Pieloch.
[arXiv:2411.08841] - Singular Legendrian unknot links and relative Ginzburg algebras. To appear in Algebr. Geom. Topol., 2025.
[arXiv:2311.03330] [slides] - Lagrangian cobordism of positroid links. Pacific J. Math., 332(1):1–21, 2024.
with Y. Bae, O. Capovilla-Searle, M. Castronovo, C. Leverson, and A. Wu.
[arXiv:2305.16232] [journal] [code] - Tangle contact homology. Internat. J. Math., 35(12):Paper No 2450044, 59, 2024.
[arXiv:2210.03036] [journal] - Simplicial descent for Chekanov–Eliashberg dg-algebras. J. Topol., 16(2):489–541, 2023.
[arXiv:2112.01915] [journal] [slides] [video] - Chekanov–Eliashberg dg-algebras for singular Legendrians. J. Symplectic Geom., 20(3):509–559, 2022.
with T. Ekholm.
[arXiv:2102.04858] [journal] [slides1] [slides2] [video] - Fiber Floer cohomology and conormal stops. J. Symplectic Geom, 19(4):777–864, 2021.
[arXiv:1912.02547] [journal] [slides1] [slides2]
Theses
- Chekanov–Eliashberg dg-algebras and partially wrapped Floer cohomology. PhD thesis, Uppsala University, 2021.
[link] [slides] - Contact homology of Legendrian knots in five-dimensional circle bundles. Master's thesis, Uppsala University, 2016.
[link] - Linking and Morse theory. Bachelor's thesis, Uppsala University, 2014.
[link]
Teaching
Fall 2025
- MAT 203 Calculus III with Applications
Previous courses
- MAT 310 Linear Algebra (Spring 2025, SBU)
- MAT 127 Calculus C (Fall 2024, SBU)
- MAT 127 Calculus C (Spring 2024, SBU)
- MAT 322/523 Analysis in Several Dimensions (Spring 2024, SBU)
Notes
- List of open problems in Floer homotopy theory
Notes taken by N. Porcelli from a discussion session during the conference Homotopy Theory and Floer homology in June 2025. - Introduction to Floer homotopy theory
Expanded notes for a mini-course given at Stony Brook University in Oct–Nov 2024.
Organization
- Symplectic Geometry, Gauge Theory, and Low-Dimensional Topology Seminar (Spring 2024–)
- Columbia Symplectic geometry and gauge theory seminar (Fall 2022–Fall 2023)
(previously the Columbia Symplectic geometry, gauge theory and categorification seminar) - Microlocal theory of sheaves in symplectic geometry (Fall 2022)