I am interested in low dimensional topology, knot theory and contact and symplectic geometry.
My research is partly supported by a topology NSF grant DMS-1811210 and NSF CAREER grant DMS-2238103.
With Robert Lipshitz, Bordered Floer homology, handlebody detection, and compressing diffeomorphisms, in prepration.
With Eugene Gorsky and Beibei Liu, Splitting maps in link Floer homology and integer points in permutahedra, ArXiv:2307.07741.
With Linh Truong and Melissa Zhang, Khovanov homology and the Involutive Heegaard Floer homology of branched double covers. ArXiv:2305.07172.
With Joan Licata, Ina Petkova and Vera Vértesi, A friendly introduction to the bordered contact invariant, The Open Book Series 5 (1), 1-30, 2022. (Published version)(ArXiv:2104.07616).
With Viktória Földvári, Kristen Hendricks, Joan Licata, Ina Petkova and Vera Vértesi, Bordered Floer homology and contact structures, Forum of Mathematics: Sigma, 11, E30. doi:10.1017/fms.2023.19. (Published version)(ArXiv:2011.08672).
With Nathan Dowlin, Relating tangle invariants for Khovanov homology and knot Floer homology, (ArXiv:1909.03865).
With Nathan Dowlin, A link invariant related to Khovanov homology and knot Floer homology, (ArXiv:1810.13406).
With Eaman Eftekhary, Knot Floer homology and the Unknotting number, Geometry&Topology 24 (5) 2435 - 2469, 2020 (Published version)(ArXiv:1810.05125)
With Eaman Eftekhary, Tangle Floer homology and cobordisms between tangles, Journal of Topology, 13: 1582-1657, 2020. (Published version) (ArXiv:1610.07122)
Akram Alishahi, Unknotting number and Khovanov homology, Pacific Journal of Mathematics, 301 (1), 15–29, 2019. (Published version)(ArXiv:1710.07874).
With Nathan Dowlin, The Lee Spectral Sequence, Unknotting Number, and the Knight Move Conjecture, Topology and its Applications, 254: 29-38, 2019.(Published version)(ArXiv:1710.07875).
With Robert Lipshitz, Bordered Floer homology and incompressible surfaces, Annales De L'Institut Fourier, Grenoble 69(4): 1525-1573, 2019. (Published Version) (ArXiv:1708.05121)
With Eaman Eftekhary, A refinement of sutured Floer homology, Journal of Symplectic Geometry, 13 (3): 609-743, 2015. (Published Version)(ArXiv:1112.3540)
With Eaman Eftekhary, On the construction of sutured Floer complex, Proceeding of 20th Gokova Geometry-Topology conference: 97–109. (Published Version)