About

• Hi, I graduated from Michigan State University in 2021, where I was working under Matthew Hedden.
• I was a postdoctoral researcher at the Max Planck Institute for Mathematics, Bonn for the 2021-22 academic year.
• In Fall-2022, I was at MSRI, Berkeley, as a Postdoctoral Fellow for the Floer Homotopy Theory program
• From Spring-2023 to Spring 2025, I will be in Rutgers University as a Hill assistant professor, working with Kristen Hendricks
• Here is an article in the Quanta Magazine on a paper that I co-authored.
• Here is my CV.
• In summer 2023, I supervised a DIMACS REU (with Hendricks). Here is an article that my students Jay Patwardhan (Rutgers), Zheheng Xiao (Columbia) wrote.
• I am teaching a graduate topics course at Rutgers titled 'Floer homology and low-dimensional topology' in Spring 2024.
• I am co-organizing a special session at the JMM, 2025, 'Concordance and Cobordism in Low Dimensions' with Maggie Miller and Ryan Stees. Together with other members of the g&t group in Rutgers, I am co-organizing the 'Rutgers Geometry and Topology Seminar'.

Research

1. Corks, involutions and Heegaard Floer homology (with Irving Dai and Matthew Hedden), Journal of the European Mathematical Society, 25(6) (2023), 2319-2389.
2. Equivariant knots and knot Floer homology (with Irving Dai and Matthew Stoffregen) Journal of Topology, 16(3) (2023), 1167-1236.
3. Knot Floer homology and surgery on equivariant knots to appear in the Journal of Topology.
4. The (2,1)-cable of the figure-eight knot is not smoothly slice (with Irving Dai, Sungkyung Kang, JungHwan Park, and Matthew Stoffregen) to appear in the Inventiones Mathematicae.
5. Rank-expanding satellites, Whitehead doubles, and Heegaard Floer homology (with Irving Dai, Matthew Hedden, and Matthew Stoffregen) to appear in the Journal of Topology.
6. From diffeomorphisms to exotic phenomena in small 4-manifolds (with Hokuto Konno, and Masaki Taniguchi).
7. Exotic Dehn twists on 4-manifolds (with Hokuto Konno, and Masaki Taniguchi).
8. Involutions and the Chern-Simons filtration in instanton Floer homology (with Antonio Alfieri, Irving Dai, and Masaki Taniguchi).
9. Gompf's cork and Heegaard Floer homology (with Irving Dai, and Ian Zemke), International Mathematics Research Notices, 2024, 18, 12663-12682.
10. On localizing groups of exotic diffeomorphisms of 4-manifolds (with Hokuto Konno).
11. A note on cables and the involutive concordance invariants (with Kristen Hendricks).
12. Exotically knotted closed surfaces from Donaldson's diagonalization for families (with Hokuto Konno, and Masaki Taniguchi).

Contact

Email: abhishek.mallick@rutgers.edu