Robert Lipshitz

Papers

Preprints

  • "Diagonals and A-infinity Tensor Products" with Peter Ozsváth and Dylan Thurston. arXiv:2009.05222. Last updated September 20, 2021.
  • "Homotopy functoriality for Khovanov spectra" with Tyler Lawson and Sucharit Sarkar. arXiv:2104.12907. Last updated September 2, 2021.
  • "A bordered HF- algebra for the torus" with Peter Ozsváth and Dylan Thurston. arXiv:2108.12488. Last updated August 27, 2021.
  • "A mixed invariant of non-orientable surfaces in equivariant Khovanov homology" with Sucharit Sarkar. arXiv:2109.09018. Last updated October 1, 2021.
  • "Categorical lifting of the Jones polynomial: a survey" with Mikhail Khovanov. arXiv:2202.02473. Last updated March 21, 2022.
  • "Khovanov homology of strongly invertible knots and their quotients" with Sucharit Sarkar. arXiv:2203.13895. Last updated March 25, 2022.

Accepted or published

Roughly, my work so far falls into four categories: bordered Heegaard Floer homology, an extension of Heegaard Floer homology to 3-manifolds with boundary; equivariant Lagrangian intersection Floer homology and its applications to Heegaard Floer homology and symplectic Khovanov homology; other topics in Heegaard Floer homology; and Khovanov homology and its stable homotopy refinement. (There is some overlap.) Papers in each category are in approximately the order they were written. A link to each paper on the arXiv and its review on MathSciNet is at the end of each entry. I have not read any of these reviews.

Bordered Heegaard Floer homology

Expository

"A faithful linear-categorical action of the mapping class group of a surface with boundary," above, is also partly expository.

Equivariant Floer homology

See also "Noncommutative Hodge-to-de Rham spectral sequence and the Heegaard Floer homology of double covers", above.

Other topics in Heegaard Floer homology

Expository

Khovanov homology and homotopy

Expository

Funding

My research has been supported by a National Science Foundation (NSF) Graduate Research Fellowship, an NSF Mathematical Sciences Postdoctoral Research Fellowship, a Sloan Research Fellowship, and NSF Grants DMS-0905796, DMS-1149800, DMS-1560783, DMS-1642067, and DMS-1810893. The support specific to each paper is listed in that paper.

Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.