https://pages.uoregon.edu/lipshitz/research/index.html I work on topology, the large-scale study of shapes. If you are not a mathematician, these pages are unlikely to have much meaning to you, but others have written many nice introductions to topology, including: Colin C. Adams, The Knot Book George K. Francis, A Topological Picture Book Jeffrey R. Weeks, The Shape of Space Overview I work on low-dimensional topology, using tools from partial differential equations (J-holomorphic curves), homological algebra (Khovanov homology), and homotopy theory. Much of my work is focused on developing these tools rather than applying them to specific questions in low-dimensional topology. Most of my work can be divided into a few themes: Hugo en-us https://pages.uoregon.edu/lipshitz/research/papers/index.html Mon, 01 Jan 0001 00:00:00 +0000 https://pages.uoregon.edu/lipshitz/research/papers/index.html Preprints “Bordered HF- for three-manifolds with torus boundary” with Peter Ozsváth and Dylan Thurston. arXiv:2305.07754. Last updated September 13, 2023. “Bordered Floer homology, handlebody detection, and compressing diffeomorphisms” with Akram Alishahi. arXiv:2408.06619. Last updated January 13, 2025. “Detecting Heegaard Floer homology solid tori” with Akram Alishahi and Tye Lidman. arXiv:2505.01217. Last updated May 2, 2025. “Real bordered Floer homology” with Peter Ozsváth. arXiv:2604.20565. Last updated April 22, 2026. 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. https://pages.uoregon.edu/lipshitz/research/code/index.html Mon, 01 Jan 0001 00:00:00 +0000 https://pages.uoregon.edu/lipshitz/research/code/index.html Bordered Heegaard Floer homology bfh_python In a sequence of papers, Peter Ozsváth, Dylan Thurston, and I gave an algorithm for computing the Heegaard Floer invariant HF-hat of a closed 3-manifold and the Ozsváth-Szabó spectral sequence associated to a link in the 3-sphere. We also gave a computer implementation of the algorithm for computing HF-hat. In his thesis, Bohua Zhan improved the algorithm, using a notion of “local DA bimodules”. He also re-implemented the original and improved algorithms, and extended the implementation to comptue the Ozsváth-Szabó spectral sequence. https://pages.uoregon.edu/lipshitz/research/talks/index.html Mon, 01 Jan 0001 00:00:00 +0000 https://pages.uoregon.edu/lipshitz/research/talks/index.html Talks AY 2025-2026 None currently scheduled, but here is a tentative plan for talks as the Minerva Visitor at Princeton in Fall 2025. Talks AY 2024-2025 Towards a Legendrian contact stable homotopy type September 12, 2024 in the Princeton Topology Seminar.