Robert Lipshitz

Robert Lipshitz is a Professor of Mathematics at the University of Oregon, specializing in low-dimensional topology and symplectic geometry. He is currently on leave for the 2025-2026 academic year to serve as the Minerva Visitor in the Mathematics Department at Princeton University, where he will deliver a series of lectures on recent techniques in low-dimensional topology. His research has significantly advanced the fields of Heegaard Floer homology and Khovanov homology, with numerous publications in top mathematics journals.

Dr. Lipshitz's research primarily focuses on developing and applying bordered Heegaard Floer homology and Khovanov homology to solve problems in low-dimensional topology. His work bridges geometric topology with algebraic structures, providing powerful new invariants for studying 3- and 4-dimensional manifolds. He has made significant contributions to understanding connections between different homology theories and their applications to classical problems in knot theory and 4-dimensional topology, often combining deep geometric insights with sophisticated algebraic techniques.

Dr. Lipshitz's recent publications demonstrate a consistent focus on refining and extending homological invariants in low-dimensional topology, particularly through the development of bordered techniques and stable homotopy refinements. His work shows increasing sophistication in connecting different branches of topology, with recent papers exploring applications to contact geometry, equivariant settings, and the detection of topological properties through algebraic invariants.

Dr. Lipshitz has received numerous prestigious awards and fellowships supporting his research:

• NSF Graduate Research Fellowship
• NSF Mathematical Sciences Postdoctoral Research Fellowship
• Sloan Research Fellowship
• Simons Foundation Fellowship in Mathematics
• Multiple NSF research grants (DMS-0905796 through DMS-2505715)

Dr. Lipshitz actively contributes to the mathematical community through editorial work as an editor for Quantum Topology and managing editor for Geometry & Topology. He serves as editor for chapter 3 of the K3 List, continuing Kirby's problem lists in low-dimensional topology. He has mentored numerous students, though specific names aren't listed on his website, and has developed computational tools including documentation for bfh_python, which implements algorithms for computing Heegaard Floer homology.

Dr. Lipshitz is deeply involved in the topology community, frequently organizing the University of Oregon topology seminar. He has created educational resources on using Blender for mathematical illustrations and is developing tools for the mathematical community, including tutorials on creating line drawings for mathematics papers using 3D graphics software. He is also planning a conference at Princeton in Summer 2027 honoring Peter Ozsváth's 60th birthday.