Jun Zhang

Guest Assistant Professor

Education

Ph.D. in Pure Mathematics - The University of Georgia, 2016
M.A., in Pure Mathematics - The University of Georgia, 2012
B.S. in Pure Mathematics - Nanjing Normal University, China, 2010

 

Research Groups

Differential Geometry, Topology

Research Area

Symplectic and contact geometry, with connections to algebraic topology and Hamiltonian dynamics

Bio

Research Interests

My research is in symplectic and contact geometry, with a particular focus on Hamiltonian dynamics and Floer theory. I study how global properties of a symplectic or contact manifold constrain its dynamics, especially the existence and behavior of periodic orbits. A recurring theme in my work is to combine Floer theory with persistent homology to obtain quantitative information, including stability under perturbations and bounds for geometric and dynamical problems.

I also study the algebraic structures underlying filtered Floer theory and their connections with microlocal analysis. These methods have applications to symplectic embeddings, contact Hamiltonian systems, and the geometry of cotangent bundles. My broader goal is to develop quantitative tools that connect topology, geometry, and dynamics and that can be applied to various rigidity questions in symplectic and contact geometry.

Selected Publications

• Persistent homology and Floer-Novikov theory (with Michael Usher). Geometry & Topology 20 (2016), no. 6, 3333-3430.
• Hamiltonian knottedness and lifting paths from the shape invariant (with Richard Hind). Compositio Mathematica 159, 2416-2457 (2023).
• Coarse distance from dynamically convex to convex (with Julien Dardennes, Jean Gutt and Vinicius G. B. Ramos), International Mathematics Research Notices, Volume 2025, Issue 12, June 2025, rnaf179, doi.org/10.1093/imrn/rnaf179.
• The shape invariant of symplectic ellipsoids (with Richard Hind), Mathematische Annalen. Volume 394, article number 63 (2026).
• Triangulation, Persistence, and Fukaya categories (with Paul Biran and Octav Cornea), Memoirs of the European Mathematical Society (2026), https://ems.press/books/mems/321.