Jun ZHANG（张俊）

I am a tenure-track assistant professor at the Institute of Geometry and Physics at the University of Science and Technology of China (USTC-IGP). I am working on SYMPLECTIC TOPOLOGY (what is it?)

Research Interests

My research interests include Hamiltonian dynamics, Floer theory, topological data analysis, and microlocal sheaf theory. More explicitly, I have been studying symplectic and contact geometric objects from various quantitative perspectives and creating new symplectic and contact invariants. My work can be found on arXiv here and my Google Scholar is here.

Contact Information

Address: No.96 Jinzhai Road, Hefei, Anhui, China 230026

Email: jzhang4518 at ustc dot edu dot cn

Employment

• 2022.07 - present. Tenure-track Assistant Professor, IGP - University of Science and Technology of China.
• 2019.09 - 2021.08. CRM-ISM Postdoctoral Fellowship, CRM - University of Montreal.
• 2016.10 - 2019.09. Postdoctoral Researcher, Tel Aviv University.

Education

• 2012.08 - 2016.08. Ph.D. in Pure Mathematics, University of Georgia.
• 2011.01 - 2012.08. M.A. in Pure Mathematics, University of Georgia.
• 2006.09 - 2010.07. B.S. in Pure Mathematics, Nanjing Normal University.

Preprints

• Strong Arnold chord conjecture via normalized capacities (with Jungsoo Kang), arxiv: 2404.05150.
• Notes on symplectic squeezing in $T^*T^n$ and spectra of Finsler dynamics (with Qi Feng), arxiv: 2401.17635.
• Spectrally-large scale geometry in cotangent bundles (with Qi Feng), arxiv: 2401.17590.
• Quantitative characterization in contact Hamiltonian dynamics - I (with Danijel Djordjević and Igor Uljarević), arxiv: 2309.00527.
• Coarse distance from dynamically convex to convex (with Julien Dardennes, Jean Gutt and Vinicius G. B. Ramos), arxiv: 2308.06604.
• Remark on non-contractible closed geodesics and homotopy groups (with Egor Shelukhin), arxiv: 2307.13877.
• Persistence K-theory (with Paul Biran and Octav Cornea), arxiv: 2305.01370.
• Triangulation, Persistence, and Fukaya categories (with Paul Biran and Octav Cornea), arxiv: 2304.01785.
• Triangulation and persistence: Algebra 101 (with Paul Biran and Octav Cornea), arxiv:2104.12258.
• The shape invariant of symplectic ellipsoids (with Richard Hind), arxiv:2010.02185.

Papers

• Hamiltonian knottedness and lifting paths from the shape invariant (with Richard Hind), Compositio Mathematica. 159, 2416-2457 (2023)
• Symplectic non-convexity of toric domains (with Julien Dardennes and Jean Gutt), Communications in Contemporary Mathematics. DOI: 10.1142/S0219199723500104 (2023).
• Hamiltonian perturbations in contact Floer homology (with Igor Uljarević), Journal of Fixed Point Theory and Applications. 24, No. 4 (2022).
• Relative growth rate and contact Banach-Mazur distance, (with Daniel Rosen), Geometriae Dedicata. 215, 1-30 (2021).
• Persistence modules, symplectic Banach-Mazur distance and Riemannian metrics (with Vukašin Stojisavljević), International Journal of Mathematics. Vol. 32, No. 07, 2150040 (2021).
• Chekanov's dichotomy in contact topology (with Daniel Rosen), Mathematical Research Letters. Vol. 27, No. 4, pp. 1165-1193 (2020).
• Symplectic structure perturbations and continuity of symplectic invariants, Algebraic & Geometric Topology. Vol. 19, Issue 7, pp. 3261-3314 (2019).
• p-cyclic persistent homology and Hofer distance, Journal of Symplectic Geometry. Vol. 17, No. 3, pp. 857-927 (2019).
• Embeddings of free groups into asymptotic cones of Hamiltonian diffeomorphisms (with Daniel Álvarez-Gavela et al.), Journal of Topology and Analysis. Vol. 11, No. 2, pp. 467-498 (2019).
• Persistent homology and Floer-Novikov theory (with Michael Usher), Geometry & Topology. Vol. 20, No. 6, pp. 3333-3430 (2016).

Books

• Topological persistence in geometry and analysis (with Leonid Polterovich, Daniel Rosen and Karina Samvelyan), University Lecture Series, American Mathematical Society. Vol. 74, e-ISBN: 978-1-4704-5679-5 (2020).
• Quantitative Tamarkin Theory, Springer Series - CRM Short Courses; Virtual Series on Symplectic Geometry, e-ISBN: 978-3-030-37888-2 (2020).

Invited Talks

• Conference on Gauged Symplectic Invariants and Related Topics, Guangzhou, December 2023.
• 拓扑学前沿趋势研讨会, 中科院数学与系统科学研究院 - 天元数学国际交流中心（昆明）, September 2023.
• Workshop on symplectic topology, University of Belgrade, Serbia, August 2023.
• Persistence homology in symplectic and contact topology, University of Toulouse, Albi, June 2023.
• Pacific Rim Complex and Symplectic Geometry Conference 2022, Kyoto University, August 2022.
• Frontiers of Quantitative Symplectic and Contact Geometry, Institut Mittag-Leffler, June 2022.
• Joint Mathematics Meetings 2021 - AMS Special Session on Applied Topology, Washington DC, January 2021.
• 2020 Winter Meeting - the Canadian Mathematical Society, Canada, December 2020.
• 2020 Georgia Topology Conference, University of Georgia, June 2020. (Postponed)
• RIMS & IBS-CGP Joint Workshop, RIMS - Kyoto University, December 2019.
• Homological algebra, microlocal analysis and symplectic geometry, CRM - University of Montreal, June 2019.
• C^0 aspects of symplectic geometry and Hamiltonian dynamics, Technion, May 2019.
• Computational Symplectic Topology, University of Cologne, July - August 2017

Seminars

• I am responsible for the symplectic and contact geometry talks in USTC-IGP Geometry&Topology seminar.
• I am one of the organizers of a joint-seminar on symplectic geometry.
• I am one of the organizers and participants of a symplectic reading seminar.

Teaching

In semester Spring 2023, I taught a graduate-level course on a general introduction to symplectic topology - MATH6435P