Research

Publications and Preprints

1. Contact quasi-states and their applications (with Igor Uljarević), arXiv: 2503.18750. 

2. Spectrally-large scale geometry via set-heaviness (with Qi Feng), arXiv:2503.14961.

3. On the spectral capacity of submanifolds (with Dylan Cant). Submitted and under review. 

4. Strong Arnold chord conjecture via normalized capacities (with Jungsoo Kang). Submitted and under review. 

5. Quantitative characterization in contact Hamiltonian dynamics - I (with Danijel Djordjević and Igor Uljarević), arxiv: 2309.00527.

6. Remark on non-contractible closed geodesics and homotopy groups (with Egor Shelukhin). arXiv: 2307.13877. 

7. Triangulation and persistence: Algebra 101 (with Paul Biran and Octav Cornea). Part of this preprint has been merged into a newer preprint (arXiv: 2304.01785). 

8. The shape invariant of symplectic ellipsoids (with Richard Hind). Submitted and under review.

9. Introduction to Quantitative Symplectic Geometry [Textbook] (with Antong Zhu), University of Science and Technology of China Press, ISBN: 78-7-312-06282-7 (2025).

10. Coarse distance from dynamically convex to convex (with Julien Dardennes, Jean Gutt and Vinicius G. B. Ramos). accepted and to appear in International Mathematics Research Notices.

11. Spectrally-large scale geometry in cotangent bundles (with Qi Feng). accepted and to appear in Israel Journal of Mathematics. 

12. Notes on symplectic squeezing in $T^*T^n$ and spectra of Finsler dynamics (with Qi Feng). Mathematische Zeitschrift. Volume 310, article number 7, (2025). 

13. Persistence K-theory (with Paul Biran and Octav Cornea). Quantum Topology, DOI: 10.4171/QT/222.

14. Triangulation, Persistence, and Fukaya categories  (with Paul Biran and Octav Cornea). To appear in Memoirs of the European Mathematical Society.

15. Hamiltonian knottedness and lifting paths from the shape invariant (with Richard Hind). Compositio Mathematica. 2023; 159(11): 2416-2457.

16. Symplectic non-convexity of toric domains (with Julien Dardennes and Jean Gutt). Communications in Contemporary Mathematics. https://doi.org/10.1142/S0219199723500104

17. Hamiltonian perturbations in contact Floer homology (with Igor Uljarević).  Journal of Fixed Point Theory and Applications. 24, No.4 (2022)

18. Relative growth rate and contact Banach-Mazur distance (with Daniel Rosen). Geometriae Dedicata. 215, 1-30 (2021)  

19. Persistence modules, symplectic Banach-Mazur distance and Riemannian metrics (with Vukašin Stojisavljević). International Journal of Mathematics. Vol. 32, No. 07, 2150040 (2021)

20. 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)

21. Quantitative Tamarkin Theory Springer Series - CRM Short Courses; Virtual Series on Symplectic Geometry.  e-ISBN: 978-3-030-37888-2 (2020)

22. Chekanov's dichotomy in contact topology (with Daniel Rosen). Mathematical Research Letters. Vol. 27, No. 4, pp. 1165-1193 (2020)

23. Symplectic structure perturbations and continuity of symplectic invariants. Algebraic & Geometric Topology. Vol. 19, Issue 7, pp. 3261-3314 (2019)

24. p-cyclic persistent homology and Hofer distance. Journal of Symplectic Geometry. Vol. 17, No. 3, pp. 857-927 (2019)

25. 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)

26. Persistent homology and Floer-Novikov theory (with Michael Usher). Geometry & Topology. Vol. 20, No. 6, pp. 3333-3430 (2016)

27. Persistent homology and Hamiltonian dynamics,  Ph.D. Thesis (2016). UGA Theses and Dissertations database

Talks and Presentations

Persistence homology in symplectic and contact topology, 2023, 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 (Virtual), January 2021.  (slides)

2020 Winter Meeting - the Canadian Mathematical Society, Canada (Virtual), December 2020. (slides)

Symplectic Zoominar, Triangulated persistence category, CRM, Princeton/IAS, Tel Aviv, and Paris, September 2020. (slides)

2020 Georgia Topology Conference, University of Georgia, June 2020. (Postponed)

RIMS & IBS-CGP Joint Workshop, Shape invariant and coarse symplectic Banach-Mazur distance, RIMS - Kyoto University, December 2019. (notes)

RIMS & IBS-CGP Joint Workshop, Symplectic Banach-Mazur distance and symplectic homology, RIMS - Kyoto University, December 2019. (slides)

CRM - University of Montreal, Large-scale geometry and sheaves, Homological algebra, microlocal analysis and symplectic geometry, June, 2019. (slides)

Technion, Stability results in symplectic geometry, C^0 aspects of symplectic geometry and Hamiltonian dynamics Conference, May, 2019. (slides)

Beijing Normal University, Submanifolds in contact geometry. Geometry Seminar, March 2019. (slides)

Stanford University, Symplectic Banach-Mazur distance, Topology Seminar, December 2018.

University of Notre Dame, Persistence modules in symplectic topology, Felix Klein Seminar, November 2018. 

University of Michigan, Sheaf methods in symplectic topology, Geometry Seminar, April 2018. 

University of Georgia, Application of persistent homology in Riemannian geometry, Topology Seminar, October 2017.

Marist College, Topological data analysis and machine learning, Department Seminar, September 2017.

Northwestern University, Application of persistent homology in symplectic and Riemannian geometry, Geometry and Physics Seminar, September 2017.

Binghamton University, Application of persistent homology in symplectic and Riemannian geometry, Geometry and Topology Seminar, September 2017.

University of Cologne, Floer-Novikov barcode and its application in Hamiltonian dynamics, Computational Symplectic Topology Conference, July-August 2017. 

Tel Aviv University, Persistent homology in symplectic/contact topology, Geometry & Dynamics Seminar, April 2017. (slides)

Beijing International Center for Mathematical Research, Peking University, Perturbation techniques in symplectic topology, Geometry Seminar, March 2017. (slides)

Beijing Normal University, Persistent homology and Hamiltonian dynamics, Geometry Seminar, February 2017.

Institute for Basic Science - Center for Geometry and Physics, Barcode in symplectic and contact topology, CGP Seminar, February 2017. 

The Australian National University, Persistent homology and Hamiltonian dynamics, Algebra and Geometry Seminar, May, 2016. 

Indiana University Bloomington, Persistent homology and singular value decomposition, Graduate Student Topology and Geometry Conference, April, 2016.  

Georgia Southern University, Persistent homology and non-Archimedean linear algebra, Colloquium, September, 2015. 

Conferences

LP60: Geometry and Dynamics. A conference in Honour of Leonid Polterovich, ETH, June 2023. 

Persistence homology in symplectic and contact topology, 2023, 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 (Virtual), January 2021. 

2020 Winter Meeting - the Canadian Mathematical Society, Canada (Virtual), December 2020. 

RIMS & IBS-CGP Joint Workshop. RIMS - Kyoto University, December 2019. 

Homological algebra, microlocal analysis and symplectic geometry. CRM (Montreal), June 2019.

C^0 aspects of symplectic geometry and Hamiltonian dynamics. Technion, May 2019.

Topological data analysis meets symplectic topology. Tel Aviv University (TAU), April - May 2018.

Computational Symplectic Topology. University of Cologne (UC), July - August 2017.

Georgia International Topology Conference. University of Georgia (UGA), May - June 2017.

Quantitative Symplectic Geometry. Simons Center for Geometry and Physics, Stony Brook, May 2017.

Georgia Topology Conference. University of Georgia (UGA), June 2016, 2015.

Computational Symplectic Topology Workshop. Institute for Computational and Experimental Research in Mathematics (ICERM), August 2015.

Computational Symplectic Topology Workshop. Tel Aviv University (TAU), May 2015.

International Congress of Mathematics (ICM 2014). Seoul, Korea, August 2014.

Homological mirror symmetry and symplectic topology. Institute for Basic Science (IBS), Center for Geometry and Physics, Korea, August 2014.

Moduli space of Pseudo-holomorphic curve. Simon Center, SUNY, New York, June and March 2014.

Summer Graduate Workshop - Geometric Analysis. IAS/PCMI, Park City, Utah, July 2013.

Seminar

I co-organized the 2020 ZOOM Reading Seminar with Weiwei Wu. 

I am co-organizing the USTC-IGP Geometry & Topology seminar (the symplectic part). 

I am co-organizing the Recent Developments in Symplectic Geometry seminar.