Publications & Preprints:

Preprints:

15. Intersections of  Dual SL3-Webs

with Zhe Sun and Daping Weng, 31 pages, Preprint, arXiv:2311.15466

14. Cluster nature of quantum groups,

 32 pages, Preprint, arXiv:2209.06258

13. Cluster structures on braid varieties, 

 with R. Casals, E. Gorsky, M. Gorsky, I. Le, and J. Simental, 67 pages, arXiv:2207.11607

12. Positive Braid Links with Infinitely Many Fillings, 

 with Honghao Gao and Daping Weng, 19 pages, Combined with the Journal Version of "Augmentations, Fillings, and Clusters", arXiv: 2009.00499

11. Quantum geometry of moduli spaces of local systems and representation theory, 

with Alexander Goncharov, 199 pages, arXiv:1904.10491  

     ---- See talks (video1, 2, 3, 4) given by Alexander B. Goncharov at IHES about the above work.

Publications:

10. The Chromatic Lagrangian: Wavefunctions and open Gromov-Witten Conjectures

with Gus Schrader and Eric Zaslow, 61 pages, Accepted by Adv. Theor. Math. Phys, arXiv: 2302.00159

9. Augmentations, Fillings, and Clusters, 

 with Honghao Gao and Daping Weng, Geometric and Functional Analysis, 34, 798-867(2024). https://doi.org/10.1007/s00039-024-00673-y, arXiv:2008.10793 

8. A=U for cluster algebras from moduli spaces of G-local systems,

with Tsukasa Ishibashi and Hironori Oya, 41 pages, Advances in Mathematics, 431(2023),  arXiv: 2202.03168

7. Duals of semisimple Poisson-Lie groups and cluster theory of moduli spaces of G-local systems, 

 International Mathematics Research Notices, Volume 2022, Issue 18, Pages 14295-14318, (2022). arXiv:2003.07901

6. Cluster Structures on Double Bott-Samelson Cells, 

with Daping Weng, Forum of Mathematics, Sigma, 9 E66 (2021). arXiv:1904.07992

5. Cyclic Sieving and cluster duality for Grassmannian, 

 with Daping Weng, SIGMA 16 (2020), 067, 41 pages, arXiv:1803.06901

4. Donaldson-Thomas transformations of moduli spaces of G-local systems, 

with Alexander Goncharov, Advances in Mathematics, 327(2018), 225-348. arXiv:1602.06479    

     ----   I gave two talks (video) at MSRI about this work. 

3. Tensor invariants, saturation problems, and Dynkin automorphisms, 

with Jiuzu Hong, Advances in Mathematics, 285(2015), 629-657. arXiv:1404.4098

2. Geometry of canonical bases and mirror symmetry, 

with Alexander B. Goncharov, Inventiones Mathematicae, 202(2015), no.2, 487-633. arXiv:1309.5922

1. Stasheff polytopes and the coordinate ring of the cluster X-variety of type A_n, 

Selecta Mathematica (New Series) 20(2014), no.3, 929-959. arXiv: 1104.3528