Professional Experiences:
September, 2012 - present
August, 2007 - August 2012
September, 2004 - August, 2007
Associate Professor of Mathematics, The George Washington University, Washington, DC
Assistant Professor of Mathematics, The George Washington University, Washington, DC
Visiting Assistant Professor of Mathematics, University of Massachusetts, Amherst, MA
Education:
September, 2004
July, 1998
Doctor of Philosophy in Mathematics, MIT, Cambridge, MA
Bachelor of Science in Mathematics, Peking University, Beijing, China
Publications:
HOMFLYPT Homology over Z_2 Detects Unlinks, J. Knot Theory Ramifications, Vol. 31, No. 11, 2250072 (2022) [arxiv download]
Betti Numbers of the HOMFLYPT Homology, J. Knot Theory Ramifications, Vol. 27, No. 14, 1850072 (2018) [arxiv download]
On the Hilbert Polynomial of the HOMFLYPT Homology, J. Knot Theory Ramifications, 27, 1850007 (2018) [20 pages] [arxiv download]
Khovanov–Rozansky homology and directed cycles, Journal of Algebraic Combinatorics, Volume 46 (2017), Issue 2, pp 403-444. [arxiv download]
A Family of Transverse Link Homologies, Algebraic & Geometric Topology 16 (2016) 41-127. DOI: 10.2140/agt.2016.16.41 [arxiv download]
Equivariant Khovanov-Rozansky Homology and Lee-Gornik Spectral Sequence, Quantum Topol. 6 (2015), 515-607. doi: 10.4171/QT/70 [arxiv download]
A colored sl(N) homology for links in S^3, Dissertationes Math. 499 (2014), doi:10.4064/dm499-0-1 (217 pages). [arxiv download] [a condensed version]
Simplified Khovanov–Rozansky chain complexes of open 2-braids, Topology and its Applications, Volume 159, Issue 14 (2012), 3190–3203. [arxiv download]
Colored Morton-Franks-Williams Inequalities, International Mathematics Research Notices 2012; doi: 10.1093/imrn/rns184 (24 pages). [arxiv download]
On the Kauffman-Vogel and the Murakami-Ohtsuki-Yamada Graph Polynomials, J. Knot Theory Ramifications Vol. 21, No. 10 (2012), 1250098 (40 pages). [arxiv download]
Equivariant colored sl(N)-homology for links, J. Knot Theory Ramifications Vol. 21, No. 2 (2012), 1250012 (104 pages). [arxiv download]
Generic deformations of the colored sl(N)-homology for links, Algebraic & Geometric Topology 11 (2011) 2037-2106. [arxiv download]
On the Quantum Filtration of the Khovanov-Rozansky cohomology, Advances in Mathematics 221 (2009), NO. 1, 54-139. [arxiv download]
Braids, Transversal Links and the Khovanov-Rozansky Theory, Trans. Amer. Math. Soc. 360 (2008) NO. 7, 3365-3389. [arxiv download]
On Legendrian Surgeries, Mathematical Research Letters 14 (2007) NO. 3, 513 - 530. [arxiv download]
Legendrian Links and the Spanning Tree Model for Khovanov Homology, Algebraic & Geometric Topology 6 (2006), 1745 - 1757. [arxiv download]
Legendrian Vertical Circles in Small Seifert Spaces, Communications in Contemporary Mathematics, Vol. 8, No. 2 (2006), 219 - 246. [download] [arxiv download part 1] [arxiv download part 2]
Tight contact structures on small Seifert spaces, PhD Thesis, MIT, 2004. [download]
Preprints
03/25 Adaptive Stochastic Gradient Descents on Manifolds with an Application on Weighted Low-Rank Approximation, with Peiqi Yang and Conglong Xu [arxiv dowload]
02/25 Weighted Low-rank Approximation via Stochastic Gradient Descent on Manifolds, with Conglong Xu and Peiqi Yang [arxiv dowload]
03/24 Decomposition of Persistent Homology and Spectral Sequences, with Peiqi Yang and Yingfeng Hu [arxiv dowload]
04/21 A Stochastic Gradient Descent Theorem and the Back-Propagation Algorithm [arxiv download]
03/14 On the Transverse Khovanov-Rozansky Homologies: Graded Module Structure and Stabilization [arxiv download]
Unpublished Notes:
03/07 The Khovanov-Rozansky Cohomology and Bennequin Inequalities [arxiv download]
05/05 On the Slicing Genus of Legendrian Knots [arxiv download]
12/03 A New Way to Compute the Thurston-Bennequin Number [arxiv download]
Talks:
Reading Seminars:
Popular Media:
I was interviewed by Radio Free Asia for a report on the social-economical realities of mathematical researchers in China.
Last updated on Mar. 18, 2025