Research Areas

Mathematics and Physics: operator algebras, subfactor theory and their connections with harmonic analysis, knot theory, lower dimensional topology, representation theory, category theory in mathematics; and constructive quantum field theory, conformal field theory, quantum information, condensed matter in physics.

Educational Background

2011-2015 Vanderbilt University, Mathematics Ph.D. Advisor: Vaughan F.R. Jones

2009-2011 University of New Hampshire

2005-2009 Peking University, Mathematics B.S.

Work Experience

2019- Tsinghua University, Professor in Mathematics

2015-2019 Harvard University, Mathematics and Physics postdoctoral fellow

Postdoctoral supervisor: Arthur Jaffe

Honors and Awards

2019 ICCM silver award

2018 ICCM Best paper award

2018 AMS-NSF travel grant for 2018 ICM

2018 NSF conference grant

2017-2020 Templeton Religion Trust 0159

2015-2017 AMS-Simons travel grant

2014 Bjarni Jónsson Prize for Research, Vanderbilt University

Publications

[1] Composed inclusions of A3 and A4 subfactors. Advances in Mathematics, 2015, 279: 307-371 https://doi.org/10.1016/j.aim.2015.03.017;

[2] 1-supertransitive subfactors with index at most 6+1/5. Communications in Mathematical Physics, 2015, 334(2): 889-922. (Joint with Scott Morrison and Dave Penneys) https://doi.org/10.1007/s00220-014-2160-4;

[3] Exchange relation planar algebras of small rank. Transactions of the AMS, 2016, 368(12): 8303-8348. https://doi.org/10.1090/tran/6582

[4] Noncommutative uncertainty principles. Journal of Functional Analysis, 2016, 270(1): 264- 311. (Joint with Chunlan Jiang and Jinsong Wu) https://doi.org/10.1016/j.jfa.2015.08.007;

[5] Quon 3D language for quantum information. PNAS, 2017, 114(10): 2947-2502 (Joint with Arthur Jaffe and Alex Wozniakowski) doi:10.1073/pnas.1621345114;

[6] Planar para algebras, reflection positivity. Communications in Mathematical Physics, 2017, 352(1): 95-133. (Joint with Arthur Jaffe) doi:10.1007/s00220-016-2779-4;

[7] Singly generated planar algebras of small dimension, part III. Transactions of the AMS, 2017, 369(4): 2461-2476. (Joint with Dietmar Bisch and Vaughan F. R. Jones) https://doi.org/10.1090/tran/6719;

[8] Uncertainty principles for locally compact quantum groups. Journal of Functional Analysis, 2018, 274(8): 2399-2445 (Joint with Chunlan Jiang and Jinsong Wu) https://doi.org/10.1016/j.jfa.2017.09.010;

[9] Uncertainty principle for Kac algebras. Journal of Mathematical Physics 2017, 58(5): 052102 (Joint with Jinsong Wu) http://dx.doi.org/10.1063/1.4983755;

[10] Young's inequality for locally compact quantum groups. Journal of Operator Theory, 2017, 77(1): 109-131. (Joint with Simeng Wang and Jinsong Wu) http://dx.doi.org/10.7900/jot.2016mar03.2104;

[11] Constructive simulation and topological design of protocols. New Journal of Physics, (Joint with Arthur Jaffe and Alex Wozniakowski) https://doi.org/10.1088/1367-2630/aa5b57

[12] The Noncommutative Fourier Transform: A survey. Acta Mathematica Sinica Chinese Series, (In honor of the 75th birthday of Bingren Li) 2017, 60(1): 69-80. (Joint with Jinsong Wu) arXiv:1611.04630;

[13] The generator conjecture for 3G subfactor planar algebras. The Proceedings of the Centre for Mathematics and its Applications, Mathematical Sciences Institute, the Aus- tralian National University: The Proceedings in honor of Vaughan F. R. Jones' 60th birthday conferences, edited by Scott Morrison and David Penneys 2017, 46: 344-366 (Joint with Dave Penneys) arXiv:1507.04794;

[14] Mathematical picture language program. PNAS, 2018, 115 (1) 81-86. (Joint with Arthur Jaffe) doi:10.1073/pnas.1710707114;

[15] Holographic software for quantum networks. Science China Mathematics, 2018, 61 (4): 593- 626 (Joint with Arthur Jaffe and Alex Wozniakowski) doi:10.1007/s11425-017-9207-3

[16] Extremal pairs of Young’s inequality for Kac algebras. Pacific Journal of Mathematics, 2018, 295 (1) 103-121. (Joint with Jinsong Wu) doi:10.2140/pjm.2018.295.103;

[17] Block maps and Fourier analysis. to appear Science China Mathematics, 2018, (Joint with Chunlan Jiang and Jinsong Wu) doi:10.1007/s11425-017-9263-7;

[18] Classification of Thurston-relation subfactor planar algebras. to appear Quantum Topology, 2018, (Joint with Corey Jones and Yunxiang Ren) arXiv:1606.00779;

[19] Lifting shadings on symmetrically self-dual subfactor planar algebras. to appear Contemporary Mathematics, 2018, (Joint with Scott Morrison and Dave Penneys) arXiv:1709.05023;

[20] An angle between intermediate subfactors and its rigidity. to appear Transactions of the AMS, 2018, (Joint with Keshab Bakshi, Sayan Das, and Yunxiang Ren) arXiv:1710.00285;

[21] Jones-Wassermann subfactors for modular tensor categories. to appear Advances in Mathematics, 2019, (Joint with Feng Xu) arXiv:1612.08573;

[22] Quon Language: Surface Algebras and Fourier Duality. Communications in Mathematical Physics, 2019, 366: 865-894 https://doi.org/10.1007/s00220-019-03361-3;

[23] De Finetti theorems for braided parafermions. to appear Communications in Mathematical Physics, 2019, (Joint with Kaifeng Bu, Arthur Jaffe, Jinsong Wu,) arXiv:1805.05990;

[24] Non-Commutative Renyi entropic uncertainty principles. to appear Science China Mathe- matics, 2019 (Joint with Jinsong Wu) arXiv:1904.04292;

[25] A Mathematical Picture Language Project (Joint with Arthur Jaffe,) to appear 2019 ICCM conference proceedings.