Research interests:

  • invariants of 3- and 4-manifolds
  • Higgs bundles
  • mirror symmetry
  • categorification
  • conformal field theory and TQFT
  • dynamics of supersymmetric gauge theories
    • various other topics in mathematical physics

    • QGM-Caltech joint postdoc, 2016-present
    • Caltech, Ph.D. 2016 (Advisor: Sergei Gukov)
    • Peking University, B.Sc. 2011.



    • "Mirror symmetry with branes by equivariant Verlinde formulae," arXiv:1712.04408 (w/ Tamas Hausel and Anton Mellit)
    • "Argyres-Douglas Theories, Chiral Algebras and Wild Hitchin Characters," JHEParXiv:1701.08782 (w/ Laura Fredrickson, Wenbin Yan and Ke Ye).
    • "BPS spectra and 3-manifold invariants," arXiv:1701.06567 (w/ Sergei Gukov, Pavel Putrov and Cumrun Vafa).
    • "The Verlinde Formula for Higgs Bundles," arXiv:1608:01761 (w/ J.E. Andersen and Sergei Gukov).
    • "Equivariant Verlinde algebra from superconformal index and Argyres-Seiberg duality,Comm. Math. Phys.arXiv:1605.06528 (w/ Sergei Gukov, Wenbin Yan and Ke Ye). 

    Ph.D Thesis:


    • 07/2018, "On Mirror Symmetry of (B,A,A)-Branes," Conference on "Quantum Fields, Geometry and Representation Theory," ICTS, Bangalore.
    • 07/2018, "2d TQFTs Labeled by Three-manifolds," CQ3MI Summer School and Workshop, University of Southern California.
    • 07/2018, "2D TQFTs Labeled by Three-manifolds," GQTA 2018, Sandbjerg estate.
    • 07/2018, Mini-course on "Verlinde formula for complex Chern-Simons theory," GQTA 2018, Geneva.
    • 06/2018, "On Mirror Symmetry of (B,A,A)-Branes," VBAC 2018, CIRM, Luminy.
    • 05/2018, "2D TQFTs Labeled by Three-manifolds," Geometry seminar, IST Austria.
    • 04/2018, "On Categorification of the WRT Invariant,'' Workshop on "Categorification in Mathematical Physics,'' Simons Center for Geometry and Physics. Video
    • 03/2018, "2D TQFTs Labeled by Three-manifolds," conference on "Quantum Knot Homology and Supersymmetric Gauge Theories," Aspen.
    • 01/2018, "BPS Spectra and Invariants for 3- and 4-Manifolds," winter school on "Partition Functions and Automorphic Forms", JINR.
    • 12/2017, "An E6 Suprise," Representation theory seminar, YMSC, Tsinghua University.
    • 11/2017, "On the Mirror Symmetry of (B,A,A)-Branes," Nielson retreat, Sandbjerg Estate.
    • 09/2017, "Can One Hear the Shape of a Drum?", Mathematical physics seminar, University of Heidelberg.
    • 09/2017, "Can One Hear the Shape of a Drum?", ADS seminar, YMSC, Tsinghua University.
    • 01/2017, "Wild Hitchin Characters," Geometry seminar, IST Austria.
    • 01/2017, "Wild Hitchin Characters," QUANTMOD — Quantization and Moduli Spaces, University of Luxembourg.
    • 09/2016, "The Verlinde formula for Higgs bundles," Hitchin70: Differential Geometry and Quantization, QGM, Aarhus. Video
    • 02/2016,  "Verlinde formula for Higgs bundles," Workshop on "Higgs Bundles in Geometry and Physics," IWH Heidelberg.
    • 10/2015, Mini-course on "New TQFT's and Equivariant Integration over Moduli Space of Higgs Bundles," NS@50, Chennai Mathematical Institute.
    • 02/2015, "The Equivariant Verlinde formula," Noncommutative Geometry Seminar, Caltech. 
    • 11/2014, "Equivariant Integration Over Hitchin Moduli Space," Workshop on "Gauged Sigma-Models in Two Dimensions," Simons Center of Geometry and Physics. Video
    • 05/2014, "TQFT and the Geometry of Moduli Spaces," GEAR Junior Retreat, University of Michigan.

    Mail Address: Caltech 452-48, Pasadena, CA 91125