Hao Shen

Hao Shen

  Assistant Professor
  Department of Mathematics
  University of Wisconsin-Madison
  Email: hshen3 at wisc or pkushenhao at gmail
  Office: Van Vleck Hall 619

Short Bio: PhD 2013 (Princeton); Postdoc 2014-2015 (Warwick);
  Ritt Assistant Professor 2015-2018 (Columbia).


  431/001, Intro-Theory of Probability 09:55 - 10:45 MWF
(Syllabus, course materials, homework are posted on Canvas.)

Here are the previous courses I have taught.


I am interested in stochastic partial differential equations, and its interaction with quantum field theory, statistical mechanics, interacting particle systems and geometric flows.

Publications and Preprints - in reversed chronological order

  1. Some recent progress in singular stochastic PDEs. (With Ivan Corwin)
  2. Local solution to the multi-layer KPZ equation. (With Ajay Chandra and Dirk Erhard)
  3. The dynamical sine-Gordon model in the full subcritical regime. (With Ajay Chandra and Martin Hairer)
  4. Stochastic Telegraph equation limit for the stochastic six vertex model. (With Li-Cheng Tsai) Proc. Amer. Math. Soc. Accepted.
  5. Stochastic PDE Limit of the Six Vertex Model. (With Ivan Corwin, Promit Ghosal and Li-Cheng Tsai)
  6. Stochastic quantization of an Abelian gauge theory.
  7. Open ASEP in the weakly asymmetric regime. (With Ivan Corwin) Comm. Pure Appl. Math. 71(10), pp.2065-2128.
  8. Glauber dynamics of 2D Kac-Blume-Capel model and their stochastic PDE limits. (With Hendrik Weber) J. Funct. Anal. Vol 275, Issue 6, (2018), 1321-1367
  9. Moment bounds for SPDEs with non-Gaussian fields and application to the Wong-Zakai problem. (With Ajay Chandra) Electron. J. Probab. Vol 22 (2017), paper no. 68.
  10. ASEP(q,j) converges to the KPZ equation. (With Ivan Corwin and Li-Cheng Tsai) Ann. Inst. Henri Poincaré (B) Probab. Stat. (2018), 54, No. 2, 995-1012.
  11. Weak universality of dynamical Φ4_3: non-Gaussian noise. (With Weijun Xu) Stoch PDE: Anal Comp (2017).
  12. A central limit theorem for the KPZ equation. (With Martin Hairer) Ann. Probab. 45(2017), no. 6B, 4167-4221.
  13. The dynamical sine-Gordon model. (With Martin Hairer) Comm. Math. Phys. 341 (2016), no. 3, 933-989
  14. The strict-weak lattice polymer. (With Ivan Corwin and Timo Seppäläinen) J. Stat. Phys. 160(2015), no. 4, 1027-1053
  15. Exact renormalization group analysis of turbulent transport by the shear flow. (With Weinan E) J. Stat. Phys. 153 (2013), no. 4, 553-571
  16. Mean field limit of a dynamical model of polymer systems. (With Weinan E) Sci. China Math. 56 (2013), no. 12, 2591-2598
  17. A renormalization group method by harmonic extensions and the classical dipole gas. Ann. Henri Poincaré 17 (2016), no. 4, 861-911
  18. Renormalized powers of Ornstein-Uhlenbeck processes and well-posedness of stochastic Ginzburg-Landau equations. (With Weinan E and Arnulf Jentzen) Nonlinear Anal. 142 (2016), 152- 193
  19. PhD Thesis: Renormalization Theory in Statistical Physics and Stochastic Analysis (Advisor: Weinan E)

Seminars and Conferences

UW-Madison, Probability Seminar (VV901 Th 2:25PM), Analysis Seminar (VV B139 Tu 4:00PM), PDE Geometric Analysis Seminar (VV901 Mon 3:30pm), Colloquia,

Probability and quantum field theory: discrete models, CFT, SLE and constructive aspects, June 10th - 21st 2019, Porquerolles (France)

Paths between Probability, PDEs, and Physics, Imperial College London, July 1st to July 5th, 2019