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).


  Here are some of the previous courses I have taught

Here are some lectures notes for mini-courses, summer schools, topics courses I taught (some are still being updated; if the link does not work please send me an email request):
Some handwritten lecture notes for supplementary classes taught at Chinese Academy of Sciences July 16-20, 2018
Typed lecture notes for mini-courses taught at "The International Program on Regularity Structures and Stochastic Systems" at Chinese Academy of Sciences July 30-Aug 03, 2018
Typed lecture notes for "Topics in SPDE" taught at Columbia University, Spring 2017


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. Stochastic Ricci Flow on Compact Surfaces. (With Julien Dubedat)
  2. Some recent progress in singular stochastic PDEs. (With Ivan Corwin) Bulletin of the AMS. Accepted.
  3. Local solution to the multi-layer KPZ equation. (With Ajay Chandra and Dirk Erhard) J. Stat. Phys. (2019) Vol 175, Issue 6, pp 1080-1106
  4. The dynamical sine-Gordon model in the full subcritical regime. (With Ajay Chandra and Martin Hairer)
  5. Stochastic Telegraph equation limit for the stochastic six vertex model. (With Li-Cheng Tsai) Proc. Amer. Math. Soc. 147 (2019), 2685-2705
  6. Stochastic PDE Limit of the Six Vertex Model. (With Ivan Corwin, Promit Ghosal and Li-Cheng Tsai)
  7. Stochastic quantization of an Abelian gauge theory.
  8. Open ASEP in the weakly asymmetric regime. (With Ivan Corwin) Comm. Pure Appl. Math. 71(10), pp.2065-2128.
  9. 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
  10. 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.
  11. 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.
  12. Weak universality of dynamical Φ4_3: non-Gaussian noise. (With Weijun Xu) Stoch PDE: Anal Comp (2017).
  13. A central limit theorem for the KPZ equation. (With Martin Hairer) Ann. Probab. 45(2017), no. 6B, 4167-4221.
  14. The dynamical sine-Gordon model. (With Martin Hairer) Comm. Math. Phys. 341 (2016), no. 3, 933-989
  15. The strict-weak lattice polymer. (With Ivan Corwin and Timo Seppäläinen) J. Stat. Phys. 160(2015), no. 4, 1027-1053
  16. Exact renormalization group analysis of turbulent transport by the shear flow. (With Weinan E) J. Stat. Phys. 153 (2013), no. 4, 553-571
  17. Mean field limit of a dynamical model of polymer systems. (With Weinan E) Sci. China Math. 56 (2013), no. 12, 2591-2598
  18. A renormalization group method by harmonic extensions and the classical dipole gas. Ann. Henri Poincaré 17 (2016), no. 4, 861-911
  19. 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
  20. 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

Summer School "New Frontiers in Singular SPDEs and Scaling Limits", HIM, Bonn, September 23-27, 2019

Workshop: Singular SPDEs and Related Topics, HIM, Bonn, October 21-25, 2019