Hao Shen
Hao Shen 


Short Bio: PhD 2013 (Princeton); Postdoc 20142015 (Warwick);

Ritt Assistant Professor 20152018 (Columbia).




Teaching
Here are some of the previous courses I have taught
Here are some lectures notes for minicourses, 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 1620, 2018
Typed lecture notes for minicourses taught at "The International Program on Regularity Structures and Stochastic Systems" at Chinese Academy of Sciences July 30Aug 03, 2018
Typed lecture notes for "Topics in SPDE" taught at Columbia University, Spring 2017
Research
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

Stochastic Ricci Flow on Compact Surfaces.
(With Julien Dubedat)

Some recent progress in singular stochastic PDEs.
(With Ivan Corwin) Bulletin of the AMS. Accepted.

Local solution to the multilayer KPZ equation.
(With Ajay Chandra and Dirk Erhard)
J. Stat. Phys. (2019) Vol 175, Issue 6, pp 10801106

The dynamical sineGordon model in the full subcritical regime.
(With Ajay Chandra and Martin Hairer)

Stochastic Telegraph equation limit for the stochastic six vertex model.
(With LiCheng Tsai)
Proc. Amer. Math. Soc. 147 (2019), 26852705

Stochastic PDE Limit of the Six Vertex Model.
(With Ivan Corwin, Promit Ghosal and LiCheng Tsai)

Stochastic quantization of an Abelian gauge theory.

Open ASEP in the weakly asymmetric regime.
(With Ivan Corwin)
Comm. Pure Appl. Math. 71(10), pp.20652128.

Glauber dynamics of 2D KacBlumeCapel model and their stochastic PDE limits.
(With Hendrik Weber)
J. Funct. Anal. Vol 275, Issue 6, (2018), 13211367

Moment bounds for SPDEs with nonGaussian fields and application to the WongZakai problem.
(With Ajay Chandra)
Electron. J. Probab. Vol 22 (2017), paper no. 68.

ASEP(q,j) converges to the KPZ equation.
(With Ivan Corwin and LiCheng Tsai)
Ann. Inst. Henri Poincaré (B) Probab. Stat. (2018), 54, No. 2, 9951012.

Weak universality of dynamical Φ4_3: nonGaussian noise.
(With Weijun Xu)
Stoch PDE: Anal Comp (2017).

A central limit theorem for the KPZ equation.
(With Martin Hairer)
Ann. Probab. 45(2017), no. 6B, 41674221.

The dynamical sineGordon model.
(With Martin Hairer)
Comm. Math. Phys. 341 (2016), no. 3, 933989

The strictweak lattice polymer.
(With Ivan Corwin and Timo Seppäläinen)
J. Stat. Phys. 160(2015), no. 4, 10271053

Exact renormalization group analysis of turbulent transport by the shear flow.
(With Weinan E)
J. Stat. Phys. 153 (2013), no. 4, 553571

Mean field limit of a dynamical model of polymer systems.
(With Weinan E)
Sci. China Math. 56 (2013), no. 12, 25912598

A renormalization group method by harmonic extensions and the classical dipole gas.
Ann. Henri Poincaré 17 (2016), no. 4, 861911

Renormalized powers of OrnsteinUhlenbeck processes and wellposedness of stochastic GinzburgLandau equations.
(With Weinan E and Arnulf Jentzen)
Nonlinear Anal. 142 (2016), 152 193

PhD Thesis: Renormalization Theory in Statistical Physics and Stochastic Analysis (Advisor: Weinan E)
Seminars and Conferences
UWMadison,
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 2327, 2019
Workshop: Singular SPDEs and Related Topics, HIM, Bonn, October 2125, 2019