Hao Shen
Hao Shen 


Short Bio:
PhD 2013 (Princeton, Advisor:Weinan E);
Postdoc 20142015 (Warwick, Mentor: Martin Hairer);
Ritt Assistant Professor 20152018 (Columbia, Mentor:Ivan Corwin).
CV.



Teaching
Here are some of the previous courses I have taught
Teaching in Spring 2023
Math833, Topics in stochastic PDE.
MWF 12:05PM  12:55PM
TEXTBOOK: Lecture notes uploaded on Canvas.
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

Invariant measure and universality of the 2D YangMills Langevin dynamic. (With Ilya Chevyrev).

A stochastic PDE approach to large N problems in quantum field theory: a survey.
J. Math. Phys. (2022)

A stochastic analysis approach to lattice YangMills at strong coupling.
(With Rongchan Zhu, Xiangchan Zhu). Comm. Math. Phys. (2022)

A new derivation of the finite N master loop equation for lattice YangMills.
(With Scott Smith, Rongchan Zhu).

Stochastic quantisation of YangMillsHiggs in 3D.
(With Ajay Chandra, Ilya Chevyrev, Martin Hairer).

An SPDE approach to perturbation theory of Φ42: asymptoticity and short distance behavior.
(With Rongchan Zhu, Xiangchan Zhu). Ann. Appl. Prob. (2022)

Large N limit of the O(N) linear sigma model in 3D.
(With Rongchan Zhu, Xiangchan Zhu) Comm. Math. Phys. (2022)

Langevin dynamic for the 2D YangMills measure.
(With Ajay Chandra, Ilya Chevyrev, Martin Hairer) Publ. Math. IHÉS. 136, 1147 (2022)

Large N limit of the O(N) linear sigma model via stochastic quantization.
(With Scott Smith, Rongchan Zhu, Xiangchan Zhu), Ann. Probab. 50 (2022), no. 1, 131202.

Scaling limit of a directed polymer among a Poisson field of independent walks.
(With Jian Song, Rongfeng Sun, Lihu Xu), J. Funct. Anal. 281 (2021), no. 5, 55pp

Stochastic Ricci Flow on Compact Surfaces.
(With Julien Dubédat) Int. Math. Res. Not. (2021).

Some recent progress in singular stochastic partial differential equations.
(With Ivan Corwin) Bulletin of the AMS. 57 (2020), no. 3, 409454.

Local solution to the multilayer KPZ equation.
(With Ajay Chandra and Dirk Erhard),
J. Stat. Phys. 175 (2019), Issue 6, 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),
Comm. Math. Phys. 375 (2020), 19452038

Stochastic quantization of an Abelian gauge theory.
Comm. Math. Phys. 384 (2021), 14451512.

Open ASEP in the weakly asymmetric regime.
(With Ivan Corwin)
Comm. Pure Appl. Math. 71 (2018), Issue 10, 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), 132.

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

Weak universality of dynamical Φ43: nonGaussian noise.
(With Weijun Xu)
Stoch PDE: Anal Comp. 6 (2018), 211254.

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 Analysis, 142 (2016), 152193

PhD Thesis: Renormalization Theory in Statistical Physics and Stochastic Analysis
(Advisor: Weinan E)
Recent news and activities
Dec 17  22, 2023.
Oberwolfach Arbeitsgemeinschaft: QFT and Stochastic PDEs
Aug 9  11, 2023.
Frontiers of Stochastic Analysis (Chicago, Organized by Cheng Ouyang and Jing Wang).
July 2428, 2023.
43rd Conference on Stochastic Processes and their Applications (Lisboa, Portugal).
June 1214, 2023.
Stochastic analysis meets QFT  critical theory (Muenster, Germany, Organized by A.Chandra, H.Weber and R.Wulkenhaar).
May 31  June 4, 2023.
The 13th AIMS Conference on Dynamical Systems, Differential Equations and Applications (Wilmington, NC).
Nov 14  16, 2022.
Stochastic PDEs and Related Topics, Maryland
September 10  11, 2022.
Graduate Student Probability Conference, Madison (Registration closed.)
Grants and Awards
My research is mainly supported by the following grants:
NSF CAREER DMS2044415 (20212026);
NSF DMS1954091 (20202023);
NSF DMS1712684 / DMS1909525 (2017  2020)