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 2022
Math635, Introduction to Brownian motion and stochastic calculus
MWF 9:55AM  10:45AM (Van Vleck B123)
TEXTBOOK:
Steele, Stochastic Calculus and Financial Applications
Grader: TBA
The course grade is based on homework assignments, one midterm, and a cumulative final exam.
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

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

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 Φ4_2: asymptoticity and short distance behavior.
(With Rongchan Zhu, Xiangchan Zhu)

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

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

Large N limit of the O(N) linear sigma model via stochastic quantization.
(With Scott Smith, Rongchan Zhu, Xiangchan Zhu) Ann. Probab. 50.1 (2022): 131202.

Scaling limit of a directed polymer among a Poisson field of independent walks.
(With Jian Song, Rongfeng Sun, Lihu Xu) J. Funct. Anal. (2021), 281(5).

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

Some recent progress in singular stochastic PDEs.
(With Ivan Corwin) Bulletin of the AMS. 57.3 (2020): 409454.

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)
Comm. Math. Phys. 375 (2020), pp 19452038

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

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)
Recent news and activities
September 10  11, 2022.
Graduate Student Probability Conference, Madison (Registration closed.)
June 27July 1, 2022:
42nd conference on Stochastic Processes and their Applications (SPA), Wuhan
2730 June 2022:
2022 IMS Annual Meeting, London
18 Apr 2022  13 May 2022:
2022 Random Matrix EurAsia 2022, Singapore
Sept 2021:
PDE and Randomness symposium,
The symposium was held online on 1st  10th of September 2021
(originally planned to take place at University of Bath, UK.)
Sept 2021:
The 10th International Conference on Stochastic Analysis and its Applications, (10th ICSAA).
The conference was held online on 610 September 2021 (originally planned to take place in September 2020
at Kyoto University, Japan.)
Aug 2021:
International Congress on Mathematical Physics, Aug 2  7, 2021,
Geneva, Switzerland.
July 2021:
BernoulliIMS 10th World Congress,
The congress was held online on July 19  23, 2021
(originally planned to take place in
Seoul, Korea.)
Grants and Awards
My research is mainly supported by the following grants:
NSF CAREER DMS2044415 (20212026);
NSF DMS1954091 (20202023);
NSF DMS1712684 / DMS1909525 (2017  2020)