Hao Shen |
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Short Bio:
PhD 2013 (Princeton, Advisor:Weinan E);
Postdoc 2014-2015 (Warwick, Mentor: Martin Hairer);
Ritt Assistant Professor 2015-2018 (Columbia, Mentor:Ivan Corwin).
CV.
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Teaching
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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
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Invariant measure and universality of the 2D Yang-Mills Langevin dynamic. (With Ilya Chevyrev).
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A stochastic PDE approach to large N problems in quantum field theory: a survey.
J. Math. Phys. (2022)
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A stochastic analysis approach to lattice Yang-Mills at strong coupling.
(With Rongchan Zhu, Xiangchan Zhu). Comm. Math. Phys. (2022)
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A new derivation of the finite N master loop equation for lattice Yang-Mills.
(With Scott Smith, Rongchan Zhu).
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Stochastic quantisation of Yang-Mills-Higgs in 3D.
(With Ajay Chandra, Ilya Chevyrev, Martin Hairer).
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An SPDE approach to perturbation theory of Φ42: asymptoticity and short distance behavior.
(With Rongchan Zhu, Xiangchan Zhu). Ann. Appl. Prob. (2022)
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Large N limit of the O(N) linear sigma model in 3D.
(With Rongchan Zhu, Xiangchan Zhu) Comm. Math. Phys. (2022)
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Langevin dynamic for the 2D Yang-Mills measure.
(With Ajay Chandra, Ilya Chevyrev, Martin Hairer) Publ. Math. IHÉS. 136, 1-147 (2022)
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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, 131-202.
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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
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Stochastic Ricci Flow on Compact Surfaces.
(With Julien Dubédat) Int. Math. Res. Not. (2021).
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Some recent progress in singular stochastic partial differential equations.
(With Ivan Corwin) Bulletin of the AMS. 57 (2020), no. 3, 409-454.
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Local solution to the multi-layer KPZ equation.
(With Ajay Chandra and Dirk Erhard),
J. Stat. Phys. 175 (2019), Issue 6, 1080-1106
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The dynamical sine-Gordon model in the full subcritical regime.
(With Ajay Chandra and Martin Hairer)
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Stochastic Telegraph equation limit for the stochastic six vertex model.
(With Li-Cheng Tsai),
Proc. Amer. Math. Soc. 147 (2019), 2685-2705
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Stochastic PDE limit of the Six Vertex model.
(With Ivan Corwin, Promit Ghosal and Li-Cheng Tsai),
Comm. Math. Phys. 375 (2020), 1945-2038
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Stochastic quantization of an Abelian gauge theory.
Comm. Math. Phys. 384 (2021), 1445-1512.
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Open ASEP in the weakly asymmetric regime.
(With Ivan Corwin)
Comm. Pure Appl. Math. 71 (2018), Issue 10, 2065-2128.
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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
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Moment bounds for SPDEs with non-Gaussian fields and application to the Wong-Zakai problem.
(With Ajay Chandra)
Electron. J. Probab. Vol 22 (2017), 1-32.
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ASEP(q,j) converges to the KPZ equation.
(With Ivan Corwin and Li-Cheng Tsai)
Ann. Inst. Henri Poincaré (B) Probab. Stat. 54 (2018), No. 2, 995-1012.
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Weak universality of dynamical Φ43: non-Gaussian noise.
(With Weijun Xu)
Stoch PDE: Anal Comp. 6 (2018), 211-254.
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A central limit theorem for the KPZ equation.
(With Martin Hairer)
Ann. Probab. 45 (2017), no. 6B, 4167-4221.
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The dynamical sine-Gordon model.
(With Martin Hairer)
Comm. Math. Phys. 341 (2016), no. 3, 933-989
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The strict-weak lattice polymer.
(With Ivan Corwin and Timo Seppäläinen)
J. Stat. Phys. 160 (2015), no. 4, 1027-1053
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Exact renormalization group analysis of turbulent transport by the shear flow.
(With Weinan E)
J. Stat. Phys. 153 (2013), no. 4, 553-571
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Mean field limit of a dynamical model of polymer systems.
(With Weinan E)
Sci. China Math. 56 (2013), no. 12, 2591-2598
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A renormalization group method by harmonic extensions and the classical dipole gas.
Ann. Henri Poincaré, 17 (2016), no. 4, 861-911
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Renormalized powers of Ornstein-Uhlenbeck processes and well-posedness of stochastic Ginzburg-Landau equations.
(With Weinan E and Arnulf Jentzen),
Nonlinear Analysis, 142 (2016), 152-193
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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 24-28, 2023.
43rd Conference on Stochastic Processes and their Applications (Lisboa, Portugal).
June 12-14, 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 DMS-2044415 (2021-2026);
NSF DMS-1954091 (2020-2023);
NSF DMS-1712684 / DMS-1909525 (2017 - 2020)