Zhiren Wang 王之任
Pennsylvania State Univ., Dept. of Mathematics
308 McAllister Building, University Park, PA 16802
zhirenw(AT)psu.edu
I am a professor in the Department of Mathematics at Pennsylvania State University. My research interests include homogeneous dynamical systems, classification of group actions, number theory, and machine learning.
Resume
Professor, Penn State Univ., 2023
Associate professor, Penn State Univ., 2019-2023
Assistant professor, Penn State Univ., 2014-2019
Gibbs assistant professor, Yale Univ., 2011-2014
Ph.D. Princeton Univ. (Advisor: Prof. Elon Lindenstrauss), 2006-2011
M.Sc. Univ. Paris-Sud, 2005-2006
M.Sc. Ecole Polytechnique, 2004-2006
B.Sc. Fudan Univ., 2001-2004
Research
• with A. Algom and F. Rodriguez Hertz, Polynomial Fourier decay and a cocycle version of Dolgopyat's method for self conformal measures
submitted [pdf]
• with E. Lindenstrauss, A. Mohammadi and L. Yang, An effective version of the Oppenheim conjecture with a polynomial error rate
research announcement [pdf]
• with E. Lindenstrauss and A. Mohammadi, Quantitative equidistribution and the local statistics of the spectrum of a flat torus
submitted [pdf]
• with E. Lindenstrauss and A. Mohammadi, Effective equidistribution for some one parameter unipotent flows
submitted [pdf] announcement appeared in Comptes Rendus Math. (2023) [announcement]
• with Z. Li and Y. Wang, Fast equilibrium of SGD in generic situations
accepted, ICLR (Int. Conf. Learning Representations) (2024). [pdf]
• with W. Huang, J. Wang and Q. Zhou, Quantitative almost reducibility and Möbius disjointness for analytic quasiperiodic Schrödinger cocycles
accepted, Peking Journal of Mathematics [pdf]
• with A. Algom, Arbitrarily slow decay in the Möbius disjointness conjecture
accepted, Ergodic Th. & Dyn. Sys. [pdf]
• with F. Rodriguez Hertz, Non-rigidity of partially hyperbolic abelian C1-actions on tori
accepted, Ergodic Th. & Dyn. Sys. [pdf]
• with A. Brown and F. Rodriguez Hertz, Smooth ergodic theory of Zd-actions, Part 3: Product structure of entropy
Journal of Modern Dynamics (2023) [pdf]
• with A. Brown and F. Rodriguez Hertz, Invariant measures and measurable projective factors for actions of higher-rank lattices on manifolds
Annals of Math. (2022) [pdf]
• with Y. Wang, Three-stage evolution and fast equilibrium for SGD with non-degenerate critical points
ICML (Int. Conf. Machine Learning) (2022) [pdf]
• with A. Brown and F. Rodriguez Hertz, The normal subgroup theorem through measure rigidity (expository book chapter)
Dynamics, Geometry, Number Theory: The Impact of Margulis on Modern Mathematics (2022) [pdf]
• with A. Algom and F. Rodriguez Hertz, Logarithmic Fourier decay for self-conformal measures
Journal of London Math. Soc. (2022) [pdf]
• with A. Algom and F. Rodriguez Hertz, Pointwise normality and Fourier decay for self-conformal measures
Advances Math. (2021) [pdf]
• with X. He, Möbius disjointness along short intervals for nilsequences
Trans. Amer. Math. Soc. (2021) [pdf]
• with F. Rodriguez Hertz, On ε-escaping trajectories in homogeneous spaces
Disc. Cont. Dyn. Sys. 25 Years Special Vol. (2021) [pdf]
• with W. Huang and X. Ye, Measure complexity and Möbius disjointness
Advances Math. (2019) [pdf]
• with M. Litman, Möbius disjointness for skew products on the Heisenberg nilmanifold
Proc. Amer. Math. Soc. (2019) [pdf]
• with W. Huang and G. Zhang, Möbius disjointness for topological models of ergodic systems with discrete spectrum
Journal of Modern Dynamics (2019) [pdf]
• Multi-invariant measures and subsets on nilmanifolds
J. Analyse Math. (2018) [pdf]
• with A. Brown and F. Rodriguez Hertz, Global smooth and topological rigidity of hyperbolic lattice actions
Annals of Math. (2017) [pdf]
• Möbius disjointness for analytic skew products
Inventiones Math. (2017) [pdf]
• with F. Rodriguez Hertz, Global rigidity of higher rank Anosov algebraic actions
Inventiones Math. (2014) [pdf]
• with U. Shapira, Remarks on Euclidean minima
J. Number Theory (2012) [pdf]
• with E. Lindenstrauss, Topological self-joinings of Cartan actions by toral automorphisms
Duke Math. J. (2012) [pdf]
• Rigidity of commutative non-hyperbolic actions by toral automorphisms
Ergodic Th. & Dyn. Sys. (2012) [pdf]
• Quantitative density under higher rank abelian algebraic toral actions
Int. Math. Res. Notices (2011) [pdf]