Pennsylvania State Univ., Dept. of Mathematics
308 McAllister Building, University Park, PA 16802
I am an associate 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.
• Associate professor, Penn State Univ., 2019-
• 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 E. Lindenstrauss and A. Mohammadi, Polynomial effective equidistribution
in preparation
• with W. Huang, J. Wang and Q. Zhou, Quantitative almost reducibility and Möbius disjointness for analytic quasiperiodic Schrödinger cocycles
submitted
• with A. Brown and F. Rodriguez Hertz, Smooth ergodic theory of Zd-actions, Part 3: Product structure of entropy
under revision
• with A. Algom, Arbitrarily slow decay in the Möbius disjointness conjecture
accepted, Ergodic Th. & Dyn. Sys.
• with F. Rodriguez Hertz, Non-rigidity of partially hyperbolic abelian C1-actions on tori
accepted, Ergodic Th. & Dyn. Sys.
• 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)
• with Y. Wang, Three-stage evolution and fast equilibrium for SGD with non-degenerate critical points
ICML (Int. Conf. Machine Learning) (2022)
• 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)
• with A. Algom and F. Rodriguez Hertz, Logarithmic Fourier decay for self-conformal measures
Journal of London Math. Soc. (2022)
• with A. Algom and F. Rodriguez Hertz, Pointwise normality and Fourier decay for self-conformal measures
Advances Math. (2021)
• with X. He, Möbius disjointness along short intervals for nilsequences
Trans. Amer. Math. Soc. (2021)
• with F. Rodriguez Hertz, On ε-escaping trajectories in homogeneous spaces
Disc. Cont. Dyn. Sys. 25 Years Special Vol. (2021)
• with W. Huang and X. Ye, Measure complexity and Möbius disjointness
Advances Math. (2019)
• with M. Litman, Möbius disjointness for skew products on the Heisenberg nilmanifold
Proc. Amer. Math. Soc. (2019)
• with W. Huang and G. Zhang, Möbius disjointness for topological models of ergodic systems with discrete spectrum
Journal of Modern Dynamics (2019)
• Multi-invariant measures and subsets on nilmanifolds
J. Analyse Math. (2018)
• with A. Brown and F. Rodriguez Hertz, Global smooth and topological rigidity of hyperbolic lattice actions
Annals of Math. (2017)
• Möbius disjointness for analytic skew products
Inventiones Math. (2017)
• with F. Rodriguez Hertz, Global rigidity of higher rank Anosov algebraic actions
Inventiones Math. (2014)
• with U. Shapira, Remarks on Euclidean minima
J. Number Theory (2012)
• with E. Lindenstrauss, Topological self-joinings of Cartan actions by toral automorphisms
Duke Math. J. (2012)
• Rigidity of commutative non-hyperbolic actions by toral automorphisms
Ergodic Th. & Dyn. Sys. (2012)
• Quantitative density under higher rank abelian algebraic toral actions
Int. Math. Res. Notices (2011)
• Discrete and Continuous Dynamical Systems, Series A, 2017-
• Journal of Modern Dynamics, 2020-
• Brin Prize in Dynamical Systems, 2022
• von Neumann Fellow, Institute for Advanced Study, 2022
• NSF CAREER grant DMS-1753042, 2018-2023
• NSF grant DMS-1501295, 2015-2018
• NSF grant DMS-1201453, 2012-2015
• AMS-Simons Travel Grant, 2011-2013
Undergraduate courses
• MATH 250, Ordinary Differential Equations, Fall 2021
• MATH 250, Ordinary Differential Equations, Fall 2020
• MATH 403, Analysis, Fall 2019
• MATH 312, Real Analysis, Spring 2019
• MATH 403, Analysis, Fall 2018
• MATH 412, Fourier series and partial differential equations, Spring 2018
• MATH 312, Real Analysis, Spring 2017
• MATH 421, Complex Analysis, Fall 2016
• MATH 250, Ordinary Differential Equations, Fall 2014
• MATH 120, Multivariable Calculus, Fall 2013
• MATH 115, Calculus: Integration, Fall 2012
• MATH 246, Ordinary Differential Equations, Spring 2012
•
Problem sessions, MAT 317, Complex
Analysis, Fall 2009
• MAT 102, Calculus, Spring 2009
Graduate courses
• MATH 597, Dynamical Systems on Nilmanifolds, Fall 2018
• MATH 508, Dynamical Systems II, Fall 2017
• MATH 616, Smooth ergodic theory, Spring 2014
• MATH 614, Diagonal Actions on Homogeneous Spaces, Spring 2013
• MATH 628, Random Walks on Homogeneous Spaces, Spring 2012
• Global rigidity and classification of actions by higher rank groups, AIM workshop, 2022
• MOU 2021 (Math Online workshop for Undergraduates), 2021
• Penn State Dynamical Systems Seminars, 2016-2018
• Special session on Smooth and Symbolic Ergodic Theory, AMS Eastern Sectional Meeting, 2015