Department of Mathematics
the University of Chicago
5734 S. University Ave, IL 60637
Office: Eckhart 409
I am a second year L.E. Dickson instructor in the Department of Mathematics at the University of Chicago. I graduated from University of Maryland, College Park in 2013 under the supervision of Prof. Dmitry Dolgopyat.
My detailed CV can be found here.
Currently I am interested in the following fields: Hamiltonian dynamics, Mather theory and weak KAM, hyperbolic dynamics, symplectic topology, optimal transport.
Education and Experiences
During the past few years, I visited the following places and was influenced by a number of mathematicians from various fields.
2013--2016, L.E.Dickson instructor, University of Chicago
2014 summer, Visitor, CIMS, NYU
2013 fall, Member, MSRI, Berkeley. Program: optimal transport/mathematical general relativity
2012 spring, Member, IAS, Princeton. Program: symplectic dynamics
2010--2011 Visiting graduate student, Penn State University
2008--2013 Graduate student, University of Maryland-College Park
2004--2008 Bachelor of science, Nanjing University
Papers and Preprints
C.-Q. Cheng, J. Xue, Arnold diffusion in nearly integrable Hamiltonian systems of arbitrary degrees of freedom. 109 pages. arXiv:1503.04153v2
J. Xue, Existence of noncontractible periodic orbits of Hamiltonian system separating two Lagrangian tori on $T^*\mathbb T^n$ with application to non convex Hamiltonian systems, 26 pages. to appear Journal of Symplectic GeometryarXiv:1408.5193
J. Xue, Noncollision singularities in a planar four-body problem, submitted. 115 pages. arXiv:1409.0048
J. Xue, D. Dolgopyat, Noncollision singularities in a planar two-center-two-body problem, 90 pages. to appear Comm. in Math. Phys.arXiv:1307.2645
J. Xue, Continuous averaging proof of the Nekhoroshev theorem, DCDS-A, Vol 30, No.8, arXiv:1210.3884
J. Xue, Arnold diffusion in a restricted planar four-body problem, Nonlinearity 27 (2014) 2887-2908. arXiv:1210.3882
2015 Fall, Calculus III, UChicago
2015 Spring, Honors Calculus, UChicago
2014 Winter, Honors Calculus, UChicago
2014 Fall, Complex analysis, UChicago
2014 Spring, Honors Calculus, UChicago
2014 Spring, Linear algebra, UChicago
2014 Winter, Multivariable Calculus, UChicago
I'm co-organizing the dynamics seminar in Fall 2014. We meet at 3:00 pm-4:00 pm each Monday.
Our scientific findings will be outdated in ten, twenty or fifty years; this is their fate and indeed their “sense”. Every fulfillment in our research raises new questions and wants to be superseded. And this process extends into the infinite… (Max Weber)