Department of Mathematics
the University of Chicago
5734 S. University Ave, IL 60637
Office: Eckhart 409
I am an 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 Professor Dmitry Dolgopyat.
My detailed CV can be found here.
Currently I am interested in dynamical systems and symplectic topology.
Education and Experiences
During the past 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
2014,2015 and 2016 summer, Visitor, CIMS, NYU
2013 fall, Member, MSRI, Berkeley
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
A. Blumenthal, J. Xue, L.-S.Young, Lyapunov exponents for random perturbations of some area-preserving maps including the standard map, to appear in Annals of Mathematics Volume 185, no. 1, pages 285–310.
(Some understanding of the standard map conjecture).
J. Xue, Existence of noncontractible periodic orbits of Hamiltonian system separating two Lagrangian tori on T^*T^n with application to non convex Hamiltonian systems, 26 pages. to appear Journal of Symplectic Geometry arXiv:1408.5193 .
(Solution of a problem of Polterovich and a problem of Arnold).
J. Xue, D. Dolgopyat, Noncollision singularities in a planar two-center-two-body problem, Communications in Mathematical Physics, August 2016, Volume 345, Issue 3, pp 797-879.
(Towards solving the Painleve conjecture).
J. Xue, Continuous averaging proof of the Nekhoroshev theorem, DCDS-A, Vol 35, No.8, 2015 arXiv:1210.3884
J. Xue, Arnold diffusion in a restricted planar four-body problem, Nonlinearity 27 (2014) 2887-2908. arXiv:1210.3882
C.-Q. Cheng, J. Xue, Arnold diffusion in nearly integrable Hamiltonian systems of arbitrary degrees of freedom. 109 pages, submitted. arXiv:1503.04153v2
(Solution of the Arnold diffusion conjecture in the smooth category).
J. Xue, Noncollision singularities in a planar four-body problem, submitted, 115 pages. arXiv:1409.0048
(Solution of the last open case of the Painleve conjecture).
A. Blumenthal, J. Xue, L.-S.Young, Positive Lyapunov exponents and exponential correlation decays of some randomly perturbed prototypical 2D maps, preprint.
J. Xue, Nekhoroshev estimates for nearly integrable commuting symplectomorphisms, preprint, submitted.
M.-C. Arnaud , J. Xue, C^1 and C^0 Liouville-Arnold theorem, preprint.
A. Wilkinson, J. Xue, Rigidity of some Abelian-by-cyclic solvable group action on torus, preprint.
J. Xue, Noncollision singularities in Newtonian N-body problem, results and perspectives, (survey), submitted, preprint.
2016 Fall, Calculus III, UChicago
2016 Spring, Analysis on Rn, UChicago
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)