Jinxin XUE

Department of Mathematics
the University of Chicago
5734 S. University Ave, IL 60637

Email: jxue@math.uchicago.edu
Office: Eckhart 409 



About Me

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. 



Research Interests

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 


Papers


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


Preprints


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.


Teaching


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


Links

I'm co-organizing the dynamics seminar in Fall 2014. We meet at 3:00 pm-4:00 pm each Monday.

Mathematics Genealogy,

Mathoverflow,

arXiv,

mathscinet,


Quote


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)