Zhihong Xia

In this Chinese name, the family name is Xia.

Zhihong "Jeff" Xia (Chinese: 夏志宏; pinyin: Xià Zhìhóng; born 20 September 1962, in Dongtai, Jiangsu, China) is a Chinese-American mathematician.

Education and career

Xia's construction proving the Painlevé conjecture

Xia received, in 1982, from Nanjing University a bachelor's degree in astronomy and in 1988, a PhD in mathematics from Northwestern University with thesis advisor Donald G. Saari, for his thesis, The Existence of the Non-Collision Singularities.[1] From 1988 to 1990, Xia was an assistant professor at Harvard University and from 1990 to 1994, an associate professor at Georgia Institute of Technology (and Institute Fellow). In 1994, he became a full professor at Northwestern University and since 2000, he has been the Arthur and Gladys Pancoe Professor of Mathematics.[2]

His research deals with celestial mechanics, dynamical systems, Hamiltonian dynamics, and ergodic theory. In his dissertation, he solved the Painlevé conjecture, a long-standing problem posed in 1895 by Paul Painlevé. The problem concerns the existence of singularities of non-collision character in the -body problem in three-dimensional space; Xia proved the existence for . For the existence proof, he constructed an example of five masses, of which four are separated into two pairs which revolve around each other in eccentric elliptical orbits about the z-axis of symmetry, and a fifth mass moves along the z-axis. For selected initial conditions, the fifth mass can be accelerated to an infinite velocity in a finite time interval (without any collision between the bodies involved in the example).[3] The case was open until 2014,[4] when it was solved by Jinxin Xue.[5][6] For , Painlevé had proven that the singularities (points of the orbit in which accelerations become infinite in a finite time interval) must be of the collision type. However, Painlevé's proof did not extend to the case .

In 1993, Xia was the inaugural winner of the Blumenthal Award of the American Mathematical Society. From 1989 to 1991, he was a Sloan Fellow. From 1993 to 1998, he received the National Young Investigator Award from the National Science Foundation. In 1995, he received the Monroe H. Martin Prize in Applied Mathematics from the University of Maryland.[7] In 1998, he was an Invited Speaker of the International Congress of Mathematicians in Berlin.[8]

Selected publications

References

  1. ^ Zhi-Hong Xia at the Mathematics Genealogy Project
  2. ^ "Zhihong Jeff Xia". Northwestern University.
  3. ^ In 1908 Edvard Hugo von Zeipel proved the surprising fact that the existence of a non-collision singularity in the -body problem necessarily causes the velocity of at least one particle to become unbounded.
  4. ^ Already in 2003, Joseph L. Gerver gave arguments (a heuristic model) for the existence of a non-collision singularity for the planar Newtonian 4-body problem — however, at the time there was still no rigorous proof. See Gerver, Joseph L. (2003). "Noncollision Singularities: Do Four Bodies Suffice?". Exp. Math. 12 (2): 187–198. doi:10.1080/10586458.2003.10504491. S2CID 23816314.
  5. ^ Xue, Jinxin (2014). "Noncollision Singularities in a Planar Four-body Problem". arXiv:1409.0048 [math.DS].
  6. ^ Xue, Jinxin (2020). "Non-collision singularities in a planar 4-body problem". Acta Mathematica. 224 (2): 253–388. doi:10.4310/ACTA.2020.v224.n2.a2.
  7. ^ "Monroe H. Martin Prize". Center for Scientific Computation and Mathematical Modeling, University of Maryland, College Park.
  8. ^ Xia, Zhihong (1998). "Arnold diffusion: a variational construction". Doc. Math. (Bielefeld) Extra Vol. ICM Berlin, 1998, vol. II. pp. 867–877.