AIM Five-Year Fellows

The American Institute of Mathematics is pleased to announce that recipients of the AIM Five-Year Fellowships for the year 2000 are Henry Cohn of Harvard University and Vadim Kaloshin of Princeton University. They were chosen from a pool of more than 120 applicants. As part of the Fellowship each will receive 60 months of full-time research support.

Henry Cohn received his S.B. in mathematics from MIT in 1995. He is finishing his PhD this year under the direction of Noam Elkies; his thesis will be entitled "New bounds on sphere packings." In his thesis, Henry develops new techniques which improve upper estimates on the packing density of spheres in Euclidean spaces of dimensions 4 through 36. His bounds in dimensions 8 and 24 are only 0.0001% and 0.07% higher than the densities of known packings (E_8 and the Leech lattice). Henry has already published several papers in combinatorics and number theory; notable are his work with N. Elkies and J. Propp, "Local Statistics for Random Domino Tilings of the Aztec Diamond," (Duke Mathematical Journal 85 (1996), and his paper with R. Kenyon and J. Propp entitled "A variational principle for domino tilings" which has been accepted for publication in the Journal of the American Mathematical Society. He is also interested in the question of the irrationality of the Riemann zeta-function for arguments which are odd integers that are 5 or more.

Vadim Kaloshin received his B.S. from Moscow State in 1994. He is finishing his PhD this year in the area of dynamical systems under the direction of John Mather. His thesis is entitled "Growth of number of periodic orbits of generic diffeomorphisms." As part of his thesis, Vadim gives a new, more elementary, proof of the Artin-Mazur result that "every smooth invertible self-map of a compact manifold can be approximated by one for which the number of periodic points of period p is less than an exponential function of p." This proof has been published in the Annals of Mathematics, vol. 150 (1999). As another part of his thesis (to appear in Communications of Mathematical Physics) he shows that the number of periodic points of period p can grow arbitrarily fast with p for a generic set of smooth invertible self-maps of a compact manifold. Other notable work includes a paper with B. Hunt (Nonlinearity, 1999) where it is shown that the Hausdorff dimension of a fractal set in a Banach space is not necessarily preserved under projection to finite dimensional Euclidean space (whereas the Hausdorff dimension is preserved under projection from one finite dimensional space to another).