1,855 research outputs found
Quantitative Version of the Oppenheim Conjecture for Inhomogeneous Quadratic Forms
A quantitative version of the Oppenheim conjecture for inhomogeneous
quadratic forms is proved. We also give an application to eigenvalue spacing on
flat 2-tori with Aharonov-Bohm flux
The NASA planetary biology internship experience
By providing students from around the world with the opportunity to work with established scientists in the fields of biogeochemistry, remote sensing, and origins of life, among others, the NASA Planetary Biology Internship (PBI) Program has successfully launched many scientific careers. Each year approximately ten interns participate in research related to planetary biology at NASA Centers, NASA-sponsored research in university laboratories, and private institutions. The PBI program also sponsors three students every year in both the Microbiology and Marine Ecology summer courses at the Marine Biological Laboratory. Other information about the PBI Program is presented including application procedure
Logarithm laws for flows on homogeneous spaces
We prove that almost all geodesics on a noncompact locally symmetric space of
finite volume grow with a logarithmic speed -- the higher rank generalization
of a theorem of D. Sullivan (1982). More generally, under certain conditions on
a sequence of subsets of a homogeneous space ( a semisimple
Lie group, a non-uniform lattice) and a sequence of elements of
we prove that for almost all points of the space, one has for infinitely many .
The main tool is exponential decay of correlation coefficients of smooth
functions on . Besides the aforementioned application to geodesic
flows, as a corollary we obtain a new proof of the classical Khinchin-Groshev
theorem in simultaneous Diophantine approximation, and settle a related
conjecture recently made by M. Skriganov
Khintchine-type theorems on manifolds: the convergence case for standard and multiplicative versions
An analogue of the convergence part of the Khintchine-Groshev theorem, as
well as its multiplicative version, is proved for nondegenerate smooth
submanifolds in . The proof combines methods from metric number
theory with a new approach involving the geometry of lattices in Euclidean
spaces.Comment: 27 page
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