Randomness in Diophantine approximation
Advances in Homogeneous Dynamics May 11, 2015 - May 15, 2015
Location: SLMath: Eisenbud Auditorium
counting points on a lattice
unimodular lattices
asymptotic formulas
Borel sets
Siegel transform
central limit theorem
11R60 - Cyclotomic function fields (class groups, Bernoulli objects, etc.)
57Q10 - Simple homotopy type, Whitehead torsion, Reidemeister-Franz torsion, etc. [See also 19B28]
37A35 - Entropy and other invariants, isomorphism, classification in ergodic theory
11K38 - Irregularities of distribution, discrepancy [See also 11Nxx]
14236
We discuss the problem of counting solutions of Diophantine inequalities. While a general asymptotic formula for the counting function has been established by W. Schmidt, finer statistical properties of this function are still not well understood. We investigate its limiting distribution and establish the central limit theorem in this context. This is a joint work with Anish Ghosh.
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14236
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