Pair correlation and equidistribution on manifolds

On the Uniform Equidistribution of Closed Horospheres in Hyperbolic Manifolds

We prove asymptotic equidistribution results for pieces of large closed horospheres in cofinite hyperbolic manifolds of arbitrary dimension. This extends earlier results by Hejhal [10] and Strömbergsson [34] in dimension 2. Our proofs use spectral methods, and lead to precise estimates on the rate of convergence to equidistribution.

Notes on Equidistribution

Equidistribution on the Sphere

A concept of generalized discrepancy, which involves pseudodiierential operators to give a criterion of equidistributed pointsets, is developed on the sphere. A simply structured formula in terms of elementary functions is established for the computation of the generalized discrepancy. With the help of this formula ve kinds of point systems on the sphere, namely lattices in polar coordinates, t...

Canonical Correlation Analysis on Riemannian Manifolds and Its Applications

Canonical correlation analysis (CCA) is a widely used statistical technique to capture correlations between two sets of multi-variate random variables and has found a multitude of applications in computer vision, medical imaging and machine learning. The classical formulation assumes that the data live in a pair of vector spaces which makes its use in certain important scientific domains proble...

Equidistribution and Primes

We begin by reviewing various classical problems concerning the existence of primes or numbers with few prime factors as well as some of the key developments towards resolving these long standing questions. Then we put the theory in a natural and general geometric context of actions on affine n-space and indicate what can be established there. The methods used to develop a combinational sieve i...