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The gallery length filling function and a geometric inequality for filling length
filling length filling function
2015/8/26
We exploit duality considerations in the study of singular combinatorial 2-discs ("diagrams") and are led to the following innovations concerning the geometry of the word problem for finite presentati...
Isoperimetric inequalities for nilpotent groups
nilpotent groups Isoperimetric inequalities
2015/8/26
We prove that every finitely generated nilpotent group of class c admits a polynomial isoperimetric function of degree c+1 and a linear upper bound on its filling length function.
We give coarse geometric conditions for a metric space X to have N-connected asymptotic cones. These conditions are expressed in terms of certain filling functions which are defined recursively on dim...
The filling radius function R of Gromov measures the minimal radii of van Kampen diagrams filling edge-circuits w in the Cayley 2-complex of a finite presentation P. It is known that the Dehn function...
EXPLICIT CLASS FIELD THEORY FOR GLOBAL FUNCTION FIELDS
EXPLICIT CLASS FIELD THEORY GLOBAL FUNCTION FIELDS
2015/8/26
Let F be a global function field and let F ab be its maximal abelian extension. Following an approach of D. Hayes, we shall construct a continuous homomorphism ρ: Gal(F ab/F) → CF , where CF is the id...
Pseudo-Poincar¶e Inequalities and Applications to Sobolev Inequalities
Sobolev Inequalities Inequalities
2015/8/26
Most smoothing procedures are via averaging. Pseudo-Poincar¶e in-
equalities give a basic Lp-norm control of such smoothing procedures in terms
of the gradient of the function involved. When av...
ON THE VORONO˘I FORMULA FOR GL(n)
Automorphic forms Voronoi formula L-functions Whittaker functions
2015/8/25
We prove a general Vorono˘ı formula for cuspidal automorphic representations of GL(n) over number fields. This generalizes recent work by Miller-Schmid and Goldfeld-Li on Maass forms. Our me...
HYBRID SUP-NORM BOUNDS FOR HECKE-MAASS CUSP FORMS
Cutting-edge characteristic value hyperbolic measure
2015/8/25
Let f be a Hecke–Maass cusp form of eigenvalue λ and square-free level N. Normalize the hyperbolic measure such that vol(Y0(N)) = 1 and the form f such that kfk2 = 1. It is shown that kfk1 ≪1...
Bounding hyperbolic and spherical coefficients of Maass forms, with V. Blomer, F. Brumley and A. Kontorovich
Maass forms Fourier coeffcients geodesics periods equidistribution Sobolev norms wave front lemma
2015/8/25
We develop a new method to bound the hyperbolic and spherical Fourier coecients of Maass forms de ned with respect to arbitrary uniform lattices.
Asymptotics and local constancy of characters of p-adic groups
Quantitative theory constancy characters subgroups structure
2015/8/25
In this paper we initiate a quantitative theory of trace characters of reductive p-adic groups when the representation varies. Our approach is based on the local constancy of characters and we su...
The Ridgelet Packets library provides a large family of orthonormal bases for functions f(x, y) in L2(dxdy) which includes orthonormal ridgelets as well as bases deriving from tilings reminiscent from...
Recovering Edges in Ill-Posed Inverse Problems: Optimality of Curvelet Frames
Ill-Posed Inverse Problems Regularization
2015/8/21
We consider a model problem of recovering a function f(x1; x2) from noisy Radon
data. The function f to be recovered is assumed smooth apart from a discontinuity
along a C2 curve { i.e. an edge. We ...
15 Years of Reproducible Research in Computational Harmonic Analysis
Computational Harmonic Analysis 15 Years
2015/8/21
Scientific Computation is emerging as absolutely central to the scientific method. Unfortunately, it is error-prone and currently immature: traditional scientific publication is
inc...
Quasi-regression is introduced for approximation of functions on the unit
cube in s dimensions. It is computationally ecient, compared to kriging,
for problems requiring a large number of function ...
Some standard numerical problems become intractable in high dimensions.
Yet successes are often achieved in practice. This may be explained in terms
of the underlying target function being somehow s...