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SURFACE GROUP REPRESENTATIONS TO SL(2, C) AND HIGGS BUNDLES WITH SMOOTH SPECTRAL DATA
SURFACE GROUP SL(2, C) HIGGS BUNDLES SPECTRAL DATA
2015/12/17
We show that for every nonelementary representation of a surface group into SL(2, C) there is a Riemann surface structure such that the Higgs bundle associated to the representation lies outside the d...
TIME-FREQUENCY AND TIME-SCALE CANONICAL REPRESENTATIONS OF DOUBLY SPREAD CHANNELS
TIME-FREQUENCY TIME-SCALE CANONICAL REPRESENTATIONS DOUBLY SPREAD CHANNELS
2015/9/29
A general technique for the generation of canonical channel models and demonstrate the application of the technique to time-frequency and time-scale integral kernel operators is developed. As an examp...
On Lipschitz Inversion of Nonlinear Redundant Representations
Lipschitz Inversion Nonlinear Redundant Representations
2015/9/29
In this note we show that reconstruction from magnitudes of frame coefficients (the so called “phase retrieval problem”) can be performed using Lipschitz continuous maps. Specifically we show that whe...
Scattering in Flatland: Efficient Representations via Wave Atoms
Fast algorithm Wave propagation Boundary integral equation Computational harmonic analysis
2015/7/14
This paper presents a numerical compression strategy for the boundary integral equation of acoustic scattering in two dimensions. These equations have oscillatory kernels that we represent in a basis ...
New Tight Frames of Curvelets and Optimal Representations of Objects with C2 Singularities
Curvelets wavelets second dyadic decomposition edges nonlinear approximation singularities thresholding Radon transform
2015/6/17
This paper introduces new tight frames of curvelets to address the problem of finding optimally sparse representations of objects with discontinuities along C2 edges.Conceptually, the curvelet transfo...
Remarks on modular representations of finite groups of Lie type in non-defining characteristic
Finite groups of Lie type unipotent representations decomposition numbers
2011/8/23
Abstract: Let $G$ be a finite group of Lie type and $\ell$ be a prime which is not equal to the defining characteristic of $G$. In this note we discuss some open problems concerning the $\ell$-modular...
Even Galois Representations and the Fontaine--Mazur conjecture II
Even Galois Representations Fontaine--Mazur conjecture II
2011/2/24
We prove, under mild hypotheses, that there are no irreducible two-dimensional po-tentially semi-stable even p-adic Galois representations of Gal(Q/Q) with distinct Hodge–Tate weights.
D-branes, surface operators, and ADHM quiver representations
D-branes surface operators ADHM quiver representations
2011/3/2
A supersymmetric quantum mechanical model is constructed for BPS states bound to surface operators in five dimensional SU(r) gauge the-ories using D-brane engineering.
Unitary representations of a loop ax+b group, Wiener measure and Gamma-function
Unitary representations loop ax+b group Wiener measure Gamma-function
2011/2/24
We construct a family of irreducible unitary representations of the loop affine group of a line (ax+b group) with central extension on the Hilbert space of square integrable functions with respect to ...
Artin representations attached to pairs of isogenous abelian varieties
Artin representations pairs of isogenous abelian varieties
2011/2/21
Given a pair of abelian varieties defined over a number field k and isogenous over a finite Galois extension L/k, we define a rational Artin representation of the group Gal(L/k) that shows a global re...
An Injectivity Theorem for Casson-Gordon Type Representations relating to the Concordance of Knots and Links
Injectivity Theorem Casson-Gordon Type Representations Concordance of Knots and Links
2010/11/24
In the study of homology cobordisms, knot concordance and link concordance, the following technical problem arises frequently: let $\pi$ be a group and let $M \to N$ be a homomorphism between project...
Free energy computations by minimization of Kullback-Leibler divergence: an efficient adaptive biasing potential method for sparse representations
Free energy Kullback-Leibler divergence
2010/11/17
The present paper proposes an adaptive biasing potential for the computation of free energy landscapes. It is motivated by statistical learning arguments and unifies the tasks of biasing the molecula...
Trianguline representations are a certain kind of p-adic representations of Gal(Qp^alg/Qp) like the crystalline, semistable and de Rham representations of Fontaine. Their definition involves the theo...
An effective isomorphy criterion for mod $\ell$ Galois representations
effective isomorphy criterion mod $\ell$ Galois representations
2010/12/15
In this paper, we consider mod ℓ Galois representations of Q. In particular, we obtain an effective criterion to distinguish two semisimple 2-dimensional, odd mod ℓ Galois representations ...
New infinite product representations of some elementary functions
Green’s function Infinite products Elementary functions
2010/9/10
The derivation of Green’s functions is revisited in a trivial case of standard boundary value problems for the two-dimensional Laplace equation. Regions of a regular shape are considered, with Dirichl...