Search
Now showing items 681-690 of 1390
Level-raising and symmetric power functoriality, III
(Duke University PressDuke Mathematical Journal, 2016-12-09)
The simplest case of the Langlands functoriality principle asserts the existence of
the symmetric powers Symn of a cuspidal representation of GL.2/ over the adèles of
F , where F is a number field. In 1978, Gelbart and ...
Harmonic Discs of Solutions to the Complex Homogeneous Monge-Ampere Equation
(SpringerPublications mathématiques de l'IHÉS, 2015-05-30)
We study regularity properties of solutions to the Dirichlet problem for the complex Homogeneous Monge-Ampere equation. We show that for certain boundary data on P^1 the solution Φ to this Dirichlet problem is connected ...
Sharp trace inequalities for fractional Laplacians
(American Mathematical SocietyProceedings of the American Mathematical Society, 2012-04-05)
The sharp trace inequality of José Escobar is extended to traces for the fractional Laplacian on Rⁿ and a complete characterization of cases of equality is discussed. The proof proceeds via Fourier transform and uses Lieb’s ...
A 2-adic automorphy lifting theorem for unitary groups over CM fields
(SpringerMathematische Zeitschrift, 2016)
We prove a ‘minimal’ type automorphy lifting theorem for 2-adic Galois representations of unitary type, over imaginary CM fields. We use this to improve an automorphy lifting theorem of Kisin for GL_2.
Spectral methods and computational trade-offs in high-dimensional statistical inference
(Department of Pure Mathematics and Mathematical Statistics, University of CambridgeUniversity of CambridgeDepartment of Pure Mathematics and Mathematical StatisticsFaculty of MathematicsSt John's College, 2016-10-04)
Spectral methods have become increasingly popular in designing fast algorithms for modern highdimensional datasets. This thesis looks at several problems in which spectral methods play a central role. In some cases, we ...
The monotone wrapped Fukaya category and the open-closed string map
(SpringerSelecta Mathematica, 2016-08-09)
We build the wrapped Fukaya category $\textit{W}$($\textit{E}$)for any monotone symplectic manifold $\textit{E}$, convex at infinity. We define the open-closed and closed-open string maps, OC : HH$_{*}$($\textit{W}$($\textit{E}$)) ...
Automorphy of some residually S$_5$ Galois representations
(SpringerMathematische Zeitschrift, 2016)
Let $\textit{F}$ be a totally real field and $\textit{p}$ an odd prime. We prove an automorphy lifting theorem for geometric representations $\rho$ : $\textit{G}_F$ → GL$_2$($\bar{\Bbb Q}_p$) which lift irreducible residual ...
Envelopes of positive metrics with prescribed singularities
(Université Paul Sabatier, ToulouseAnnales de la Faculté des Sciences de Toulouse, 2016)
We investigate envelopes of positive metrics with a prescribed singularity type. First we generalise work of Berman to this setting, proving C$^{1,1}$ regularity of such envelopes, showing their Monge-Ampère measure is ...
Alpha Invariants and K-Stability for General Polarizations of Fano Varieties
(Oxford University PressINTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2014-09-26)
We provide a sufficient condition for polarisations of Fano varieties to be K-stable in terms of Tian’s alpha invariant, which uses the log canonical threshold to measure singularities of divisors in the linear system ...
On the rigid cohomology of certain Shimura varieties.
(SpringerResearch in the Mathematical Sciences, 2016)
We construct the compatible system of $\textit{l}$-adic representations associated to a regular algebraic cuspidal automorphic representation of GL$_{n}$ over a CM (or totally real) field and check local-global compatibility ...