Now showing items 1-20 of 468

• #### 2-Selmer groups and Heegner points on elliptic curves ﻿

(2015-05-07)
This thesis studies several aspects of the arithmetic of elliptic curves. In particular, we explore the prediction of the Birch and Swinnerton-Dyer conjecture when the 2-Selmer group has rank one. For certain elliptic ...
• #### The 2.1-D Sketch ﻿

(IEEE Computer Society Press, 1990)
A model is described for image segmentation that tries to capture the low-level depth reconstruction exhibited in early human vision, giving an important role to edge terminations. The problem is to find a decomposition ...
• #### 2D-Shape Analysis Using Conformal Mapping ﻿

(Springer Verlag, 2006)
The study of 2D shapes and their similarities is a central problem in the field of vision. It arises in particular from the task of classifying and recognizing objects from their observed silhouette. Defining natural ...
• #### 4-Manifolds With Inequivalent Symplectic Forms and 3-Manifolds With Inequivalent Fibrations ﻿

(International Press, 1999)
We exhibit a closed, simply connected 4-manifold $X$ carrying two symplectic structures whose ﬁrst Chern classes in $H^2 (X, \mathbb{Z})$ lie in disjoint orbits of the diffeomorphism group of $X$. Consequently, the ...
• #### A p-adic Jacquet-Langlands Correspondence ﻿

(2017-05-16)
In this paper, we construct a candidate p-adic Jacquet-Langlands correspondence. This is a correspondence between unitary continuous admissible representations of GL2(Qp) valued in p-adic Banach spaces, and unitary continuous ...
• #### The ABC's of Number Theory ﻿

(Harvard University, 2007)
The ABC conjecture is a central open problem in modern number theory, connecting results, techniques and questions ranging from elementary number theory and algebra to the arithmetic of elliptic curves to algebraic geometry ...
• #### About Hermann Weyl’s “Ramifications, Old and New, of the Eigenvalue Problem” ﻿

(American Mathematical Society (AMS), 2012-05-01)
• #### Abstract 2374: Reconstructing the evolutionary history of metastatic cancers ﻿

(American Association for Cancer Research (AACR), 2016)
Reconstructing the evolutionary history of metastases is critical for understanding their basic biological principles and has profound clinical implications. Genome-wide sequencing data has enabled modern phylogenomic ...
• #### Abundance Conjecture ﻿

(International Press, 2010)
We sketch a proof of the abundance conjecture that the Kodaira dimension of a compact complex algebraic manifold equals its numerical Kodaira dimension. The proof consists of the following three parts: (i) the case of ...
• #### Accumulation of Driver and Passenger Mutations During Tumor Progression ﻿

Major efforts to sequence cancer genomes are now occurring throughout the world. Though the emerging data from these studies are illuminating, their reconciliation with epidemiologic and clinical observations poses a major ...
• #### The Alexander Polynomial of a 3-Manifold and the Thurston Norm on Cohomology ﻿

(Elsevier, 2002)
Let M be a connected, compact, orientable 3-manifold with $b_1(M)>1$, whose boundary (if any) is a union of tori. Our main result is the inequality ${\parallel \phi \parallel}_A \le {\parallel \phi \parallel}_T$ between ...
• #### An Algebraic Surface with $K$ ample, $(K^2)= 9, p_g = q = 0$ ﻿

(Johns Hopkins University Press, 1979)
• #### Algebraicity Criteria and Their Applications ﻿

(2016-05-04)
We use generalizations of the Borel–Dwork criterion to prove variants of the Grothedieck–Katz p-curvature conjecture and the conjecture of Ogus for some classes of abelian varieties over number fields. The Grothendieck–Katz ...
• #### Algorithms and Models for Genome Biology ﻿

(2014-02-25)
New advances in genomic technology make it possible to address some of the most fundamental questions in biology for the first time. They also highlight a need for new approaches to analyze and model massive amounts of ...
• #### Alternate Compactifications of Hurwitz Spaces ﻿

(2012-12-19)
We construct several modular compactifications of the Hurwitz space $H^d_{g/h}$ of genus g curves expressed as d-sheeted, simply branched covers of genus h curves. They are obtained by allowing the branch points of the ...
• #### Amenability, Poincaré Series and Quasiconformal Maps ﻿

(Springer Verlag, 1989)
Any covering $Y \rightarrow X$ of a hyperbolic Riemann surface$X$ of finite area determines an inclusion of Teichmüller spaces $Teich(X) \hookrightarrow Teich(Y)$. We show this map is an isometry for the Teichmüller ...
• #### Amenable Coverings of Complex Manifolds and Holomorphic Probability Measures ﻿

(Springer Verlag, 1992)
• #### Amplification on Undirected Population Structures: Comets Beat Stars ﻿

(Springer Nature, 2017)
The fixation probability is the probability that a new mutant introduced in a homogeneous population eventually takes over the entire population. The fixation probability is a fundamental quantity of natural selection, and ...
• #### Anabelian Intersection Theory ﻿

(2012-12-19)
Let F be a field finitely generated and of transcendence degree 2 over $\bar{\mathbb{Q}}$. We describe a correspondence between the smooth algebraic surfaces X defined over $\bar{\mathbb{Q}}$ with field of rational ...
• #### Analysis of Some PDEs over Manifolds ﻿

(2013-02-14)
In this dissertation I discuss and investigate the analytic aspect of several elliptic and parabolic partial differential equations arising from Rimannian and complex geometry, including the generalized Ricci flow, Gaussian ...