Browsing by FAS Department "Mathematics"
Now showing items 1-20 of 486
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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 ... -
3264 and all that
(Cambridge University Press, 2016) -
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 ... -
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
(National Academy of Sciences, 2010)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 ... -
Achiral symmetry breaking and positive Gaussian modulus lead to scalloped colloidal membranes
(2017)In the presence of a non-adsorbing polymer, monodisperse rod-like particles assemble into colloidal membranes, which are one rod-length thick liquid-like monolayers of aligned rods. Unlike 3D edgeless bilayer vesicles, ... -
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 ... -
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 ...