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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 ...
Cascades in the Dynamics of Measured Foliations
(Elsevier Masson, 2014-03-14)
Modularity of some elliptic curves over totally real fields
(2014-06-06)
In this thesis, we investigate modularity of elliptic curves over a general totally real number field, establishing a finiteness result for the set non-modular j-invariants. By analyzing quadratic points on some modular ...
Regeneration of Elliptic Chains with Exceptional Linear Series
(2014-06-06)
We study two dimension estimates regarding linear series on algebraic curves. First, we generalize the classical Brill-Noether theorem to many cases where the Brill-Noether number is negative. Second, we extend results of ...
The complex geometry of Teichmüller space
(2014-06-06)
We study isometric maps between Teichmüller spaces and bounded symmetric domains in their Kobayashi metric. We prove that every totally geodesic isometry from a disk to Teichmüller space is either holomorphic or anti-holomorphic; ...
The Eigencurve is Proper
(2014-06-06)
Coleman and Mazur constructed a rigid analytic curve Cp,N, called the eigencurve, whose points correspond to all finite slope overconvergent p-adic eigenforms. We prove the conjecture that the eigencurve Cp,N is proper ...
Arithmetic Properties of Moduli Spaces and Topological String Partition Functions of Some Calabi-Yau Threefolds
(2014-06-06)
This thesis studies certain aspects of the global properties, including geometric and arithmetic, of the moduli spaces of complex structures of some special Calabi-Yau threefolds (B-model), and of the corresponding topological ...
Open Gromov-Witten Invariants on Elliptic K3 Surfaces and Wall-Crossing
(2013-10-08)
We defined a new type of open Gromov-Witten invariants on hyperK\"aher manifolds with holomorphic
Compact Generation of the Category of D-Modules on the Stack of G-Bundles on a Curve
(2013)
The goal of the paper is to show that the (derived) category of D-modules on the stack \(Bun_G(X)\) is compactly generated. Here X is a smooth complete curve, and G is a reductive group. The problem is that \(Bun_G(X)\) ...
Contractibility of the space of rational maps
(Springer Science + Business Media, 2012)
We define an algebro-geometric model for the space of rational maps from a smooth curve X to an algebraic group G, and show that this space is homologically contractible. As a consequence, we deduce that the moduli space ...