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Now showing items 1-10 of 67

#### Towards an Instanton Floer Homology for Tangles

(2012-08-10)

In this thesis we investigate the problem of defining an extension of sutured instanton Floer homology to give an instanton invariant for a tangle. We do this in three separate steps. First, we investigate the representation ...

#### The Arithmetic of Simple Singularities

(2012-08-10)

We investigate some arithmetic orbit problems in representations of linear algebraic groups arising from Vinberg theory. We aim to give a description of the orbits in these representations using methods with an emphasis ...

#### Local-Global Compatibility and the Action of Monodromy on nearby Cycles

(2012-12-19)

In this thesis, we study the compatibility between local and global Langlands correspondences for \(GL_n\). This generalizes the compatibility between local and global class field theory and is related to deep conjectures ...

#### 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 ...

#### D-Modules on Spaces of Rational Maps and on Other Generic Data

(2012-12-13)

Fix an algebraic curve X. We study the problem of parametrizing geometric data over X, which is only generically deﬁned. E.g., parametrizing generically deﬁned maps from X to a fixed target scheme Y. There are three methods ...

#### 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 ...

#### The Geometry of the Weil-Petersson Metric in Complex Dynamics

(2014-06-06)

In this work, we study an analogue of the Weil-Petersson metric on the space of Blaschke products of degree 2 proposed by McMullen. We show that the Weil-Petersson metric is incomplete and study its metric completion. Our ...

#### 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; ...

#### Chiral Principal Series Categories

(2014-06-06)

This thesis begins a study of principal series categories in geometric representation theory using the Beilinson-Drinfeld theory of chiral algebras. We study Whittaker objects in the unramified principal series category. ...

#### Relative Jacobians of Linear Systems

(2014-06-06)

Let X be a smooth projective variety. Given any basepoint-free linear system, |D|, there is a dense open subset parametrizing smooth divisors, and over that subset, we can consider the relative Picard variety of the universal ...