Now showing items 1-10 of 11
Open Gromov-Witten Invariants on Elliptic K3 Surfaces and Wall-Crossing
We defined a new type of open Gromov-Witten invariants on hyperK\"aher manifolds with holomorphic
Dynamics of HIV treatment and social contagion
Modern-day management of infectious diseases is critically linked to the use of mathematical models to understand and predict dynamics at many levels, from the mechanisms of pathogenesis to the patterns of population-wide ...
Holomorphically parametrized L2 Cramer's rule and its algebraic geometric applications
Suppose $f,g_1,\cdots,g_p$ are holomorphic functions over $\Omega\subset\cxC^n$. Then there raises a natural question: when can we find holomorphic functions $h_1,\cdots,h_p$ such that $f=\sum g_jh_j$? The celebrated Skoda ...
Singularities, Supersymmetry and Combinatorial Reciprocity
This work illustrates a method to investigate certain smooth, codimension-two, real submanifolds of spheres of arbitrary odd dimension (with complements that fiber over the circle) using a novel supersymmetric quantum ...
Entropy, Dimension and Combinatorial Moduli for One-Dimensional Dynamical Systems
The goal of this thesis is to provide a unified framework in which to analyze the dynamics of two seemingly unrelated families of one-dimensional dynamical systems, namely the family of quadratic polynomials and continued ...
Rational Point Counts for del Pezzo Surfaces over Finite Fields and Coding Theory
The goal of this thesis is to apply an approach due to Elkies to study the distribution of rational point counts for certain families of curves and surfaces over finite fields. A vector space of polynomials over a fixed ...
The Geometry of Hurwitz Space
We explore the geometry of certain special subvarieties of spaces of branched covers which we call the Maroni and Casnati-Ekedahl loci. Our goal is to understand the divisor theory on compactifications of Hurwitz space, ...
On Newforms for Split Special Odd Orthogonal Groups
The theory of local newforms has been studied for the group of \(PGL_n\) and recently \(PGSp_4\) and some other groups of small ranks. In this dissertation, we develop a newform theory for generic supercuspidal representations ...
Moduli of Galois Representations
The theme of this thesis is the study of moduli stacks of representations of an associative algebra, with an eye toward continuous representations of profinite groups such as Galois groups. The central object of study is ...
Pencils of quadrics and Jacobians of hyperelliptic curves
Using pencils of quadrics, we study a construction of torsors of Jacobians of hyperelliptic curves twice of which is Pic^1. We then use this construction to study the arithmetic invariant theory of the actions of SO2n+1 ...