Now showing items 1-11 of 11

• #### 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 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 ...
• #### Automorphisms of Even Unimodular Lattices and Unramified Salem Numbers ﻿

(Elsevier, 2002)
In this paper we study the characteristic polynomials $S(x)=\det(xI−F| II_{p,q})$ of automorphisms of even unimodular lattices with signature $(p,q)$. In particular, we show that any Salem polynomial of degree $2n$ ...
• #### Cyclotomic Factors of Coxeter Polynomials ﻿

(Elsevier, 2009)
In this paper we show that the cyclotomic factors of the En Coxeter polynomials depend only on the value of $n$ mod 360, and come exclusively from spherical subdiagrams.
• #### A Formula for Some Shalika Germs ﻿

(2015-05-17)
In this article, for nilpotent orbits in (the Lie algebras of) ramified quasi-split unitary groups with two Jordan blocks, we give the values of their Shalika germs at certain equi-valued elements with half-integral depth ...
• #### On Cubic Rings and Quaternion Rings ﻿

(Elsevier, 2009)
In this paper, we show that the orbits of some simple group actions parametrize cubic rings and quaternion rings.
• #### On Newforms for Split Special Odd Orthogonal Groups ﻿

(2013-09-18)
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 ...
• #### On the Arithmetic of Hyperelliptic Curves ﻿

(2016-05-06)
My research involves answering various number-theoretic questions involving hyperelliptic curves. A hyperelliptic curve is a generalization of elliptic curves to curves of higher genus but which still have explicit ...
• #### On the Moy-Prasad Filtration and Stable Vectors ﻿

(2016-05-19)
Let K be a maximal unramified extension of a nonarchimedean local field of residual characteristic p > 0. Let G be a reductive group over K which splits over a tamely ramified extension of K. To a point x in the Bruhat–Tits ...
• #### Pencils of quadrics and Jacobians of hyperelliptic curves ﻿

(2013-10-08)
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 ...
• #### A Rigid Irregular Connection on the Projective Line ﻿

(Princeton University, 2009)
In this paper we construct a connection ∇ on the trivial G-bundle on P1 for any simple complex algebraic group G, which is regular outside of the points 0 and ∞, has a regular singularity at the point 0, with principal ...