Browsing Mathematics (Faculty of) by Supervisor "McKinnon, David"
Now showing items 1-6 of 6
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Approximation Constants for Closed Subschemes of Projective Varieties
(University of Waterloo, 2019-06-19)Diophantine approximation is a branch of number theory with a long history, going back at least to the work of Dirichlet and Liouville in the 1840s. The innocent-looking question of how well an arbitrary real algebraic ... -
Divisibility of Discriminants of Homogeneous Polynomials
(University of Waterloo, 2023-08-28)We prove several square-divisibility results about the discriminant of homogeneous polynomials of arbitrary degree and number of variables, when certain coefficients vanish, and give characterizations for when the discriminant ... -
Generalized GCDs as Applications of Vojta’s Conjecture
(University of Waterloo, 2023-08-31)Starting with an analysis of the result that for any coprime integers a and b, and some ϵ > 0, we have eventually that gcd(a^n − 1,b^n − 1) < a^ϵn holds for all n, we are motivated to look for geometric reasons why this ... -
Hurwitz Trees and Tropical Geometry
(University of Waterloo, 2016-01-21)The lifting problem in algebraic geometry asks when a finite group G acting on a curve defined over characteristic p > 0 lifts to characteristic 0. One object used in the study of this problem is the Hurwitz tree, which ... -
The Liftable Mapping Class Group
(University of Waterloo, 2017-07-19)Broadly, this thesis lies at the interface of mapping class groups and covering spaces. The foundations of this area were laid down in the early 1970s by Birman and Hilden. Building on these foundations, there has been a ... -
Rational approximations on smooth rational surfaces
(University of Waterloo, 2019-08-09)In this thesis, we study a conjecture made by D. McKinnon about rational approximations to rational points in algebraic varieties. The conjecture states that if a rational point P on a variety X lies on a rational curve, ...