Gregory Knapp | PIMS - Pacific Institute for the Mathematical Sciences

PIMS Postdoctoral Fellow, University of Calgary

Greg grew up in Centerville, Ohio in the US and graduated with his bachelor’s and master’s degrees from Case Western Reserve University. His master’s thesis was completed under the supervision of Colin McLarty and covered Minkowski’s Linear Forms Theorem in Elementary Function Arithmetic, a subsystem of first-order arithmetic. Greg then went to the University of Oregon for his PhD, and he completed his dissertation on the topic of polynomial root distribution and Thue equations under the supervision of Shabnam Akhtari. Greg is now a PIMS postdoctoral fellow at the University of Calgary where he is working with Khoa Nguyen. Outside of math, he enjoys rock climbing, disc golf, learning new hobbies, and playing all types of games.

Distances between the roots of a fixed polynomial appear organically in many places in number theory. For any $f(x) \in \mathbb{Z}[x]$, let $\operatorname{sep}(f)$ denote the minimum distance between distinct roots of $f(x)$. Mahler initiated the...

Let $d>k$ be positive integers. Motivated by an earlier result of Bugeaud and Nguyen, we let $E_{k,d}$ be the set of $(c_1,\ldots,c_k)\in\mathbb{R}_{\geq 0}^k$ such that $\vert\alpha_0\vert\vert\alpha_1\vert^{c_1}\cdots\vert\alpha_k\vert^{c_k}\geq 1$...

In 1909, Thue proved that when $F(x,y)$ is an irreducible, homogeneous, polynomial with integer coefficients and degree at least 3, the inequality $\left\| F(x,y) \right\| \leq h$ has finitely many integer-pair solutions for any positive $h$. Because...

In 1909, Thue proved that when $F(x,y) \in \mathbb{Z}[x,y]$ is irreducible, homogeneous, and has degree at least 3, the inequality $|F(x,y)| \leq h$ has finitely many integer-pair solutions for any positive $h$. Because of this result, the inequality...