Greg Knapp
Positions
Postdoctoral Associate
Faculty of Science, Department of Mathematics and Statistics
Contact information
Background
Educational Background
PhD Mathematics, University of Oregon,
MS Mathematics, Case Western Reserve University,
BS Mathematics, Case Western Reserve University,
BA Philosophy, Case Western Reserve University,
Research
Areas of Research
I search for efficient bounds on the number of integer solutions to Thue equations. My work has thus far focused on improving a counting technique often associated with the gap principle and I have concrete improvements for explicit bounds on the number of integer solutions to trinomial Thue equations.
I am investigating bounds on the separation of a polynomial in terms of that polynomial's Mahler measure. The separation of a polynomial is the minimum distance between two roots of that polynomial. While lower bounds on the separation have been thoroughly studied, I focus on finding upper bounds on separation as a way to quantify how "uniform" the distribution of roots of polynomials with real coefficients is.
Courses
| Course number | Course title | Semester |
|---|---|---|
| MATH 211 | Linear Methods I | Fall 2023 |
Awards
- Anderson Graduate Teaching Award, University of Oregon Department of Mathematics. 2022
Publications
- The Number of Solutions to the Trinomial Thue Equation. Functiones et Approximatio Commentarii Mathematici.
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