Visiting Assistant Professor
The University of Wisconsin-Madison
office: Van Vleck 413
office hours for Spring 2017: by appointment. Send me an email!
Before I came to Madison, I did my PhD at the University of Texas at Austin under the supervision of Jeffrey D. Vaaler. You can see my old webpage from graduate school here.
Fall 2016: Math 221: Calculus and Analytic Geometry
Fall 2015: Math 221: Calculus and Analytic Geometry
Spring 2014: Math 341: Linear Algebra (Honors)
Fall 2014: Math 221: Calculus and Analytic Geometry
I like algebraic number theory, heights, and diophantine geometry. What does this mean?
I am interested in the solutions of polynomial equations in one variable (the theory of algebraic numbers), and in the algebraic solutions to polynomial equations in several variables (diophantine geometry). I am especially interested in heights, which are real-valued functions that measure the complexity of an algebraic number or an algebraic point on a variety. Most of my research has focused on studying properties of heights (especially lower bounds) over infinite extensions of the rational numbers. This is motivated by applications to diophantine equations, where a powerful tool is to compare height estimates to prove that equations don't have too many solutions. I'm also interested in lower bounds for heights for their own sake, and especially in Lehmer's Problem.
I also like: elliptic curves, Galois theory, group theory, arithmetic statistics, computing things (SAGE, GAP, MAGMA).
Here are my papers, etc.
⊕ 9/7/13-9/8/13: PANTS XX, Davidson College
⊗ 10/5/13-10/6/13: Maine-Québec Number Theory Conference, University of Maine
⊕ 11/25/13-12/4/13: Heights in diophantine geometry, group theory, and combinatorics, ESI, Vienna
⊕ 7/14/14-7/25/14: Second ERC: Diophantine Geometry, Unlikely Intersections and Algebraic Dynamics, Cetraro, Italy
⊗ 5/1/15-5/3/15: Atkin Memorial Lecture and Workshop: Expansion in Linear Groups, University of Illinois at Chicago
⊕ 8/11/15-8/15/15: Arithmetic 2015: Silvermania, Brown University
⊗ 10/5/15-10/9/15: The Geometry, Algebra, and Analysis of Algebraic Numbers, Banff International Research Station
⊕ 1/6/16-1/9/16: Joint Math Meetings, Seattle
⊗ 3/12/16-3/16/16: Arizona Winter School 2016, Tucson
⊗ 4/2/16-4/3/16: SERMON XXIX James Madison University
⊕ 9/10/16-9/11/16: Super QVNTS: Kummer Classes and Anabelian Geometry University of Vermont
⊗ 10/8/16-10/9/16: Québec-Maine Number Theory Conference, Université Laval
⊕ 12/3/16-12/4/16: PANTS XVII, University of South Carolina
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