Benjamin L. Weiss
Department of Mathematics & Statistics
University of Maine
5752 Neville Hall, Room 333
Orono, ME 04469-5752
Office: 418 Neville Hall, University of Maine
Office Phone: (207) 581-3902
Here is my
I am interested in most forms of number theory and geometry. My main focus is analytic and algebraic number theory. I also enjoy convex geometry and its applications. I am particularly fond of function fields and local fields. I have worked with Galois groups, class groups, quadratic forms, and applications of Poisson summation.
My thesis research is in classifying pairs of polynomials f(X), g(Y), so that f(X) = g(Y) has infinitely many rational solutions. This work is based on papers of R.M. Avanzi and U.M. Zannier, as well as Bilu and Tichy, Michael Fried, and Ritt.
Much of my work has been in density theorems, and probabilistic number theory. I am also doing research in additive number theory, and some circle method techniques. I enjoy sieve methods, although I have not done any original research in these areas.
I also enjoy ergodicity, in particular Mahler measure.
My graduate advisers were Michael Zieve, and Jeffrey Lagarias.
- “ Irreducible Curves G(X)=H(Y) With Genus At Most One.” My Doctoral Thesis, University of Michigan July 2011.
- “Chebyshev Mappings of Finite Fields,” American Math Monthly, 119-2 (2012), 151-155. Joint with Julian Rosen, Zachary Scherr, and Michael Zieve
- “Galois Groups of p-Adic Polynomials of Fixed Degree,” Journal of Number Theory, Volume 133, Pages 1537--1563. (2013).
- “Splitting Behavior of Sn-Polynomials,” Research in Number Theory, Volume 1, (2015). Joint with Jeffrey Lagarias.
- “The emergence of 4-cycles in polynomial maps over the extended integers.” With SMALL REU. Co-authors Andrew Best, Patrick Dynes, Steven Miller, Jasmine Powell
-Decompositions of differential equations from medical imaging. Joint with Douglas Weathers.
I have advised one masters student to date. Douglas Weathers graduated in Spring 2015 with the thesis Decompositions of the Kuchment-Lvin Polynomials.
I have also advised Addison Labonte (class of 2016) on her senior honors thesis about multi-magic squares and sudoku.
I am currently teaching Abstract Algebra (MAT 463)
I am also teaching Problem Solving Seminar (MAT 329)
Previously at UMaine I've taught
- MAT 563 and MAT 564 (the graduate algebra sequence)
- MAT 228 (Multi-Variable Calculus)
- MAT 261 (Introduction to Proofs)
- MAT 262 (Linear Algebra)
- MAT 463 (Undegraduate Abstract Algebra)
Here is an incomplete list of textbooks and repositories of textbooks that are using open licenses. Please browse at your leisure, and contact me with any missing books or repositories that you have found useful.
In my free time I enjoy playing bridge. In the summer of 2009, four Michigan students and I won the Grand National Teams
in flight C. You can read about it here.
I have previously spent many years tap dancing, performing some theatre, and volunteering as an EMT.
These days most of my free time is spent chasing my son, Joel, and daughter, Shoshanah. My wife's photoblog can be found here.
Last updated on October 28th, 2016.
Thank you to Zach Scherr for the website design.