I am a Professor in the Mathematics Department at the University of Michigan.
Want to know more about me? Here is my curriculum vitae.
Trying to find me? Here is my schedule.
Teaching and Mentoring |
I am currently teaching Math 677 (Diophantine Problems).
My current PhD student is Trevor Hyde. My former PhD students are Brian Wyman, Ben Weiss, Alex Mueller, Zach Scherr, and Sijun Liu.
I am also the mentor of the NSF Postdoctoral Fellow Danny Neftin and the AMS-Simons Travel Grant mentor of my former students Zach Scherr and Ben Weiss, and I have mentored several REU students. Here is my full list of educational activities, and here is a page of electronic resources for Michigan faculty and students.
Undergraduate research |
This summer I will lead a group of about eight students in a research project in which students will do combinatorial and group-theoretic work in order to make progress on important problems in topology and algebra. In addition to proving new results, students will learn relevant tools from group theory, topology, and analysis that lie behind the connection of the concrete questions being studied with the topological and algebraic problems that motivate it. Interested students are encouraged to email me.
Research |
My research covers topics in algebra, number theory, algebraic geometry,
dynamical systems, discrete mathematics, complex analysis, theoretical computer science, and cryptography.
I have written 54 papers with
51 coauthors.
I previously worked at the
Center for Communications Research
in Princeton,
where I wrote over thirty proprietary papers.
Selected papers |
See also my full publication list and list of abstracts.
33. | Linear relations between polynomial orbits, with D. Ghioca and T. Tucker, Duke Math. J. 161 (2012), 1379–1410. | |
27. | A new family of exceptional polynomials in characteristic two, with R. Guralnick and J. Rosenberg, Annals of Math. 172 (2010), 1367–1396. | |
26. | Polynomials with PSL(2) monodromy, with R. Guralnick, Annals of Math. 172 (2010), 1321–1365. | |
24. | Intersections of polynomial orbits, and a dynamical Mordell-Lang conjecture, with D. Ghioca and T. Tucker, Inventiones Math. 171 (2008), 463–483. | |
12. | Curves of every genus with many points, II: Asymptotically good families, with N. Elkies, E. Howe, A. Kresch, B. Poonen and J. Wetherell, Duke Math. J. 122 (2004), 399–422. |
Coauthors |
Ram Abhyankar (Purdue) Simeon Ball (Catalunya) Bob Beals (Reinaissance) Manjul Bhargava (Princeton) Steve Cohen (Glasgow) János Csirik (D.E. Shaw) David desJardins (philanthrope) Iwan Duursma (Illinois) Noam Elkies (Harvard) Xander Faber (Hawaii) Rainer Fuhrmann (IBM) Arnaldo Garcia (IMPA) Dragos Ghioca (UBC) Danny Goldstein (IDA/CCR-L) Bob Guralnick (USC) Everett Howe (IDA/CCR-L) Ben Hutz (Florida Tech) |
Patrick Ingram
(Colorado State) Rafe Jones (Carleton) Neeraj Kayal (Microsoft) Andrew Kresch (Zurich) Dijana Kreso (Graz) Holly Krieger (MIT) Greg Kuperberg (UC Davis) Hendrik Lenstra (Leiden) Aaron Levin (Michigan State) Karl-Olaf Lindahl (Växjö) Richard Lyons (Rutgers) Michelle Manes (Hawaii) Ariane Masuda (City Tech) Gwyneth Moreland (Michigan) Gary Mullen (Penn State) Peter Müller (Würzburg) Harald Niederreiter (RICAM) |
Bjorn Poonen (MIT) Eric Rains (Caltech) Joel Rosenberg (IDA/CCR-L) Julian Rosen (Waterloo) Zach Scherr (Penn) Ari Shnidman (Michigan) Igor Shparlinski (UNSW) Fernando Torres (Campinas) Tom Tucker (Rochester) Felipe Voloch (Texas) Ben Weiss (Maine) Joe Wetherell (IDA/CCR-L) Doug Wiedemann (IDA/CCR-P) Brian Wyman (Pinnacle Entertainment) Jiaowen Yang (Tsinghua) Yu Yasufuku (Nihon) David Yuen (Lake Forest) |
Disambiguation |
I am not a midwestern artist versed in eastern spirituality, a Minneapolis motorcyclist nicknamed "The Dude", or an MIT basketball player who played high school tennis in Seattle. However, I am the winner of the Cryan tennis tournament and other tournaments in New Jersey.