I am a Professor in the Mathematics Department at the University of Michigan.
Want to know more about me? Here is my curriculum vitae.
Teaching and Mentoring |
In Fall 2020 I am teaching Math 493 and Math 676
My current PhD students are GilYoung Cheong and Yifeng Huang. My former PhD students are Trevor Hyde, Sijun Liu, Alex Mueller, Andrew O'Desky, Zach Scherr, Ben Weiss, and Brian Wyman (and officially Qian Yin, although she was really a student of Mario Bonk).
I am also the AMS-Simons Travel Grant mentor of Zach Scherr. Here is my full list of educational activities, and here is a page of electronic resources for Michigan faculty and students.
I frequently mentor the research of high school students, especially through MIT's PRIMES program, and REU students.
Research |
My research uses algebraic methods to treat topics in various areas of math, including
algebra, number theory, algebraic geometry,
dynamical systems, discrete mathematics, complex analysis, algebraic topology,
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) Zhiguo Ding (Hunan) Thao Do (Akuna) Iwan Duursma (Illinois) Noam Elkies (Harvard) Xander Faber (IDA/CCS) Rainer Fuhrmann (IBM) Arnaldo Garcia (IMPA) Dragos Ghioca (UBC) Danny Goldstein (IDA/CCR-L) Bob Guralnick (USC) Everett Howe (Minister) Ben Hutz (Saint Louis) |
Patrick Ingram
(York) Rafe Jones (Carleton) Zhan Jiang (Michigan) Neeraj Kayal (Microsoft) Andrew Kresch (Zurich) Dijana Kreso (Graz) Holly Krieger (Cambridge) Greg Kuperberg (UC Davis) Goyar Kyureghyan (Rostock) Hendrik Lenstra (Leiden) Aaron Levin (Michigan State) Karl-Olaf Lindahl (Linnæus) Richard Lyons (Rutgers) Michelle Manes (Hawaii) Ariane Masuda (City Tech) Gwyneth Moreland (Harvard) Gary Mullen (Penn State) Peter Müller (Würzburg) Danny Neftin (Technion) Harald Niederreiter (RICAM) |
Bjorn Poonen (MIT) Xiaoer Qin (Yangtze) Eric Rains (Caltech) Joel Rosenberg (IDA/CCR-L) Julian Rosen (Maine) Zach Scherr (Susquehanna) Ari Shnidman (Jerusalem) Igor Shparlinski (UNSW) Kenta Suzuki (high school) Fernando Torres (Campinas) Tom Tucker (Rochester) Felipe Voloch (Canterbury) Ben Weiss Joe Wetherell (IDA/CCR-L) Doug Wiedemann (IDA/CCR-P) Brian Wyman (Innovation) Jiaowen Yang (Facebook) Yu Yasufuku (Nihon) David Yuen (Hawaii) |
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.