Courses taught:

At Michigan:
Fall 2012: Math 593: Algebra I
Fall 2012: Math 676: Algebraic Number Theory
Fall 2011: Math 185: Honors Calculus I
Winter 2011: Math 389: Explorations in Mathematics
Fall 2010: Math 676: Algebraic Number Theory
Winter 2010: Math 711: The Arithmetic of Dynamical Systems
Fall 2009: Math 156: Applied Honors Calculus II

At Rutgers:
Fall 2007: Math 481: Mathematical Theory of Statistics

At USC:
Fall 1998: Number Theory
Fall 1998: Engineering Calculus
Fall 1997: Engineering Calculus
Fall 1997: Business Calculus

Graduate (PhD) students supervised:
Sijun Liu
Alex Mueller
Zach Scherr (will graduate in 2013 and be a postdoc at Penn)
Ben Weiss  (graduated 2011; will begin a tenure-track position at Maine in September 2013)
Brian Wyman  (graduated 2010; works at Edgestream Partners, L.P.)

Postdoctoral researcher supervised:
Danny Neftin, 2011– present. (will begin an NSF Postdoctoral fellowship in September 2013)

High school research supervised:
Gwyneth Moreland, 2013 (Mathematics Research course for high school credit)
Zhi Ren, 2012 (won the Silver Medal at the 2012 Shing-Tung Yau High School Mathematics Awards)

Undergraduate research supervised:
2012: 16 students: see my REU webpage
2011: Molly Logue & Dominic Spadacene
2011: Geoffrey Iyer & Feiqi Jiang
2010: Alex Carney & Ruthi Hortsch
2010: Augustus Odena
2002: Kate Gruher, Andrew Snowden, and three others at NSA's DSP program

Awards: Kate won the Schafer prize in 2003; Ruthi was runner-up in 2011; in 2013, my student Susan Xia was the runner-up, and my student Thao Do received honorable mention.

I will not mentor REU students in 2013, due to lack of funding.


Joint papers with undergraduates, graduate students, or postdocs since 2007:
17. Planar monomials in characteristic 2, with Z. Scherr, submitted for publication.
16. On the set of periodic orbits of a polynomial over a ring, with G. Iyer and F. Jiang, in preparation.
15. Polynomial decomposition over rings, with B. Wyman, in preparation.
14. On the rate of growth of backwards orbits of rational functions, with arithmetic applications, with M. Logue and D. Spadacene, in preparation.
13. Uniform bounds on polynomial preimages, with A. Carney and R. Hortsch, in preparation.
12. Variants of Belyi's theorem, with E. Brooks, J. Rosen, Z. Scherr and B. Weiss, in preparation.
11. How to beat the Taxman, with D. Spadacene, in preparation.
10. A new proof of the Segre–Bartocci conjecture, with K. Carde, in preparation.
9. Integral points in grand orbits, with A. Shnidman, submitted for publication.
8. Uniform bounds on primitive prime divisors in dynamical sequences, with J. Rosen, submitted for publication.
7. Chebyshev mappings of finite fields, with J. Rosen, Z. Scherr and B. Weiss, Amer. Math. Monthly 119 (2012), 151–155.
6. Two questions on polynomial decomposition, with B. Wyman, Quarterly Journal of Math. (Oxford) 63 (2012), 507–511.
5. On hyperbolic fixed points in ultrametric dynamics, with K.-O. Lindahl, p-Adic Numbers, Ultrametric Analysis and Applications 2 (201), 232–240.
4. Uniform bounds on pre-images under quadratic dynamical systems, with X. Faber, B. Hutz, P. Ingram, R. Jones, M. Manes and T. Tucker, Math. Research Letters 16 (2009), 87–101.
3. Permutation binomials over finite fields, with A. Masuda, Trans. Amer. Math. Soc. 361 (2009), 4169–4180.
2. Rational functions with linear relations, with A. Masuda, Proc. Amer. Math. Soc. 136 (2008), 1403–1408.
1. Nonexistence of permutation binomials of certain shapes, with A. Masuda, Electronic J. Combinatorics 14 (2007), N12.



Seminar:
Since arriving in Michigan in Fall 2009, I have run the Number Theory Learning Seminar, aimed at exposing graduate students to various topics. In Winter 2010 this included background lectures in preparation for the Michigan Lectures in Number Theory.


Conferences organized:
Global Arithmetic Dynamics  (March 2012)
Midwest Number Theory Day  (November 2010)
Midwest Number Theory Conference for Graduate Students and Recent PhD's  (November 2010)


Other activities:
In 2012 I served as a judge for high school research contests in Hong Kong and Beijing.
In 2012 I ran Michigan's REU program, and doubled the size of the program while increasing the number of applicants by 500%.
In 2011 I initiated a series of talks by Michigan's REU students, which has now become a fixture in our REU program.
In 2011 I was a judge of undergraduate research at the OSU Young Mathematicians Conference, and served on a panel about graduate programs there.
In 2010–2012 I ran two sessions of Michigan's Math Circle for high school students, and four for middle school students.
In 2010 I gave a lecture for high school students in the AMS program Who Wants to be a Mathematician.
In 2003 I gave a lecture for the Thomas Grover Middle School Math Club, and visited the club several times after that.
From 2000–2005 I was a problem supported for the USA Mathematics Talent Search.
In 2000 I gave lectures and mentored four students at the Arizona Winter School, where I also served on a panel about mathematical opportunities outside academia. Three of my mentees became mathematicians: Frank Calegari, Hiren Maharaj, and David Savitt.