Courses taught:

Fall 2018 (Michigan): Math 676: Algebraic Number Theory
Fall 2018 (Michigan): Math 116: Calculus II
Fall 2017 (Michigan): Math 116: Calculus II
Winter 2016 (Michigan): Math 594: Graduate Algebra II
Fall 2015 (Michigan): Math 419: Linear Spaces and Matrices
Winter 2015 (Michigan): Math 677: Diophantine Problems
Fall 2014 (Michigan): Math 676: Algebraic Number Theory
Fall 2014 (Michigan): Math 525: Probability
Spring 2014 (Tsinghua): Research Seminar on Functional Equations
Fall 2013 (Tsinghua): Algebraic Curves and Related Topics
Fall 2012 (Michigan): Math 593: Graduate Algebra I
Fall 2012 (Michigan): Math 676: Algebraic Number Theory
Fall 2011 (Michigan):
Math 185: Honors Calculus I
Winter 2011 (Michigan): Math 389: Explorations in Mathematics
Fall 2010 (Michigan): Math 676: Algebraic Number Theory
Winter 2010 (Michigan): Math 711: The Arithmetic of Dynamical Systems
Fall 2009 (Michigan): Math 156: Applied Honors Calculus II
Fall 2007 (Rutgers): Math 481: Mathematical Theory of Statistics
Fall 1998 (USC): Math 430: Number Theory
Fall 1998 (USC): Math 125: Engineering Calculus
Fall 1997 (USC): Math 125: Engineering Calculus
Fall 1997 (USC): Math 118: Business Calculus



Graduate (PhD) students supervised:
Andrew O'Desky (current)
GilYoung Cheong (current)
Yifeng Huang (current)
Trevor Hyde (current)
Sijun Liu  (graduated 2014 and moved to industry)
Alex Mueller  (graduated 2013 and joined a startup company)
Zach Scherr  (graduated in 2013 and became a postdoc at Penn)
Ben Weiss  (graduated 2011; subsequently tenure-track at Maine)
Brian Wyman  (graduated 2010; first job was at Edgestream Partners, L.P.)



Postdoctoral researchers supervised:
Efrat Bank, 2015–2018
Danny Neftin, 2011– 2015. (NSF Postdoctoral fellow 2013–2015)



High school research supervised:
Noah Luntzlara, 2017
Franklyn Wang, 2017 (MIT PRIMES program) (2018 Davidson Fellow, Siemens National Runner-Up, Regeneron National Finalist)
Felix Wang, 2016 (MIT PRIMES program) (2017 Davidson Fellow, Regeneron National Finalist)
Kenz Kallal, Matt Lipman and Felix Wang, 2015 (MIT PRIMES program) (Siemens Regional Finalists)
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:
(for more details, see my REU webpage)
2017: 2 students remotely
2015: 9 students
2014: 6 students at Tsinghua University
2012: 16 students
2011: Molly Logue and Dominic Spadacene
2011: Geoffrey Iyer and Feiqi Jiang
2010: Alex Carney and 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.



Joint papers with undergraduates, graduate students, or postdocs since 2007:
16. On the rate of growth of backwards orbits of rational functions, with arithmetic applications, with M. Logue and D. Spadacene, in preparation.
15. Near-injectivity of polynomial functions on number fields, with A. Carney and R. Hortsch, in preparation.
14. How to beat the Taxman, with D. Spadacene, in preparation.
13. Integral points in grand orbits, with A. Shnidman, submitted for publication.
12. Uniform bounds on primitive prime divisors in dynamical sequences, with J. Rosen, submitted for publication.
11. On factorizations of maps between curves, with D. Kreso, submitted for publication.
10. Uniform boundedness of S-units in arithmetic dynamics, with H. Krieger, A. Levin, Z. Scherr, T. Tucker, and Y. Yasufuku, Pacific J. Math. 274 (2015), 97–106.
9. Separated Belyi maps, with Z. Scherr, Math. Research Letters, to appear.
8. Some planar monomials in characteristic 2, with Z. Scherr, Annals of Combinatorics 18 (2014), 723–729.
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 and programs organized:
Workshop on Arithmetic Dynamics   (December 2015)
BIRS Workshop on The Art of Iterating Rational Functions over Finite Fields  (May 2013)
ICERM Workshop on Global Arithmetic Dynamics  (March 2012)
ICERM Semester Program on Complex and Arithmetic Dynamics  (January–May 2012)
AMS Special Session on Recent Directions in Number Theory  (October 2011)
Midwest Number Theory Day  (November 2010)
Midwest Number Theory Conference for Graduate Students and Recent PhD's  (November 2010)



Other activities:
In 2014 I taught a 22-hour course for high school students at the inaugural Tsinghua University Shing-Tung Yau Mathematics Summer Camp.
In 2013 I taught a semester-long course on elliptic curves as a volunteer at Community High School in Ann Arbor.
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.