## REUs Archive: 2012

### Research Experiences for Undergraduates at Emory University

**Number Theory**

#### Instructors

- David Zureick-Brown, Assistant Professor.
- Ken Ono, Asa Griggs Candler Professor.
- Robert Lemke Oliver, Emory PhD student.

#### Description of the 2012 project areas.

#### Participants

- Jennifer Bryson (Texas A&M University)
- David Corwin (Princeton University)
- Tony Feng (Harvard University)
- Zane Kun Li (Princeton University)
- Keenan Monks (Harvard University)
- Sarah Peluse (University of Chicago): 2014 Schafer Prize Winner
- Sarah Pitman (Emory University)
- Sarah Trebat-Leder (Princeton University)
- Lynnelle Ye (Stanford University)

#### Their results

- J. Bryson, K. Ono, S. Pitman, R. C. Rhoades,
Unimodal sequences and quantum and mock modular forms,
Proc. Natl. Acad. Sci. USA,
**109**No. 40 (2012), pages 16063-16067. - D. Corwin, T. Feng, Z. Li, and S. Trebat-Leder,
Elliptic curves with full 2-torsion and maximal adelic Galois representations,
Math. Comp.,
**83**(2014), pages 2925-2951. - K. Monks, S. Peluse, L. Ye,
Strings of special primes in arithmetic progressions,
Arkiv Math.,
**101**(2013), pages 219-234. - K. Monks, S. Peluse, L. Ye, Congruence properties of Borcherds product exponents,
Int. J. Numb. Th.,
**9**(2013), pages 1563-1578. - K. Monks and L. Ye, Congruences of concave composition functions, submitted for publication.
- S. Peluse, An infinite family of lacunary series, Ramanujan J., accepted for publication.

#### Application Materials (Due February 1, 2012)

A completed application consists of an application form , personal statement, two letters of recommendation, and current transcripts. These materials should be sent to:

Ken Ono

Department of Mathematics and Computer Science

Emory University

400 Dowman Drive

Atlanta, Georgia 30322