### Research Experiences for Undergraduates at Emory University

**Number Theory**

#### Dates: June 8- July 17, 2015.

#### Math Building, Rooms E406 and E408

#### Instructors

- David Zureick-Brown, Assistant Professor.
- Ken Ono, Asa Griggs Candler Professor.
- Michael Mertens Postdoctoral Fellow, (Emory)
- Jesse Thorner, (Emory) Graduate Student.
- Sarah Trebat-Leder, NSF Graduate Fellow, (Emory)

#### Basic Information

The PI has been organizing REU programs since 2003 (formerly at U. Wisconsin (Madison) from 2003-2009). He has advised over 100 students including 4 Morgan Prize Winners and 4 Schafer Prize winners. The REU alums have won numerous other honors including Marshall Scholarships, NSF Graduate Fellowships (over 30), etc...

Thanks to the generous support of the National Science Foundation and Emory University, we are again organizing a summer Research Experience in Mathematics for the summer of 2014 on the beautiful campus of Emory University (adjacent to the Centers for Disease Control and Prevention (CDC)). We seek to fill 8-10 openings in the REU. Most of the participants will be US citizens or permanent residents who are presently enrolled in a US undergraduate institution or high school. We have offered openings to high school students who are adequately prepared for the program. NSF supported participants will receive a $3600 stipend and free accomodations.

#### 2015 Project areas

- Elliptic curves and Galois representations
- Mock modular and quantum modular forms
- Additive Number Theory
- Distribution of Primes
- Moonshine

#### Participants

- Lea Beneish (Indiana University)
- Evan Chen (2019 Morgan Prize, Runner-Up) (MIT)
- Claire Frechette (Brown University)
- Aaron Landesman (Harvard University): 2017 Morgan Prize, Runner-Up
- Hannah Larson (Harvard University), 2017 Schafer Prize Winner, 2024 Breakthrough Mirzakhani New Frontiers Prize
- Maddie Locus (University of Georgia)
- Peter Park (Princeton University)
- Peter Ruhm (Stanford University)
- Ashvin Swaminathan (Harvard University) (2018 Morgan Prize Winner)
- Robin Zhang (Stanford University)

#### Their results

- E. Alwaise, R. Dicks, J. Friedman, L. Gu, Z. Harner, H. Larson, M. Locus, I. Wagner, and J. Weinstock, Shifted distinct-part partition identities in arithmetic progressions, Annals of Combinatorics,
**21**(2017), 479-494. - L. Beneish and C. Frechette, p-adic properties of certain half-integral weight modular forms, J. Number Theory
**168**(2016), 413-432. - E. Chen, P. Park, and A. Swaminathan, Linnik's Theorem for Sato-Tate laws on elliptic curves with complex multiplication, Research in Number Theory
**1**(2015), 28. - E. Chen, P. Park, and A. Swaminathan, On logarithmically Benford sequences, Proceedings of the American Mathematical Society
**144**(2016), 4599-4608. - E. Chen, P. Park, and A. Swaminathan, Elliptic curve variants of the least quadratic nonresidue problem and Linnik's Theorem, Int. J. Number Th.
**14**(2018), 255-288. - A. Landesman, P. Ruhm, and R. Zhang, Spin canonical rings of log stacky curves, Annales de L'Insitut Fourier
**66**(2016), 2339-2383. - A. Landesman, P. Ruhm, and R. Zhang, Section rings of Q-divisors on minimal rational surfaces, Mathematical Research Letters,
**25**(2015), 1329-1357. - H. Larson, Generalized Andrews-Gordon style identities, Research in Number Theory
**1**(2015), 13. - H. Larson, Modular units from quotients of Rogers-Ramanujan style q-series Proceedings of the American Mathematical Society
**144**(2016), 4169-4182. - H. Larson, Proof of a conjecture regarding the level of Rose's generalized sum-of-divisor functions, Research in Number Theory
**1**(2015), 16. - H. Larson, Coefficients of McKay-Thompson series and distributions of the moonshine module, Proceedings of the American Mathematical Society,
**144**(2016), 4183-4197.