2020 Participants
- Malik Amir
- Aaron Benda
- Talia Blum
- Caroline Choi
- Spencer Dembner
- Kristen Fukunaga
- Mitsuki Hanada
- Alexandra Hoey (2022 Alice T. Schafer Prize, Honorable Mention)
- (Carina) Letong Hong (2023 Morgan Prize Winner, 2022 Alice T. Schafer Prize Winner, 2022 Rhodes Scholar)
- Jonas Iskander
- Vanshika Jain (2021 Alice T. Schafer Prize, Honorable Mention)
- Tanmay Khale
- Kaya Lakein
- Dounia Lazreq
- Nathan Li
- Rachana Madhukara
- Chloe Marcum
- Thomas Martinez
- Sarah Nicholls
- Andrew Nguyen
- Cooper O'Kuhn
- Apoorva Panidapu
- Madelynn Roche
- Alec Sun
- Sabrina Traver
- Devin Vanyo
- Chase Wilson
- Shengtong Zhang
2020 Activities
June 8, 2020: First Day of the Program
June 10, 2020: Black Lives Matter Observance
Geometry and Topology Research Projects
- 2D-TQFTs
- Subgroups of PSL_2(R)
- Braided disks in 4-space
Number Theory Research Projects
- Distribution of Primes
- Class Numbers and Elliptic curves (Lower bounds for class numbers)
- Modular forms (Variants of Lehmer's Conjecture)
REU Invited Speakers
- Ken Ribet (UC Berkeley): June 16 (Tuesday): 4:00pm
"A brief History of Fermat's Last Theorem for REU Students"
Slides Here
Cloud Recording (Password: 0Y*t8g%!) - Sang-hyun Kim (Korea Institute for Advanced Study): June 24 (Wednesday): 8:00pm
"Acute triangulations of the sphere."
Slides Here - James Maynard (Oxford University): June 25 (Thursday): 10:00am
"Patterns in Primes"
Slides Here
Cloud Recording (Password: 2Q.FhJW=) - Lillian Pierce (Duke University): June 30 (Tuesday): 4:00pm
"The method of Moments: Examples in Number Theory" - Henri Darmon (McGill University): July 7 (Tuesday): 4:00pm
"The theory of complex multiplication and the arithmetic of real quadratic fields”
Slides Here
Cloud Recording(coming soon) - Maryna Viazovska (EPFL, Lausaunne): July 9 (Thursday), 10:00am
"From uncertainty principles to sphere packings"
Slides Here
Cloud Recording (Password: 3R+5wHS.)
REU Mini-Courses (1:00pm - 2:00pm)
- Essentials of topology and geometry of manifolds (First week)
(Instructors: Julie Bergner, Thomas Koberda, Tom Mark) - Beyond the Mordell-Weil Theorem (June 11, 12, 15)
(Instructor: Charlotte Ure) - Complex multiplication: Constructing Hilbert class fields (June 16, 17, 18)
(Instructor: Jinbo Ren) - Representation Theory and Symmetric Groups (June 19, 22, 23, 24, 25, 26)
(Instructor: You Qi) - Brauer Groups: What are they and what are they good for? (June 29, 30, July 1, 2, 3)
(Instructor: Evangelia Gazaki)
July 4, 2020: 4th of July Holiday
July 17, 2020: Research Symposium
2020 Results
- M. Amir and L. Hong, On L-functions of modular elliptic curves and certain K3 surfaces, Ramanujan Journal, accepted for publication.
- T. Blum, C. Choi, A. Hoey, J. Iskander, K. Lakein, and T. Martinez, On class numbers, torsion subgroups, and quadratic twists of elliptic curves, Transactions of the American Mathematical Society, 375 (2021), no.1, 351–368.
- S. Dembner and V. Jain, Hyperelliptic curves and newform coefficients, Journal of Number Theory, 225 (2020), 214-239.
- S. Dembner and V. Jain, A note on congruences for weakly holomorphic modular forms, Proceedings of the American Mathematical Society, 149 (2021), 3683-3686.
- M. Hanada and R. Madhukara, Fourier coefficients of level 1 Hecke eigenforms, Acta Arithmetica, 200 (2021), no. 4, 371–388
- L. Hong and S. Zhang, Towards Heim and Neuhauser's unimodality conjecture on the Nekrasov-Okounkov polynomials, Research in Number Theory, 7 (2021), Art. 17.
- L. Hong and S. Zhang, Proof of the Ballantine-Merca Conjecture and theta function identities modulo 2, Proceedings of the American Mathematical Society, accepted for publication.
- T. Khale, C. O'Kuhn, A. Panidapu, A. Sun, and. S. Zhang, A Bombieri-Vinogradov Theorem for primes in short intervals and small sectors, Journal of Number Theory (229), 2021, 142-167.
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A. Panidapu and J. Thorner, The CM Sato-Tate distribution in short intervals, Involve, accepted for publication.
REU Management Team: Julie Bergner, Thomas Koberda, Thomas Mark, and Ken Ono