REUs Archive: 2020

2020 Participants

  • Malik Amir
  • Aaron Benda
  • Talia Blum
  • Caroline Choi
  • Spencer Dembner
  • Kristen Fukunaga
  • Mitsuki Hanada
  • Alexandra Hoey
  • (Carina) Letong Hong
  • 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  

  1.  M. Amir and L. Hong, On L-functions of modular elliptic curves and certain K3 surfaces, Ramanujan Journal, accepted for publication.     
  2. 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, accepted for publication.
  3. S. Dembner and V. Jain, Hyperelliptic curves and newform coefficients,  Journal of Number Theory, 225 (2020), 214-239.  
  4. S. Dembner and V. Jain, A note on congruences for weakly holomorphic modular forms, Proceedings of the American Mathematical Society, accepted for publication.  
  5. M. Hanada and R. Madhukara, Fourier coefficients of level 1 Hecke eigenforms, Acta Arithmetica, recommended for publication.         
  6. 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.
  7. 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.
  8. 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.
  9. A. Panidapu and J. Thorner, The CM Sato-Tate distribution in short intervals, submitted.     

 

REU Management Team: Julie Bergner, Thomas Koberda, Thomas Mark, and Ken Ono