REUs Archive: 2022

Number Theory and Representation Theory (June 6 - July 15, 2022)


  • Arithmetic functions over function fields
  • Arithmetic statistics
  • Modular forms
  • Partitions
  • Sato-Tate distributions for K3 surfaces

Number Theory and Representation Theory Participants 

  • Quanlin Chen
  • Catherine Cossaboom
  • Sanjana Das
  • Henry Glunz 
  • Annemily Hoganson (2023 Goldwater Scholar)
  • Daniel Hu 
  • Hari Iyer (2023 Goldwater Scholar)
  • Faye Jackson (2023 Alice T. Schafer Prize winner; 2024 Morgan Prize winner)
  • Thomas Jaklitsch
  • Hana Lang 
  • Misheel Otgonbayar
  • Sasha Shashkov  (2023 Goldwater Scholar)
  • Eric Shen 
  • Hamilton Wan 
  • Nancy Xu 
  • Sharon Zhou

Number Theory Colloquia Speakers (Thursdays at 3pm)

  • June 9th: Bjorn Poonen (MIT)
    "Ranks of elliptic curves
  • June 14th: Robert Schneider (Michigan Tech)
    "Making music with logarithms."
  • June 16th: James Maynard (Oxford) 
    "Patterns in the primes"
  • June 23rd: Lillian Pierce (Duke) 
  • June 30th: Jennifer Balakrishnan (Boston U) 
    "Mordell's conjecture and the last 100 years."
  • July 7th: Ken Ribet (UC Berkeley) 
    "A meandering history of Fermat's Last Theorem for UVA REU students"
  • July 12th at 2:00pm: Jacob Tsimerman (U Toronto)
    "The Ax-Grothendieck Theorem"
  • July 12th at 3:15pm: Robert Schneider (Michigan Tech)
    "Multiplicative theory of integer partitions"
  • July 14th: 2:00pm Toni Bluher (NSA) 
    “Difference sets, Galois theory, and an accidental isomorphism
  • July 14th: 3:00pm Amanda Folsom (Amherst) 
    "Quantum Jacobi forms and applications in number theory, topology, and mathematical physics"

Mini-Courses (1:00pm-2:00pm)

  • June 13, 15, 17: Prof. Valia Gazaki "Abelian Varieties"
  • June 20, 22, 24: Prof. You Qi "Representation Theory of the Symmetric Group"
  • June 27, 29, July 1: Prof. Charlotte Ure "Beyond the Mordell-Weil Theorem"

Number Theory Papers

  1. Quanlin Chen and Eric Shen, On effective Sato-Tate distributions for surfaces arising from products of elliptic curves, submitted for publication.
  2. Catherine Cossaboom and Sharon Zhou, Hecke nilpotency for modular form mod 2 and an application to partition numbers, Ramanujan J., recommended for publication.
  3. Sanjana Das, Asymptotic properties of maximal p-core p'-partitions, J. Combinatorial Theory, Series A, 193 Volume 193, (2023), 105685.
  4. Sanjana Das, Hana Lang, Hamilton Wan, and Nancy Xu, The distribution of k-free effective divisors and the summatory totient function in function fields, submitted for publication.
  5. Sanjana Das, Hana Lang, Hamilton Wan, and Nancy Xu,The distribution of error terms of smoothed summatory totient functions, Proceedings of the American Mathematical Society, accepted for publication.
  6. Hana Lang, Hamilton Wan, and Nancy Xu, Distributions of hook lengths divisible by 2 or 3, J. Number Theory, 246 (2023), 227-251.
  7. Henry Glunz, Significant digits of primes in subsets, Integers, 23 (2023), Article 46.
  8. Annemily Hoganson and Thomas Jaklitsch, On certain McKay numbers for symmetric groups, Ramanujan Journal, accepted for publication.
  9. Daniel Hu, Hari Iyer and Shasha Shashkov, Modular forms and an explicit Chebotarev variant of the Brun-Titchmarsh theorem, Research in Number Theory, 9 (2023), Art. 46.
  10. Faye Jackson and Misheel Otgonbayar, Biases among congruence classes for parts in k-regular partitions, submitted for publication.
  11. Faye Jackson and Misheel Otgonbayar,Unexpected biases between congruence classes for parts in k-indivisible partitions, Journal of Number Theory, accepted for publication.
  12. Faye Jackson and Misheel Otgonbayar, Parts in k-indivisible partitions always display biases between residue classes, submitted for publication.


Topology (June 6 - July 29, 2022)

Topology Participants

  • Mahalo Blackburn
  • Isaiah Dailey 
  • Grace Davis
  • Clara Huggins 
  • Lindsay Marjanski
  • Fredrick Mooers 
  • Semir Mujevic 
  • Andrew Niu
  • Chloe Shupe
  • Vincent Solon 
  • Frank Zheng
  • Kathleen Zopff

Topology Colloquia

  • June 21 and 23: Inna Zakharevich (Cornell) (remote)
  • July 13: Diana Hubbard (Brooklyn College) (remote)
  • Sang-hyun Kim (Korea Institute for Advanced Studies) (remote)

Mini Courses

  • Walker Stern: "A crash course on categories"
  • Mark Pengitore: "Topological and geometric models of groups" 
  • William Balderrama: "Simplicial complexes and simplicial homology" 

Professional development/social activities

  • Latex Course
  • Graduate School and Job panel
  • Diversity panel

Topology Papers

  1. Lindsay Marjanski, Vincent Solon, Frank Zheng, and Kathleen Zopff, Geodesic growth of numbered graph products, Journal of Groups, Complexity, Cryptology, Vol. 14, Issue 2 (2023).