Number Theory and Representation Theory (June 6 - July 15, 2022)
Projects
- 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 (2024 Goldwater Scholar)
- 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, 2023 Churchill 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)
"Superorthogonality" - 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
- Quanlin Chen and Eric Shen, On effective Sato-Tate distributions for surfaces arising from products of elliptic curves, submitted for publication.
- Catherine Cossaboom and Sharon Zhou, Hecke nilpotency for modular form mod 2 and an application to partition numbers, Ramanujan J., recommended for publication.
- Sanjana Das, Asymptotic properties of maximal p-core p'-partitions, J. Combinatorial Theory, Series A, 193 Volume 193, (2023), 105685.
- 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.
- 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.
- Hana Lang, Hamilton Wan, and Nancy Xu, Distributions of hook lengths divisible by 2 or 3, J. Number Theory, 246 (2023), 227-251.
- Henry Glunz, Significant digits of primes in subsets, Integers, 23 (2023), Article 46.
- Annemily Hoganson and Thomas Jaklitsch, On certain McKay numbers for symmetric groups, Ramanujan Journal, accepted for publication.
- 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.
- Faye Jackson and Misheel Otgonbayar, Journal of Number Theory, Parts in k-indivisible Partitions Always Display Biases between Residue Classes,submitted for publication for publication.
- Faye Jackson and Misheel Otgonbayar,Unexpected biases between congruence classes for parts in k-indivisible partitions, submitted for publication.
- Faye Jackson and Misheel Otgonbayar, Parts in k-indivisible partitions always display biases between residue classes, Journal of Number Theory, accepted 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
- 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).