REUs Archive: 2021

Number Theory and Representation Theory Participants 

  • Mateo Attanasio 
  • Caroline Choi
  • Yunseo Choi (2021 Regeneron Science Talent Search 1st Prize)
  • Kevin Gomez       
  • Alexandra Hoey (2022 Alice T. Schafer Prize, Honorable Mention)
  • Daniel Hu
  • Jonas Iskander
  • Steven Jin
  • Ikuya Kaneko
  • Kaya Lakein
  • Anne Larsen
  • Sean Li (2021 Davidson Fellow)
  • Jerry Lu
  • Andrei Mandelshtam (2021 Davidson Fellow, Honorable Mention)
  • Spencer Martin
  • Margaret Michael
  • Apoorva Panidapu (2021 Davidson Laureate)
  • Carl Schildkraut
  • Casia Siegel
  • Fernando Trejos Suárez         

Topology Participants

  • Rebecca Bell
  • Katherine Betts
  • Ethan Clelland
  • Allison Eckert
  • Alexandra Emmons
  • Calvin Godfrey
  • Luz Grisales
  • Troy Larsen
  • Ryan Pesak
  • Avery Schweitzer
  • Jeffrey Utley
  • Avalon Vanis

Number Theory and Representation Theory (June 7- July 16, 2021)

Projects

  • Brauer groups for elliptic curves
  • Divisors of Hecke trace modular forms and complex multiplication
  • Elliptic curve Tamagawa products: Arithmetic statistics over number fields
  • Lehmer-type conjectures for modular forms
  • Mertens-type speculations for Mobius sums over number fields

Invited Speakers (Thursdays at 3pm)

  • June 10th: Jennifer Balakrishnan (Boston University)
    "A tale of three curves"
  • June 17th: Kannan Soundararajan (Stanford University)
    "Distribution of prime numbers"
  • June 24th: Melanie Matchett Wood (Harvard University)
    "Distributions of class groups and unramified extensions"
  • July 1st: Andrei Okounkov (Columbia University)
    "Partitions, q-series, and multiple q-zeta values"
  • July 8th: Jordan Ellenberg (University of Wisconsin)
    “Heights of rational points on stacks”
  • July 12th: Toni Bluher (NSA, Not on a Thursday)
    “Dickson polynomials, Chebyshev polynomials, and Wilson-like theorems”

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

  • Abelian Varieties  (June 14, 16, 18; Instructor: Prof. Evangelia Gazaki)
  • Diophantine Approximation (June 21, 23, 25; Instructor: Postdoc Jinbo Ren)
  • Representation Theory of S_n (June 28, 30, July 2; Instructor: Prof. You Qi)

Topology (June 7-July 30, 2021)

 Projects

  • Equivariant finite spaces and topological complexity (Mentor: Walker Stern)
  • Alexander invariants of trisected 2-knots (Mentor: William Olsen)
  • The tri-pants graph of the twice punctured torus (Mentor: Filippo Mazzoli)

Colloquia

  • Tarik Aougab (Haverford)
  • Jessica Purcell (Monash)
  • Sang-hyun Kim (KIAS)
  • Henry Segerman (Oklahoma State), June 16th at 4:00pm
    "Triangulating the figure 8 knot complement"
  • Wojciech Chachólski (KTH), July 14th at 10:00am
    "How to enable a machine to sense geometry"

Mini Courses

  • An introduction to the fundamental group (Walker Stern)
  • Curves on surfaces (Filippo Mazzoli)
  • A crash course in knot theory (William Olsen)

Professional development/social activities

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

Number Theory Papers

  1. Mateo Attanasio, Caroline Choi, Andrei Mandelshtam, and Charlotte Ure, Symbol Length in Brauer Groups of CM Elliptic Curves, Proceedings of the American Mathematical Society, recommended for publication.
  2. Yunseo Choi, Sean Li, Apoorva Panidapu, and Casia Siegel, Tamagawa products of elliptic curves over number fields, submitted for publication.
  3. Kevin Gomez, Kaya Lakein, and Anne Larsen, Supersingular loci from traces of Hecke operators, submitted for publication.
  4. Alexandra Hoey, Jonas Iskander, Steven Jin and Fernando Trejos Suarez, An unconditional explicit bound on the error term in the Sato-Tate conjecture, submitted for publication.
  5. Daniel Hu, Ikuya Kaneko, Spencer Martin, and Carl Schildkraut, Order of zeros of Dedekind zeta functions, preprint.
  6. Daniel Hu, Ikuya Kaneko, Spencer Martin, and Carl Schildkraut, On the Mertens Conjecture over Number fields 
  7. Ikuya Kaneko and Jesse Thorner, A Uniform Prime Number Theorem for Rankin–Selberg L-Functions, coming soon.
  8. Kaya Lakein and Anne Larsen, Some remarks on small values of Ramanujan's tau(n), Archiv der Mathematik (Basel), accepted for publication.
  9. Kaya Lakein and Anne Larsen, A proof of Merca's conjectures on sums of odd divisor functions, Bulletin of the Australian Mathematical Society, accepted for publication.