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


  • 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)



  • 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)


  • 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