Summer School: Polynomial Methods

Dates: June 7-11, 2021
Venue: HIM lecture hall, Poppelsdorfer Allee 45, Bonn

Organizers: Valentin Blomer, Farrell Brumley, Philip Gressman, Marina Iliopoulou, Lillian B. Pierce

Description:

Powerful progress on a wide selection of problems spanning across harmonic analysis and number theory has involved methods using auxiliary polynomials. On the more number-theoretic side, this includes the recent resolution of the dimension growth conjecture via the determinant method, as well as Stepanov’s method for proving square-root cancelation of exponential sums, and results in transcendence theory related to open conjectures in algebraic number theory. On the more analytic side, applications of polynomial methods include the resolution of the Kakeya conjecture over finite fields, progress in incidence geometry, and new methods for tackling difficult questions on restriction inequalities.This summer school gathers together all these "polynomial methods" with accessible lecture series from each of these perspectives. Graduate students and postdocs will gain intuition and technical skills for how these methods can be applied in a wide range of settings. While the polynomial methods presented in this summer school may have “evolved” independently, the lecture series and collaborative problem sessions will explore connections and parallels that unify the methods.

Lecture series by:

  • Valentin Blomer (University of Bonn)
  • Samit Dasgupta (Duke University)
  • Roger Heath-Brown (University of Oxford)
  • Marina Iliopoulou (University of Kent)
  • Hong Wang (Institute for Advanced Study)

Further information regarding application will be available in due time.