Penn State - Göttingen
International Summer School on Number Theory
Göttingen, Germany
July 29 – August 18, 2012

The Mathematics Department of the Pennsylvania State University and the Institute of Mathematics of Göttingen University will host a Summer School on Number Theory in Göttingen, Germany, from July 29 to August 18, 2012. This program is designed to provide educational and research experience for advanced undergraduate and beginning graduate mathematics students enrolled in universities in the United States and countries of the European Union. The program consists of mini-courses, problem sessions, and projects with computer lab and theoretical components. All projects will be performed in teams with students from different countries to provide a first-hand international experience. Each participant will receive a stipend to cover travel expenses and lodging.

There will be a research conference on number theory during the last week of the program. Many of the talks will be expository and should be accessible to students.

Summer School Poster

Summer School Website in German

Schedule


Mini-courses

  • Automorphic form with applications (Valentin Blomer, Göttingen University)
    • Introduction to automorphic forms
    • Arithmetic of Fourier coefficients
    • Ramanujan conjecture
    • Ramanujan graphs
    Projects and Exercises
  • Counting rational points on algebraic varieties (Jörg Brüdern, Göttingen University)
    • Introduction to the circle method
    • Manin's conjecture for algebraic varieties
    • Advanced analytic methods for point counting
    Projects and Exercises
  • Probabilistic Galois theory (Rainer Dietmann, University of London)
    • Density of points on curves and surfaces
    • Distribution of Galois groups
    • Hilbert's irreducibility theorem
    • Large sieve
    Projects and Exercises
  • L-functions and equidistribution (Gergely Harcos, Central European University / Alfréd Rényi Institute of Mathematics)
    • L-functions of cusp forms
    • The subconvexity problem
    • Shifted convolution problems
    • Applications to equidistribution of Heegner points on the modular surface
  • Computational number theory and cryptography (Preda Mihailescu, Göttingen University)
    • Introduction to elliptic curves and abelian varieties
    • Algorithms of computational number theory
    • Point counting on elliptic curves
    • Curves of higher genus
    Projects and Exercises
  • Drinfeld modules (Mihran Papikian, The Pennsylvania State University)
    • Arithmetic of function fields
    • Carlitz zeta function
    • Introduction to Drinfeld modules
    Projects and Exercises

Selected Student Projects

Funded by the
National Science Foundation