LLP-IP at the Faculty of Mathematics and Computer Sciences 2012

This Intensive Programme is designed to provide educational and research experience for advanced undergraduate and beginning graduate students. The scientific program consists of six mini-courses, problem sessions, and projects with computer lab and theoretical components. Projects will be performed in teams with students from different countries to provide a first-hand international experience.

Schedule - final version! (PDF)

Mini-courses


  • Automorphic forms with applications (Valentin Blomer, Georg-August-Universität Göttingen)
    • introduction to automorphic forms
    • arithmetic of Fourier coefficients
    • Ramanujan conjecture
    • Ramanujan graphs



  • Counting rational points on algebraic varieties (Jörg Brüdern, Georg-August-Universität Göttingen)
    • introduction to the circle method
    • Manin's conjecture for algebraic varieties
    • advanced analytic methods for point counting



  • 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



  • 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, Georg-August-Universität Göttingen)
    • introduction to elliptic curves and abelian varieties
    • algorithms of computational number theory
    • point counting on elliptic curves
    • curves of higher genus



  • Drinfeld modules (Mihran Papikian, The Pennsylvania State University)
    • arithmetic of function fields
    • zeta-functions
    • introduction to Drinfeld modules