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