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

**Kontakt**

PD Dr. Hartje Kriete

Mathematische Fakultät

Georg-August-Universität Göttingen

Bunsenstr. 3/5

37073 Göttingen

Tel.: +49 (0) 551 39-7781

Fax : +49 (0) 551 39-22985

E-mail: summer@math.uni-goettingen.de