Algebraische und Arithmetische Geometrie und Zahlentheorie
Algebraic geometry is the qualitative study of systems of polynomial equations, which are ubiquitous in science. This study is carried out via a wide range of geometric, topological and cohomological methods. Number theory, the study of the integers, is one of the oldest areas of mathematics; it has recently received enormous impetus via the Langlands program that connects number theory to representation theory, and via applications in computer science and cryptography. Arithmetic Geometry may be regarded as a modern unification of Algebraic Geometry and Number Theory.
The research and teaching at HU Berlin in these areas covers a large variety of topics including:
- Algebraic curves and abelian varieties, algebraic groups
- Hodge theory and transcendental properties of algebraic varieties
- Number Theory and Representation Theory; p-adic Langlands program
- Moduli spaces in algebraic geometry
- Singularities, D-modules and perverse sheaves
- Commutative algebra and syzygies