# Algebraic Geometry and Number Theory

## Faculty

- Laure Flapan
- Francois Greer
- Rajesh S Kulkarni
- Aaron D Levin
- Georgios Pappas
- Igor Rapinchuk
- Michael Shapiro
- Preston Wake
- Joseph Waldron

Algebraic Geometry is the field of Mathematics which studies systems of polynomial equations in several unknowns and their solutions sets in rational, real or complex numbers. Number Theory is probably the oldest mathematical discipline: It studies whole numbers (integers) and their properties. The two subjects are very closely connected and there are many interactions with other fields, including Algebra, Combinatorics, Geometry, Topology, and even Applied Mathematics and Mathematical Physics. The interests of our faculty in these areas are very diverse and cover several topics such as:

- Integral and rational points on algebraic varieties.
- Diophantine approximation (and its relations with Nevanlinna theory).
- Arithmetic dynamics.
- Moduli spaces of curves and of abelian varieties, Shimura varieties.
- Galois group actions and Galois module structure.
- Moduli spaces of vector bundles.
- Non-commutative geometry and the Brauer group.
- Enumerative and tropical algebraic geometry.
- Topology of real algebraic sets.