## Algebra KU Leuven

NUMBER THEORY AND ALGEBRAIC GEOMETRY

1) Study of the number of solutions of polynomial equations in several variables over finite fields and residue class rings, with emphasis on the relation to geometric and topological invariants of the equations, Igusa's local zeta function, p-adic exponential sums.

2) Connections between (1) and the theory of singularities, resolution of singularities, Log Minimal Model Program, topological ...