Institute of Mathematical Sciences, C.I.T., Chennai. Algebraic number theory, algebraic geometry.

Joetsu University of Education. Algebraic number theory: the distribution of the discriminants of algebraic number fields, class numbers of binary forms, zeta functions associated with prehomogeneous vector spaces and Igusa's local zeta functions.

Universität Ulm. Integral representations of finite groups and lattices, orthogonal representations of finite groups and group rings over p-adic integers.

Institut de Mathématiques de Jussieu. Algebraic number theory, arithmetic algebraic geometry.

Computations on primes, prime gaps, prime constellations (twins, triplets, and quadruplets) and their reciprocal sums (to extrapolate estimates for the corresponding Brun's constants). Description of the infamous Pentium division bug.