Pascal Schweitzer: On zero divisors with small support in group rings of torsion-free groups

Kaplanski's Zero Divisor Conjecture envisions that the group ring of a torsion-free group over an integral domain does not contain non-trivial zero divisors. For group rings of torsion-free groups over the rationals, I will show that if a product of two non-trivial elements in the group ring is zero, then the size of the support of the two elements cannot be simultaneously small. I will also describe an algorithmic, computer assisted approach, with which one can obtain strengthened conclusions of the same flavor.