The Kaplansky conjectures
Giles Gardam (Münster)
There is a series of four long-standing conjectures on group rings that are attributed to Kaplansky. For example, the zero divisor conjecture states that the group ring of a torsion-free group over a field has no zero divisors. I will discuss what is known about these conjectures and my recent disproof of the unit conjecture.