Föredrag för den matematiskt intresserade allmänheten. Lecture for the mathematically interested general public.

A natural question arising when solving a linear equation Tx = y is if there exist solutions and if it does, is the solution unique? Five quarters of a century ago, Ivar Fredholm studied this question for particular classes of integral operators and from abstract principles proved that in this class existence was in fact equivalent to uniqueness. This abstract principle is nowadays called the Fredholm alternative and was the first instance of an index theorem. We shall in this talk discuss what index theory is, and how this soft approach to linear equations provides surprising links between geometry, topology, and analysis.

https://www.maths.lth.se/LMS/