Mathematics

In 1985, Casson defined a topological invariant for (real) 3-folds with the homology of the sphere; not much later Taubes gave a gauge-theoretic construction of the Casson Invariant as a signed “virtual count” of flat SU(2)-connections, up to gauge equivalence. In 1998, Donaldson and Thomas proposed to use a similar approach to count holomorphic structures on vector bundles over a Calabi-Yau 3-fold;  we shall see that this problem has several analogies with the previous one. In this case, however, there doesn't seem to be a differential-geometric way of doing the virtual count. This led Thomas to consider the problem from an algebro-geometric point of view, which will be the topic of the next seminars.