Math Seminar Talk by Dr. Mikio Furuta, February 25, 2020.

Prof. Mikio Furuta from the University of Tokyo gave a talk at the Math Seminar on February 25, 2020. The title of his talk was "Index of the Wilson-Dirac operator revisited: a discrete version of Dirac operator on a finite lattice". His talk was based on his recent collaboration with both mathematicians and physicists. The main goal of his talk is to give an equality between the index of the Dirac operator, which is defined on a continuous space, and that of the Wilson-Dirac operator, which is defied on a discrete lattice. This equality is given in a suitable K-group, which is defined as a collection of (some equivalence classes of) pairs of Hilbert spaces and operators acting on them. The key point in the proof of the main result is to compare two different Hilbert spaces somehow, and he explained an idea of the construction of a map needed for this comparison. This talk included many new ideas, and both of mathematicians and physicists enjoyed it very much.