Index of the WilsonDirac operator revisited: a discrete version of Dirac operator on a finite lattice
 Date
 February 25 at 16:00  18:10, 2020 (JST)
 Speaker

 Dr. Mikio Furuta (Professor, The University of Tokyo)
 Venue
 Language
 English
The WilsonDirac operator is a discrete version of Dirac operator defined on regular lattices. When the discrete version is a fine approximation of the Dirac operator on a Z/2graded Clifford module on a torus, it is known that (1) an integervalued index is defined for the WilsonDirac operator, and (2) the index is equal to the AtiyahSinger index of the Dirac operator on the torus.
These have been well established up to around 2000. The strategy of all the previous works is to make use of the discrete version of the heat kernel for Neuberger's overlap Dirac operator. Therefore the strategy cannot be generalized to mod 2 index nor family version of index.
In this talk I would like to explain a new approach to the index of WilsonDirac operator which can be immediately generalized to these various cases.
Joint work with H. Fukaya, S. Matsuo, T. Onogi, S. Yamaguchi and M. Yamashita.