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SUMMARY:Seminar\, 深谷英則 Hidenori Fukaya (Osaka University)
DTSTART;VALUE=DATE-TIME:20250612T043000Z
DTEND;VALUE=DATE-TIME:20250612T053000Z
UID:433030175698
DESCRIPTION:Title: The index of lattice Dirac operators and K-theoryAbstra
 ct:We show that the Wilson Dirac operator in lattice gauge theory can be i
 dentified as a mathematical object in K-theory and that its associated spe
 ctral flow is equal to the index. In comparison to the standard lattice Di
 rac operator index\, our formulation does not require the Ginsparg-Wilson 
 relation and has broader applicability to systems with boundaries and to t
 he mod-two version of the indices in general dimensions. We numerically ve
 rify that the K and KO group formulas reproduce the known index theorems i
 n continuum theory. We examine the Atiyah-Singer index on a flat two-dimen
 sional torus and\, for the first time\, demonstrate that the Atiyah-Patodi
 -Singer index with nontrivial curved boundaries\, as well as the mod-two v
 ersions\, can be computed on a lattice.
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