"Dirac operators and Curvature on Large Riemannian Manifolds"
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In 1920s,Dirac discovered the differential operator D,such that
D2=-Laplacian operator,which is called Dirac operator now.In 1960s,Atiyah
and Singer discovered another type of Dirac operator,which now is called
Atiyah-Singer Operator,then applied the Atiyah-Singer index theorem in this
special case,solved a series of important problem in geometry and
topology.In 1980s,Gromov proposed Large Remannian Manifolds,(worked with
Lawson)and used new Dirac operator techniques and ideas to get scalar
curvature results on high dimensional Torus.My talk will be around these
stuff.