3/4/2005

Selman Akbulut
Michigan State University and IAS

Calibrated Manifolds and Gauge theory

Calibrated geometries (introduced by Harvey and Lawson) give Interesting class of 3 and 4 dimensional submanifolds of 7 and 8 manifolds with exceptional holonomies G_2 and Spin(7). They are called associative and Cayley submanifolds. We will relate the deformation theory of these submanifolds to their gauge theories (recent joint work with Sema Salur), e.g. Seiberg-Witten equations appear as deformation equations of certain calibrated submanifolds. We will discuss how to associate invariants to G_2 manifolds from Seiberg-Witten for families.