3:00 p.m., Friday (Feb. 28th)
Math Annex 1100
Naichung Conan Leung
School of Mathematics
University of Minnesota
Geometry over R, C, H and O
We develop a unifed theory to study geometry of manifolds
with different holonomy groups.
They are classified by (1) real, complex, quaternion or octonion
number they are defined over and (2) being special/orientable or not.
For example, special Riemannian A-manifolds are oriented Riemannian,
Calabi-Yau, Hyperkahler and G_2-manifolds respectively.
For vector bundles over such manifolds, we introduce (special)
A-connections. They include holomorphic, Hermitian Yang-Mills,
Anti-Self-Dual and Donaldson-Thomas connections. Similarly we
introduce (special) A/2-Lagrangian submanifolds as maximally real
submanifolds. They include (special) Lagrangian, complex Lagrangian,
Cayley and (co-)associative submanifolds.