AbstractGeometric engineering provides a rich class of 5D supersymmetric gauge theories with eight supercharges, arising from M-theory compactification on non-compact Calabi-Yau threefolds. The counting of BPS states in the low-energy gauge theory is determined by the degeneracies of M2-branes wrapping holomorphic two-cycles in the Calabi-Yau threefold X. These degeneracies can also be calculat...
Abstract：I will describe a complete set of numerical invariants for deciding whether a real vector bundle is stably trivial. These invariants are integers and rational angles which will be a priori given in contrast to the usual theory of secondary characteristic classes. The definition of these invariants features a duality between the reals and quaternions, moreover a quaternionic version of...
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