Yalong Cao

Last Update 2022/11/21
My research lies in the intersection between algebraic geometry, differential geometry and string theory. More specifically, I have been studying DonaldsonThomas type theory on CalabiYau 4folds, which is a way to count 'instantons' or coherent sheaves on CY4.
DT4 theory could be viewed as a complexification of Donaldson's theory on oriented 4manifolds. Formally, DT4 theory should fit into a topological quantum field theory relating instanton countings on Spin(7), G2 and CY3 manifolds. Nevertheless, I prefer restricting to the algebraic subcase for CY4 and CY3. Basically, for a simple degeneration Xt of CY4 into two 4folds glued along their anticanonical divisor Y, we expect a gluing formula relating DT4 invariant of the generic fiber of Xt and relative DT4 invariants of those two 4folds (which are elements in the DT3 cohomology of Y)
Back to Member List.