People

Yalong Cao
Position
Project Researcher (from 2019/03/16 )
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Research Field
Mathematics
E-Mail
<yalong.cao _at_ ipmu.jp> 
URL
http://www.maths.ox.ac.uk/people/yalong.cao
PHOTO

Last Update 2019/02/06

My research lies in the intersection between algebraic geometry, differential geometry and string theory. More specifically, I have been studying Donaldson-Thomas type theory on Calabi-Yau 4-folds, 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 4-manifolds. 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 4-folds glued along their anti-canonical divisor Y, we expect a gluing formula relating DT4 invariant of the generic fiber of Xt and relative DT4 invariants of those two 4-folds (which are elements in the DT3 cohomology of Y)


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