Algebraic Geometry Seminar

DATE2018-01-04 14:10-15:00


SPEAKERJason Lo 助理教授(California State University, Northridge (CSUN)

TITLEStability, Counting Invariants and Symmetries

ABSTRACT In algebraic geometry, any time we have a notion of `stability for coherent sheaves or complexes of coherent sheaves on a smooth projective variety $X$, we can consider moduli spaces of the stable objects. When the moduli spaces have good enough properties, we can define associated `counting invariants' on $X$, such as Donaldson-Thomas (DT) invariants and Pandharipande-Thomas (PT) invariants. When $X$ possesses an internal symmetry, the symmetry can induce relations between different stable objects, and relations between different counting invariants. In this talk, I will talk about some recent developments in this area on threefolds and possible future directions.