ncku-talk2018-01-04

PDE Seminar

DATE 2018-01-04　14:10-15:00

PLACE 數學館3F會議室

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

TITLE Stability, 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.

PDE Seminar

DATE	2018-01-04　14:10-15:00

PLACE	數學館3F會議室

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

TITLE	Stability, 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.