Algebraic Geometry Seminar DATE 2018-01-04¡@14:10-15:00 PLACE ¼Æ¾ÇÀ]3F·|Ä³«Ç SPEAKER Jason Lo §U²z±Ð±Â¡]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. In this talk, I will talk about some recent developments in this area on threefolds and possible future directions.