Colloquium
DATE	2019-10-31　16:10-17:00
PLACE	數學館3174教室
SPEAKER	葉弘裕 博士（中央研究院數學研究所）
TITLE	Stability Filtrations, Weakly Ample Sequences and Numerical Vectors in Categories
ABSTRACT	Stability, first introduced by Mumford in the 1960's, is used as a tool to construct moduli space of sheaves on algebraic varieties and later generalized to objects in arbitrary abelian category. On the other hand, motivated by homological mirror symmetry conjecture and Douglas' Pi stability on the category of B-branes Bridgeland introduces stability conditions on triangulated categories which depends on the existence of Harder-Narasimhan (HN) filtration and central charges on the relevant K group of associated triangulated categories. In this talk, I would like to present main ideas in my current work and introduce a notion of stability filtration in arbitrary categories which is equivalent to the existence of HN filtration on objects. Indeed it is equivalent to existences of a zero morphism, a partial order on objects, and a collection of some universal sequences. One may give a suitable addition with this zero morphism on the Hom space which makes this category an additive category. Then with weakly ample sequences in the additive category embedded in an ambient triangulated category under suitable conditions, we could obtain a numerical polynomial or central charge of objects by calculating the Euler characteristic of weakly ample sequences and objects, inducing a partial order and HN filtration. At the end, I would give some easy examples in algebraic curves and surfaces.