|Colloquium, 中央研究院數學研究所 / 邱聖夫博士|
Thursday, October 17, 16:10—17:00 數學系3174
Title: Unsharpness Principle and Function Theory
Abstract:A bunch of quantum phenomena have their counterparts in symplectic topology, which allows one to deal with more classical functions on more complicated geometry objects called symplectic manifolds. In my previous NCKU colloquium talk I tried to relate the famous uncertainty principle to symplectic and contact non-squeezing properties, and this time I will stress another phenomena called unsharpness. Roughly speaking, measuring a quantum state is like capturing a point of a symplectic manifolds. While the uncertainty principle sets a theoretical limit for the preciseness of such measurements, the unsharpness principle sets a threshold for registration procedures of points. The talk is accessible for those who knows calculus and is not afraid of the notion of manifold
|Colloquium, 中央大學數學系 / 陳志瑋教授|
Friday, October 25, 16:10—17:00 數學系3174
Title: Tilting Modules for the Periplectic Lie Superalgebra
Abstract:The periplectic Lie superalgebra p(n) is a superanalogue of the orthogonal or symplectic Lie algebra. While the BGG categories O for the other finite-dimensional simple Liesuperalgebras are not well understood at present, the character of tilting modules for most of them have been worked out with the exception of p(n). In this talk, we will introduce a version of Ringel duality of arbitrary BGG category O for p(n) which give rise to an approach to the problem of tilting characters. This talk is based on joint work with Shun-Jen Cheng and Kevin Coulembier.
|Colloquium, 中央大學數學系 / 葉弘裕博士|
Thursday, October 31, 16:10—17:00 數學系3174
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.