[轉錄] 從鋼琴調音談數學與音樂

閏餘成歲, 律呂調陽。— 〈千字文〉。

http://www.math.sinica.edu.tw/math_media/d331/33102.pdf

這是教官在二○○七年全國高中數學能力競賽的專題演講，
後來登在數學傳播上
http://www.math.sinica.edu.tw/media/media.jsp?voln=331

我覺得相當的精彩

Algorithms on Parking Functions and Related Multigraphs

國立高雄大學應用數學系專題演講
主講人：賴俊儒先生（國家科學理論研究中心）
講      題：Algorithms on Parking Functions and Related Multigraphs
演講時間：99年11月24日（星期三）下午2：30
演講地點：應用數學系多媒體教室（理學院408室）
摘要：
Parking functions were introduced and enumerated by Konhein and Weiss in a
study of hashing problems in computer science. Its structure is realted to
labeled trees, critical configurations of the dollar game and alcoves for
affine Coxeter arrangement. In this talk, we will introduce various
generalizations of parking functions, their related multigraphs and two
enumerative methods: the triple-labeled algorithm establishes a family of
bijections between generalized parking functions and multigraphs, while the
cycle lemma for words leads to results with restrictions such as symmetry and
periodic property.
投影片 http://tinyurl.com/24hojur

[Notes] Representations of Semisimple Lie Algebras in the Category O Chp 3.9~15

Chapter 3: Category O: Methods
這是充滿了箭頭的一篇筆記 \o\

sl(2,C) 中的 nontrivial extension

這又是一個 Humphreys 沒講清楚的地方了

本篇目標是要證

g = sl(2,C) 中

看 positive integral weight λ 和他的 linked pair μ = -λ-2

L(μ) 的 projective cover P(μ) is self-dual

即 P(μ) = Q(μ)

Homological Algebra Used in Lie Algebra Representation Theory

禮拜五學長問了程舜仁使用 homological algebra 來處理李代數表現論的動機:
我大略簡記一下 有誤麻煩請糾正我 @@

How to survive as a mathematician in US

http://www.math.wustl.edu/~sk/books/newsurv.pdf

Enough!! projectives....

今天證完 Category O 有 enough projectives
讓我真想說 夠了! projectives...

Chapter 3: Category O: Methods

Hom and Ext
Duality in O
Duals of Highest Weight Modules
The Reflection Group W_[λ]
Dominant and Antidominant Weights
Tensoring Verma Modules with Finite Dimensional Modules
Standard Filtrations
Projectives in O