ncku-talk2013-09-26

NCTS(South)/ NCKU Math Colloquium

DATE 2013-09-26　15:30-16:30

PLACE R204, 2F, NCTS, NCKU

SPEAKER 黃一樵教授（中央研究院數學所）

TITLE Convolution Identities and Their Structure

ABSTRACT Beginning with Euler's formula $$ \sum_{i=0}^n\binom{n}{i}B_iB_{n-i}=(1-n)B_n-nB_{n-1} $$ for the sum of products of two Bernoulli numbers, there are many generalizations, for example, to the sum of products of more Bernoulli numbers or to analog formulas for other numbers (such as Euler numbers and Fibonacci numbers). We show that these convolution identities come from parametrizations of varieties with a vector field. A Weyl algebra and the universal enveloping algebra of a Lie algebra appear in the framework.

NCTS(South)/ NCKU Math Colloquium

DATE	2013-09-26　15:30-16:30

PLACE	R204, 2F, NCTS, NCKU

SPEAKER	黃一樵教授（中央研究院數學所）

TITLE	Convolution Identities and Their Structure

ABSTRACT	Beginning with Euler's formula $$ \sum_{i=0}^n\binom{n}{i}B_iB_{n-i}=(1-n)B_n-nB_{n-1} $$ for the sum of products of two Bernoulli numbers, there are many generalizations, for example, to the sum of products of more Bernoulli numbers or to analog formulas for other numbers (such as Euler numbers and Fibonacci numbers). We show that these convolution identities come from parametrizations of varieties with a vector field. A Weyl algebra and the universal enveloping algebra of a Lie algebra appear in the framework.