2012-12-10 16:00 ~ 2012-12-10 17:00
黃一樵 教授 (中研院數學所)
國立清華大學綜三館R631
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.
Tea Time: 3:30PM, R707
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