MaPSS: Maths Postgraduate Seminar Series: Steven Luu -- Sums for divergent series

Hello all,

The next MaPSS seminar will be held at 17:00 on Mon 7th in Carslaw 535.
It’s a great opportunity to see an interesting talk, meet some fellow postgrads,
and get some free pizza and soft drink. 

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Speaker: Steven Luu (The University of Sydney) 

Title: Sums for divergent series

Abstract:  "Divergent series are the invention of the devil, and it is shameful to base
on them any demonstration whatsoever." - N. H. Abel, 1828. 

Divergent series have appeared in various branches of mathematics where they primarily
appear as asymptotic series. In asymptotic theory, a function asymptotic to a divergent
series can, under certain conditions, approximate the function to exponential accuracy. 

The infamous result, 1 + 2 + 3 + ... = - 1/12, has been used in the context of quantum
field theories, for which experimental evidence has been found to agree with the
theoretical predictions up to an astonishing degree of accuracy. 

In this talk, we discuss how divergent series can be ’summed’ by extending the notion
of summation, which is consistent with the usual summation rules. Although many
summation methods for divergent series exist, we will consider Borel summation and
use this to reproduce the result: 1 - 1! + 2! - 3! + 4! - 5! + ... = 0.59637255..., 
originally derived by Euler (1760).

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See you there!

Details can also be found on the school’s new Postgraduate Society website: 
http://www.maths.usyd.edu.au/u/MaPS/mapss.html 
 
Cheers,
Alexander