14 October 2007

Divergent Series take 1

The following talk is significantly too long. Some parenthetical remarks are easy enough to excise, but what else should I drop?

The talk is available here (pdf). I will give it on Thursday at "Many Cheerful Facts", a brown-bag student-organized talk series in which different graduate students present general-audience material: if you know the subject already, you won't learn anything in the talk. Someone bakes something tasty each week.

Abstract: Whereas modern physicists write down divergent series all the time, mathematicians through the ages have been variously terrified or only mildly scared of such sums. In this talk, I will survey the most important methods of summing divergent series, and make general vague remarks about them. I will quote many results, but will studiously avoid proving anything.

2 comments:

Papin said...

Nice write-up on divergent series. When I went to school only those interested in statmech wanted to know about them. The rest agreed with Abel. At one point I was into the black art of non-linear transformations of series, stuff like Shanks' transform and its many cousins (needed to get good exponents from series).

yasiru89 said...

The theory of divergent series has come a long way since Abel.

The paper was generally well-written, but I had ready Hardy's exceptional account beforehand. I'm currently surveying divergent series on my blog,

http://mathrants.blogspot.com