Some thoughts on mathematics

We are deep into summer conference season, so let's talk about them.    Often times it’s hard to figure out how to best spend your energy at a conference.  Senior person X might be giving a talk and so you don’t want to be seen missing it.  But maybe she gives terrible talks or you’ve seen it 4 times before and it’s never made sense?  Perhaps if you could understand it, you'd have have the key result you were missing to finish your thesis result.  Or you’re worried she’ll notice you’re not there and is going to think less of you!  On the other hand, you just saw hotshot postdoc Y skipping out on the talk and what if you could get an hour to talk with them?  You’re also almost done with a paper and your collaborator is there – it could be the best time to just knock out the last details while you’re in the same space as him.  You could just be really damn tired from the last 3 days of the conference and going to one more talk is going to drain...

This is a short series on the Smith Conjecture and Smith theory in general   Equivariant topology is always in style, so I figure I should have a blog post about it.  In low-dimensional topology, we're always taking covers (branched or unbranched).  For example, many problems in knot theory are approached by studying the topology of the branched double cover.  (For example, the branched double cover of an unknotting number one knot is Dehn surgery on a knot by something called the "Montesinos trick", and so unknotting numbers get studied in this way.)  So, how can you study group actions on a space: * What is the fixed point set? * What is the quotient manifold? Roughly, if you have a smooth action of a finite group $X^G$ on a smooth manifold $X$, then the fixed point set $X^G$ will be a nice smooth submanifold.  If it is a $p$-group action, where $p$ is prime, then we can really understand the fixed point set well by what is referred to as Smith Theor...