Expert in a Dying Field

I don't necessarily think the various areas I discuss below are more or less important than the others, just what I view as their popularity.  Others likely have a different view. 

Recently, I was listening to The Beths' "Expert in a Dying Field".  It's a break-up song about all the minutia you learn about a person which no longer feels relevant when the relationship ends.  (Don't worry, I'm not going through a breakup/angst phase.  I just like the song.)  When I listen to it, I often times think about Heegaard Floer homology.  

Heegaard Floer homology, developed by Ozsvath and Szabo, exploded in the early 2000s.  It seemed to pack most of the punch of gauge theory while being super computable.  When I started grad school there was this incredible flurry of activity, both in theory building (e.g. bordered Floer homology) and applications (e.g. structure of the knot concordance group, classifying fillable contact structures).  Hot fields often have very material and visible impacts: there were lots of Heegaard Floer homology postdocs, a ton of papers went into good journals, people got desirable jobs and competitive grants, etc.  During most of this flurry there was a lot less activity in closely related areas, say in Yang-Mills or Seiberg-Witten gauge theory.  While I certainly benefited from this, I think it's a bit unfortunate - often in the shadow of a trendier field, lots of good math happens that does not necessarily get the credit it deserve.  

Over the past 15 years, I feel it is not as popular as it used to be, as the landscape has really changed - many subfields of low-dimensional topology are having a resurgence (applications of gauge theory, exotic four-manifolds) and some feel like they're slowing down (concordance, Dehn surgery).  I think it is a good thing for a field to wax and wane on what is popular, since it brings in connections with different areas and prevents things from becoming stagnant.  While most of my earlier work was in Heegaard Floer homology, I've grown less interested in it as I've expanded into other fields.  Some of that is realizing how powerful tools from other areas can be for the problems I've always been interested in.  Some of it is for being able to work with other (really cool!) mathematicians.  And some of it was probably some intrinsic hipster desire to do something less mainstream.  Also, don't get me wrong - I still write papers in Heegaard Floer homology and there's lots of problems in the area I like.  However, it's not what I'm most excited to work on and not the default thing I want to talk to other mathematicians about.

Unfortunately, it does pay to get results in a trendy field.  That said, I don't recommended trying to work heavily in an area you really don't enjoy, unless it's to solve a problem you're excited about.  Also, since things don't stay trendy forever, it's valuable to stay abreast of what's going on in neighboring areas and get involved in projects that stretch your breadth.  In my view, the more you have a working knowledge of, the easier it is to use one of your skills to solve an interesting problem, especially as big projects often call for a variety of skills.  It's helpful even just for the purpose of having more productive mathematical conversations with people and getting more out of talks.  So, if you're grumpy that your area of math doesn't get the play it deserves, hopefully your time to shine is coming soon!  

I'm curious what other folks think are the areas that are really trendy now vs those which are going out of style.  If you see me at a conference, tell me what you think will be the next big thing and what is so last summer!