I’ve finally found some time to look around the web to see what has been happening at conferences this summer. In this blog post I’ll point to a few on the math/physics interface featuring interesting talks. This area now (I think it may be Greg Moore’s fault) has started to acquire the name of “Physical Mathematics”, to distinguish itself from old-school “Mathematical Physics”. At this point though I’d be hard-pressed to provide a useful definition of either term.

- Talks from last month’s 2017 Bonn Arbeitstagung are available here. This conference was in honor of Yuri Manin and supposedly devoted to Physical Mathematics (although I suspect some of the speakers might not realize that they are doing Physical Mathematics). Dan Freed and Jacob Lurie gave two characteristically lucid series of talks, well worth watching.
A very active area of physics these days with significant overlap with mathematics (of the sort discussed by Freed) is the study of topological superconductors and other materials in which topology plays a large role. For an introduction to this topic, Davide Castelvecchi at Nature has a new article The strange topology that is reshaping physics.

- CERN has just finished running an institute on the topic of the Geometry of String and Gauge Theories. It included a colloquium talk by Greg Moore on d=4 N=2 Field Theory and Physical Mathematics. I’ve always been fascinated by the d=4 N=2 super Yang-Mills theory in its “twisted” topological version. The mathematics involved is deep and amazing, and it is frustratingly close to the Standard Model…
- Pre-string math 2017 was this past week, and String Math 2017 will be next week. All sorts of interesting talks at both of these, relatively few of which have much to do with string theory. That’s of course also true of Strings 2017, but I’ll write about that elsewhere.

Other suggestions of interesting mathematically related summer schools with talks available are welcome. On the physics side, please wait for a succeeding blog entry on that topic.

I wonder if the difference is something like the difference between Physical Chemistry and Chemical Physics … the former uses Chemistry jargon while the latter used Physics jargon, but they are otherwise identical.

Arnold Sommerfeld referred to physical mathematics in the forward to his book on Partial Differentail Equations

Commenting here because your Physical Mathematics post doesn’t have a “leave a reply” section. (Weird, is it just my computer?).

Kishore Marathe is the one who coined the term “Physical Mathematics”. see the intro of his book “topics in physical mathematics” for some discussion of what the term means. (I take it to mean (as in mathematical physics) the drive to find the correct mathematical way to express physical theories (perfecting physics such that it becomes math), but then (unlike in mathematical physics) physical mathematicians go beyond physics and care about interesting mathematical structures inspired by physics which don’t look like they describe our physical universe (as long as these structures are mathematically interesting). Some (many?) physical mathematicians even care more about the mathematical interest of the structures than the physical interest.)

https://books.google.com/books?id=Rf7pqYEb4PQC&printsec=frontcover&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false