The folks at The n-Category Café wet my appetite today with 2 very interesting posts:
The second one, by Urs, touches in a topic that i hold dear: Knot Theory and QFT — and how these are related to gerbes, and how 2-gerbes are the fundamental geometric objects in Chern-Simons. Urs provides a series of references in a very rational way. Computing the Configuration space (which he called “Space of States”) of certain QFTs has been in my mind quite heavily for quite some time now, including for Chern-Simons. However, the question I have in mind has more to do with Wilson Loops and how their combination is related to Knot Theory; more to the point, how would combination of Wilson Loops in different representations relate to [Spontaneous] Symmetry Breaking. This definitely needs a better explanation than what’s here… but, it’ll have to wait (i’m a bit late to meet some friends! 😉 ).
As for the first link, by John Baez, …, what can i say: Apparently Modular Forms show up in every interesting place nowadays! I had a vague idea about their appearance in Fermat’s Last Theorem but, given that they are related to Hecke operators, they also show up in Langland’s Geometrical Conjecture! And this is the part that really gets to me: the connections between Number Theory and Physics (specially Symmetry Breaking — as can be seen via a Higgs Bundle construction) have always seemed completely magical to my eyes. 🙂
Anyway, now I’m really late… more on this later. 😉