⇤Math diary
May 8, 2023:
Today I went to a talk by Hikaru Nakajima, about coulomb branches. I just spent a whole semester learning about Coloumb branches, and even organizing a whole seminar, so I actually had enough background to understand it! It was a nice change of pace, to follow the string math talks most of the way through. The talk itself was cool, it extended the previously known theory for a special case that used to be just out of reach.
Math wise, I went back and really did out and understood the stuff from the first paragraph of yesterday, about the conformal group of minkowski space. Now I’m trying to understand central extentions. In particular, the Viasoro algebra is the unique central extention of the le algebra of vector fields on a circle. But why is it unique? Aparently, this is an infetesimal version of the central extention of $\text{Diff}(S^1)$, which is defined by the Schwartzian derivative. So, it has to do with the many magic properties of the Schwartzian. Theres some very cool and deep stuff here, and quite a alot of it, so I have my work cut out for me.