The site mathoverflow is a forum populated by professional mathematicians in which posts are up voted if they are considered good answers to posted questions. In this post I will collect postings that I hope to follow up on in future posts and my own private study.
Unfortunately Grothendieck didn’t examine, that we know of, the foundations of physics although some people suggest that he avoided the subject because he found the foundations to be too non-mathematical, or to put it more directly nonexistent.
Peter Woit’s blog not even wrong is a very interesting site that not only talks about mathematical physics but also briefly makes forays into pure mathematics. Here are some interesting recent posts:
The word deformation is in reference to the notion introduced initially by Kodaira and Spencer in their important work in the late 1950s. My primary interest is in Grothendieck’s reformation of this theory in the context of scheme theory as described in his fondements de geometrie algebrique.
The notion of homotopy, as originally introduced by Henri Poincare, has morphed into a vast framework that encompasses much of modern mathematics. It is my hope to explore this notion in the context of modern algebraic geometry as envisaged by Grothendieck in his so called derivators, a theory that is expounded in a 2000 page letter that he wrote in early 1990s and which is being transcribed into LaTeX by George Maltsiniotis and his collaborators.
The title of this post refers primarily to the work of Shinichi Mochizuki, in particular, his claim for a proof of the ABC conjecture. He is no quack but appears to be very reputable mathematician who is, in fact, quite brilliant. Unfortunately the papers he’s posted with respect to the ABC conjecture appears to be buried in vast jungle that he refers to as “Inter-universal Teichmuller theory” or as I prefer to refer to it, arithmetic deformation theory. Some mathematicians have described reading these papers as reading papers from the future or from outer space.
In this posting I will document my attempts to understand how representation theory in the “classical” sense can be reduced to a subtopic of algebraic geometry as is asserted by a number of survey articles and books, particularly Geometric Methods in Representation Theory of Hecke Algebras and Quantum Groups by Victor Ginzburg which is summary of a book he wrote along with N. Chriss. I found the article because it is cited in a note by David Ben-Zvi.