I’ve recently run across various interesting mathematically oriented sites, each with some connection to physics:
Alain Connes now has a web-site. He’s now a professor at Vanderbilt University as well as at the College de France. I can see him in Robert Altman’s movie “Nashville”. His site contains quite a few interesting things, including most of his research articles and some interesting survey articles about his work on non-commutative geometry. For instance, take a look at his “A View of Mathematics”, which starts off with a wonderful description of doing mathematical research and some interesting history of geometry, before surveying his recent work relating non-commutative geometry and physics.
David Ben-Zvi at Austin is organizing a new lecture series to be made available over the web called GRASP (for Geometry, Representations and Some Physics), which sounds promising although it is just getting started.
The MIT math department sponsors something called the Talbot workshops. Last year the topic was elliptic cohomology, this year geometric Langlands. Notes from the lectures are available courtesy of Megumi Harada who also maintains a useful website of geometry conferences, many of which have some sort of physics component.
Speaking of links, the readers of Peter can be marginally interested on the schedule of the Strings 2005 conference, early this July.
http://www.fields.utoronto.ca/programs/scientific/04-05/string-theory/strings2005/program.html
I learnt a lot of things in this blog of yours Peter. A you can see many links come from your posts.
I have included a correction to previous post quotation. I might have given the wrong link. I had to give credit to Alain Connes for the statement, and it did not show this. I stand corrected here now.
I think that Connes idea of a “map” between geometrical items and operator ones is interesting, but I doubt that we can obtain some really fundamental.
I am not sure of that noncommutative geometry solves some of the more difficult open questions in differential geometry. See, e.g. my criticism to infinitesimals on page 5 of Official launching
Moreover, It is unlikely that noncommutative geometry alone can be the key for our understanding of quantum gravitation.
I followed Connes up through ds=1/D then he sort of lost me. But that’s a great read. Anything with Desargue’s Theorem in it is worth reading.
-drl
Part of the ability of good mathematicians is to provide new language where our previous discriptions were lacking
Part of the ability of good scientists is to provide new models of nature where our previous discriptions were lacking
A mixture of bad math more bad physics is of litte interest for us.
Humm. Bad math more bad physics. where do i read some similar?… perhaps in some 10D universe in my last travel?
0 + 0 = 2·0 = nothing vibrating.
An additional dimension does not change the result.
Most mathematicians adopt a pragmatic attitude and see themselves as the explorers of this mathematical world” whose existence they don’t have any wish to question, and whose structure they uncover by a mixture of intuition, not so foreign from poetical desire”, and of a great deal of rationality requiring intense periods of concentration.
Each generation builds a mental picture” of their own understanding of this world and constructs more and more penetrating mental tools to explore previously hidden aspects of that reality.
Like Lenny Susskind?
Isn’t this part of the ability of good mathematicians is to provide new language where our previous discriptions were lacking? New forms/models of math?
He.
I’m reading your blog for some time now and enjoy it very much. Personally, I’m more on the “mathematical side” but with some interest in how ideas from physics motivate new mathematical questions and insights (like the paper of Witten on Morse-Theory or the one by Kontsevich on Deformation Quantization) and I appreciate the mathematical posts very much.
Best regards,
Florian.
Just wanted to say that I always appreciate the math links. Thanks.
Thanks. “Integral conformal invariants” sound interesting 🙂
-drl
Hi Danny,
Kind of too big a topic, since “geometry” in one form or another covers maybe at least a third of all mathematics research. For some idea of the range of things people work on, there’s a conference here at Columbia this week in honor of a great geometer, my colleague Masatake Kuranishi, who is 80 and retired this past year. See
http://www.math.columbia.edu/%7Ewoit/kuranishi_schedule.html
One hot topic is the curvature flow technique pioneered by Richard Hamilton, and used by Perelman to give at least an outline of a proof of the Poincare conjecture. Besides trying to nail down the details of this, people are applying this kind of technique to questions in complex geometry.
Could you give an overview of what is going on in geometry these days?
-drl