The new Center for the Topology and Quantization of Moduli Spaces (CTQM) at Aarhus University wins my award for the most specialized pure mathematics institute. It will be hosting an opening symposium in a couple weeks featuring several talks that look interesting. If one is going to choose a specialized subject, this is an excellent one. Over the last couple decades the study of the moduli space of curves and of the moduli space of flat connections on a bundle over a surface has led to the discovery of many previously unsuspected relations between different parts of mathematics and between mathematics and physics. The fact that this subject is so fruitful remains somewhat of a mystery, and there is undoubtedly much more to be learned.
The National Academy of Sciences EPP 2010 committee should soon be producing a report with a 15 year plan for the future of high energy physics in the U.S. At the last meeting of the group last month Fermilab director Pier Oddone gave a presentation, focusing on opportunities in neutrino physics, strategy concerning the ILC, and the future of Fermilab.
Last week there was a conference on Particle Physics at the Verge of Discovery at Aspen. Lot of interesting talks on experimental particle physics. For an overview, see the summary talk by Paul Grannis.
The Templeton funded Foundational Questions Institute (FQXi) has announced that it will be publishing its inaugural request for proposals on Monday. This organization is led by Max Tegmark, who will be here at Columbia that day giving a physics department colloquium on From Derision Cosmology to Precision Cosmology. Unfortunately I have to be away that day and will miss the talk although I would have liked to attend it.
Steve Hsu, a physicist with a serious interest in economics, writes:
You might think science is a weighing machine, with experiments determining which theories survive and which ones perish. Healthy sciences certainly are weighing machines, and the imminence of weighing forces honesty in the voting. However, in particle physics the timescale over which voting is superseded by weighing has become decades — the length of a person’s entire scientific career. We will very likely (barring something amazing at the LHC, like the discovery of mini-black holes) have the first generation of string theorists retiring soon with absolutely no experimental tests of their *lifetime* of work. Nevertheless, some have been lavishly rewarded by the academic market for their contributions.
Scott Aaronson describes his field of computational complexity theory as “quantitative theology”, and goes on to note:
Incidentally, it’s ironic that some people derisively refer to string theory as “recreational mathematical theology.” String theory has to earn the status of mathematical theology — right now it’s merely physics! A good place for string theorists to start their theological training is this recent paper by Denef and Douglas.
Lee Smolin is giving a course on background independent quantum theories of gravity at the Perimeter Institute, with the lectures available online.
David Corfield has an interesting posting on research programs in mathematics. It includes links to various things from Ronald Brown including a new paper on Ehresmann’s work on groupoids, and his web-page on “Higher Dimensional Group Theory”. Among other things worth reading at Brown’s site is his account of the origins of Grothendieck’s “Pursuing Stacks”.
The biggest problem, in my opinion, is to come up with a specific vision of where homotopy theory should go, analogous to the Weil conjectures in algebraic geometry or the Ravenel conjectures in our field in the late 70s. You can’t win the Fields Medal without a Fields Medal-winning problem; Deligne would not be DELIGNE without the Weil conjectures and Mike Hopkins would not be MIKE HOPKINS without the Ravenel conjectures.
I first met Mike Hopkins at a conference in Guanajuato around 1990, and he made a big impression on me. One thing that most impressed me (besides his joking comment that he went into topology because it was a field full of hard-drinking and living guys who got into gun-fights (this last part was a reference to Dennis Sullivan)), was the mathematical ambition he demonstrated. He said that he had up till then made his reputation proving other people’s conjectures, but now wanted to start making his own. Mike definitely followed through on this, since a sizable number of Hovey’s problems are inspired by him. His talk on elliptic cohomology in Guanajuato was a revelation, and he has over the years continued to work in that area, coming up with dramatic new ways of thinking about the subject.
Update: There is an extensive discussion of the Smolin lectures at Christine Dantas’s website.