I was in Berkeley the other day, chatting with David Eisenbud about an upcoming Hot Topics workshop at MSRI, and it made me wonder: why don’t we have Cold Topics workshops? In the sense of “cold cases.” There are problems that the community has kind of drifted away from, because we don’t really know how to do them, but which are as authentically interesting as they ever were. Maybe it would be good to programatically focus our attention on those cold topics from time to time, just to see whether the passage of time has given us any new ideas, or cast these cold old problems in a new and useful light.
If this idea catches on, we could even consider having an NSF center devoted to these problems. The Institute for Unpopular Mathematics!
What cold topics workshops would you propose to me, the founding director of the IUM?
Finite groups !
I know that some people still work on the subject but I find it quite amazing (maybe a little bit sad too) that a topic that was at the center of mathematical research a few decades ago is now widely ignored.
The Deligne-Luztig theory (about wich I know nothing) seems to indicate that with modern mathematics one might be able to simplify some things in the classical theory of finite groups.
I would definitely be interested in a CTW on the subject.
Describe explicitly the moduli space of (say, complex) surfaces of general type with p_g=q=0. So popular when I was a young – a quarter century ago.
How about the Standard Conjectures (on motives)?
That was the one I suggested to Eisenbud!
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I think the there should be a bit of a philosophy of science consideration of very basic concepts, like time, space, temperature, etc.
Physics seems to treat them as measures to be plugged into formulae, with the assumption that nothing else matters. As in “shut up and calculate.”
The need for this occurred to me some decades ago, when it occurred to me that while we think of time as the present moving from past to future and this is codified by treating it as measures of duration, it is actually the changing configuration of what is, that turns future into past. Yesterday, today and tomorrow don’t exist along some fourth dimension. Tomorrow becomes yesterday because the earth turns.
Duration is simply the state of the present, as these events come and go.
Alan Watts used the analogy of a boat and its wake to explain this problem. In that the past, the wake doesn’t determine the direction of the boat, the boat creates the wake. Events are first in the present, then in the past. This means that cause yields determination, not the other way around.
So the reason different clocks will run at different rates is because they are separate actions. A faster clock will use energy quicker.
This makes time an effect and measure of action and therefore similar to temperature. When we measure time, it is frequency being measured, while temperature is a combination of amplitude and frequency. It is just that our minds function as a sequence of events and so multiple such sequences are the noise from which each of us extracts the signal of our own perception.
That is why to measure time, we isolate a particular action, from rotations of the planet, to cycles of a cesium atom, but there is no universal measure of time.
The reason time is asymmetric is because it is created by action, of which the primal fact is inertia. That it is acting in one manner and not any other.
Given the linear effect of narrative is foundational to history and thus civilization, this is a much deeper issue than just physics, but I find that physicists take the issue quite personally when I try raising it.
A very cold case.
Yes, too bad there is no such a thing like “Cold topics in Physics”.