Mathematical Structures^1594.8 Discussion
N. Seiberg I have a question to the current speaker. Putting derivatives in expo-
nentials is very common when you consider fields in non-commutative spaces.
Is there any connection to your work?
M. Atiyah I do not know. Non-commutative geometry/analysis is a very inter-
esting part of mathematics and physics has a link to all these things. It could
well be. I approach this from a very different point of view. I just naively ask
certain philosophical questions and I am led to this by the nature of the for-
malism. I have not had time to search the literature, but I would be delighted
if it links up with anything else you or anybody else knows in physics, or in
non-commutative geometry. The hope is, of course, that all the ideas we have
been talking about, string theory, non-commutative geometry, and so on, are
obviously related in some way. We want to cleax the ground and find out what
the real relations are. If this plays any role, I would be delighted.H. Ooguri I would like to reserve some time for general discussions. I recently
read the history of this conference and there is a preface that was written by
Werner Heisenberg who commented that this conference has been held for the
purpose of attacking problems of unusual difficulty rather than exchanging the
results of recent scientific work. In that spirit I would like to raise the question:
What would be the important physics programs that are still waiting for some
new mathematical tool? Or maybe are there some hidden tools that we are not
aware of, that we should try to make use of?M. Douglas I am coming back actually to answer the question of Harvey and also
Seiberg’s second question, which I hope are the kind of general questions you
were asking. There is all this wealth of mathematics and structures, but we
are physicists and we have to address some physical question to make progress.
The basic physical questions are the combination of the ones that we started
to work on twenty years ago: trying to get the standard model out of stringcompactifications. This has made twenty years of progress and inspired a lot of
the mathematics that Dijkgraaf talked about. Also, there is the recent discovery
of the dark energy, which in the simplest models is a positive cosmological
constant. Those are the experimental facts that seem the most salient to the
type of work that we were discussing.
Let me turn then to Seiberg’s second question. We have this big number of
Calabi-Yaus, and this potentially vaster number of non Calabi-Yaus. We have
an even vaster number of flux vacua. What number of them looks like the real
world? That is obviously a very hard question. I think this mathematics is
relevant because it gives us tools for addressing problems that we, as physicists,
have had very little experience with. Namely, exploring this vast mathematical
space of possibilities in string theory. Experimental input is essential, such as
the standard model and what will be discovered at LHC, but also this math-