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Department of Mathematics
Johns Hopkins University
Baltimore, MD 21218
office: Krieger 218; (410) 516-7409
Fax: (410) 516-5549
e-mail: jack@math.jhu.edu
Hopkins Mathematics Home Page
 | My principal interests are algebraic topology and global
analysis, and I try to work on questions where they overlap. In recent years
I have concentrated on applications of homotopy theory to modern quantum
field theory.
More specifically, this usually involves techniques from cobordism and K-theory,
applied to problems from equivariant topology (e.g. free loopspaces,
orbifolds, Tate cohomology of spectra), or to the theory of operads and
configuration spaces (with applications to moduli spaces of Riemann
surfaces). Some of my earlier work involved questions in number theory, e.g.
unit groups in division algebras, which are some kind of motivic groups for
the stable homotopy category; I try to keep up with that subject as best I
can. I am currently trying to catch up with recent developments in the study
of four-manifolds and Goodwillie calculus.
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| In terms of mathematical physics, my main interests are
conformal field theory and Donaldson theory, and related (semi-infinite)
cohomology theories. I am currently trying (without great success) to learn
about relations between Seiberg-Witten and integrable systems theory. I have
a long-term interest in questions involving the Yamabe problem, expansionary
cosmologies, and bubbling, and I'd like to know more about the current big
brane theories ...
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| I am currently director of the JAMI
program, which seeks to foster exchanges and interactions between
mathematicians in the US and Japan.
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| Other interests include: processing of stereo images in the
visual cortex, applications of mathematics in the social sciences,
springboard diving and trampolines, and the great Black Sea flood ... |
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