Background
Research
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I am currently primarily involved in a joint project with
D. Sinha
extending our work on
Lie coalgebras and
related structures in algebraic topology. Our initial
application was in rational homotopy theory, but we plan
extensions to characteristic p, infinite fundamental
groups and the topological setting,
as well as applications to the word problem in group theory,
to cohomology of symmetric groups, a generalized Hopf invariant
one question, and general operad theory.
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Related to this, I have spent a lot of time thinking about
dg and topological operad theory. I have contributed work in
cooperad and coalgebra theory in an ongoing project to better
understand cooperads in general symmetric monoidal categories.
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My dissertation was on Goodwillie's homotopy calculus of
functors. I am still interested in applications of this as well
as Weiss' orthogonal calculus of functors.
B. Munson
and I have preliminary work constructing a new calculus
of graph functors which we hope to use to streamline
computations of chromatic
numbers of graphs à la Babson and Kozlov.
Teaching
Papers (and Works in Progress)
Random Other Notes
Algebraic Topology Stuff
|......
|..i...
+..!..! If I were a NetHack
monster, I would
be a tengu. I'm always in the right place at the right time,
and am quick to
avoid people that I'd rather not be with. |
Misc Links
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I do not say, that Mathematicians, as such, are Infidels; or that
Geometry is a Friend to Infidelity....
-- G. Berkeley, A Defence of Free-Thinking in Mathematics
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math.purdue.edu