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Proposal Number: 0901226
Panel Summary:
Panel Summary
The PI is proposing to continue his research program of developing
algorithms for proving (or in some cases, discovering and proving)
combinatorial identities that arise in many different areas of
mathematics.
The panel consensus is that the PI has had a tremendous impact in
combinatorics, with several spectacular successes, such as the first
proof of the Robbins ASM conjecture, and the development of the W-Z
method. The work from his prior (5 year grant) seems to be continuing
at a high level, and the number of papers produced (30 listed) is
impressive. One concern of the panel is that the techniques the PI has
developed, when applied to specific problems, tend to provide proofs
that yield no insight. Another concern is that the proposal itself is
neither well-written nor convincing. The panel's favorable view of the
intellectual merit of the proposal is primarily based on his prior
record.
The panel consensus is that the proposal is also very strong in
terms of broader impacts. Particularly notable is his record of 6
doctoral students supervised during the term of the previous grant, and
his practice of developing and freely sharing software for proving
identities.
The panel places this proposal in the highly recommended for funding category.
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