REU Students

Summer 2000

Debbie Grier, currently an undergrad at Cornell, will be a graduate student in mathematics at Columbia University in Fall 2002.

Geir Helleloid, currently an undergrad at Wisconsin--Madison, will be a graduate student in mathematics at Stanford University in Fall 2002.

Michael Levin, a 2001 Harvard graduate, is studying Theoretical Physics at MIT.
New Michael's research won Honorable Mention for the 2001 Morgan Prize. This is a prize given for outstanding undergraduate research in mathematics.

Adnan Rubai, a 2001 graduate of Binghamton University, is a graduate student in mathematics at Binghamton University.

References:

A probabilistic approach to the descent statistic, by R. Ehrenborg, M. Levin and M. Readdy, Journal of Combinatorial Theory, Series A, 98 (2002), 150-162.

Quadratic inequalities for the descent set of permutations are developed using a probabilistic reformulation of the descent statistic.

Summer 1997

Dan Johnston is currently an undergrad at Washington University in St. Louis.

Mohan Rajagopalan, an Oberlin undergrad, is currently a graduate student in Logic at Cornell.

Harold Fox entered the MIT Artificial Intelligence Lab in Fall 2001.

References:

Cutting polytopes and flag f-vectors, by R. Ehrenborg, D. Johnston, R. Rajagopalan and M. Readdy, Discrete and Computational Geometry, 23 (2000), 261-271.

We show how the flag f-vector changes when cutting off any face of a polytope. The result is expressed in terms of explicit linear operators on cd-polynomials. The operation of contracting any face of the polytope is also considered.

Inequalities for cd-indices of joins and products of polytopes, by R. Ehrenborg and H. Fox, to appear in Combinatorica.

Explicit expressions for the cd-index of the free join of two polytopes and the Cartesian product in terms of the cd-basis are determined, as well as an inequality relating these two operations on polytopes. This inequality gives evidence for Stanley's conjecture on Gorenstein* lattices.