Dr. Russ Woodroofe
Assistant Professor of Mathematics
Research interests: Geometric combinatorics, including connections to group theory and commutative algebra; shellable and Cohen-Macaulay posets and complexes, subgroup and coset lattices.
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My research is in connections between combinatorics, topology, and algebra. I often study problems that are related to subgroup lattices, or to commutative algebra. Given a subgroup lattice, or indeed any lattice, there is a standard way of associating a simplicial complex. What can you say about the underlying group (or more generally lattice) from the topology of the associated simplicial complex?
Some recent work that I'd like to highlight is with my colleague Jay Schweig. We've discovered a lattice-theoretic analogue of the condition of solvability for finite groups. Our work on these lattices gives a unified proof of shellability for many examples that weren't previously known to be closely connected.
Degree: Ph.D. in Mathematics, 2005, Department of Mathematics, Cornell University