Working with colleagues from the University of Texas at El Paso and the University of Kansas, Caroline Klivans (a Senior Lecturer in applied mathematics and computer science at Brown University and Associate Director of the Institute for Computational and Experimental Research in Mathematics) has achieved a rare feat: disproving a conjecture first put forth in 1979.
In mathematics, a simplicial complex is a set composed of points, line segments, triangles, and their n-dimensional counterparts. In 1979, Richard Stanley made the Partitionability Conjecture: that all simplicial complexes that met a certain algebraic condition also met a particular combinatorial condition. Until the counterexample provided by Caroline and colleagues, the conjecture was widely perceived in the community to be true. Questions of how various algebraic, geometric, topological and combinatorial properties interact have now been reopened.
Their research is featured in the Notices of the American Mathematical Society and is available here.