Caroline Jane (Carly) Klivans is an American mathematician specializing in algebraic combinatorics, including work on cell complexes associated with matroids and on chip-firing games.
Lebanon High School,[1] Kilvan attended Cornell University where she was the 1999 winner of the Alice T. Schafer Prize of the Association for Women in Mathematics.
[3] Her dissertation, Combinatorial Properties of Shifted Complexes, was supervised by Richard P.
[6] Her research contributions include a disproof of a 50-year-old conjecture of Richard Stanley that every abstract simplicial complex whose face ring is a Cohen–Macaulay ring can be partitioned into disjoint intervals, each including a facet of the complex.
Such a partition generalizes a shelling and (if it always existed) would have been helpful in understanding the h-vectors of these complexes.