Caroline Klivans

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. She is an associate professor of applied mathematics at Brown University, and associate director of the Institute for Computational and Experimental Research in Mathematics at Brown.

Education and career

As an undergraduate at Cornell University, Klivans was the 1999 winner of the Alice T. Schafer Prize of the Association for Women in Mathematics for excellence in mathematics by an undergraduate woman, for an undergraduate research project involving robot navigation algorithms.[1] She graduated from Cornell in 1999, and completed her Ph.D. at the Massachusetts Institute of Technology in 2003.[2] Her dissertation, Combinatorial Properties of Shifted Complexes, was supervised by Richard P. Stanley.[3]

After postdoctoral research at the Mathematical Sciences Research Institute and the University of Chicago, where she was an L. E. Dickson Instructor, and positions as a researcher and lecturer at the University of Chicago and Brown University, she became associate director of the Institute for Computational and Experimental Research in Mathematics at Brown in 2015, and obtained a regular-rank faculty position as associate professor there in 2018.[2]

Contributions

Klivans is the author of the book The Mathematics of Chip-Firing (CRC Press, 2018).[4]

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.[5]

gollark: I would be willing to take that chance for unreasonably large amounts of money.
gollark: There are a bunch of annoying questions which I could resolve much more easily with information from future versions of me, except I *also* probably need access to the counterfactuals somehow.
gollark: Oh, I assumed you were analogizing the random future things to a giftcard, but great?
gollark: You have a good point, giftcard bad.
gollark: If it can conveniently be brought back and doesn't rely on difficult future infrastructure, I suppose.

References
  1. Alice T. Schafer Prize for Excellence in Mathematics by an Undergraduate Woman 1999, Association for Women in Mathematics, retrieved 2020-05-12
  2. Curriculum vitae (PDF), retrieved 2020-05-12
  3. Caroline Klivans at the Mathematics Genealogy Project
  4. Reviews of The Mathematics of Chip-firing:
    • Dreyer, Paul A. Jr., Mathematical Reviews, MR 3889995CS1 maint: untitled periodical (link)
    • Perkinson, David (August 2019), "Review", MAA Reviews, Mathematical Association of America
    • Glass, Darren (January 2020), The American Mathematical Monthly, 127 (2): 189–192, doi:10.1080/00029890.2020.1685835CS1 maint: untitled periodical (link)
  5. Davies, Emily (April 3, 2017), "Faculty member disproves established math conjecture: Caroline Klivans, senior lecturer, discredits long-accepted Partionability Conjecture theory", Brown Daily Herald
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