Topic: Distinct Partial Sums in Cyclic Groups
Abstract:
It has been conjectured that one may always order any subset of the non-zero integers modulo n in such a way that all the partial sums are distinct. We discuss our progress on this conjecture using the polynomial method.
This is joint work with Jacob Hicks (U. Georgia) and Matt Ollis (Marlboro College).
Biography:
John Schmitt (homepage) is an Associate Professor of Mathematics and has been at Middlebury College since 2005. He received his B.A. from Providence College, his M.S. from the University of Vermont, and a Ph.D. from Emory University.
His research interests are in combinatorics (the art of counting) and graph theory (the study of networks), with a particular fondness for implementing the polynomial method. He has co-authored numerous research articles. His Erdös number is two. His research has been supported by the following external sources: National Science Foundation, National Security Agency and VT-EPSCoR. He has held visiting positions at the Institute for Pure and Applied Mathematics at UCLA and at Carnegie Mellon University.
Professor Schmitt enjoys teaching students how to count and play (combinatorial) games – things they thought they already knew. Students are frequently involved with his research. His efforts in teaching were recognized by students in 2016 with the Perkins Award.
John has a passion for growing his own organic produce. His favorite new sport is wake-foiling.