The Index Conjecture in Zero-Sum Ramsey Theory, Resolved

Start Date: October 28, 2026
End Date: October 28, 2026
Event Start Time: 12:15 PM
Event End Time: 1:15 PM
Seminar Type: Current Seminars
Seminar location:
Graduate Student Lounge | 7th Floor | Hill Center
Seminar Series: Graduate Combinatorics Seminar
Presenter(s): Andrew Pendleton, Rutgers University, Math
Abstract:
Zero-sum sequences over a finite cyclic group Z/nZ are long-studied objects in additive combinatorics. For almost 40 years, mathematicians have been working to understand an invariant of these sequences called the index. The index of a minimal zero-sum sequence was well understood in all cases except for sequences of length 4 with n coprime to 6. This mysterious exception is the subject of the index conjecture, and it has resisted attacks from many sophisticated techniques. In this talk, we will discuss the history of the conjecture and its recent resolution through the application of Fourier analysis on Dirichlet characters.

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