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Week of Events
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State Polytopes of Combinatorial Neural Codes (Rob Davis, HMC)
State Polytopes of Combinatorial Neural Codes (Rob Davis, HMC)
Combinatorial neural codes are 0/1 vectors that are used to model the co-firing patterns of a set of place cells in the brain. One wide-open problem in this area is to determine when a given code can be algorithmically drawn in the plane as a Venn diagram-like figure. A sufficient condition to do so is […]
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Applications of Cayley Digraphs to Waring’s Problem and Sum-Product Formulas (Yesim Demiroglu, Harvey Mudd)
Applications of Cayley Digraphs to Waring’s Problem and Sum-Product Formulas (Yesim Demiroglu, Harvey Mudd)
Abstract: In this talk, we first present some elementary new proofs (using Cayley digraphs and spectral graph theory) for Waring's problem over finite fields, and explain how in the process of re-proving these results, we obtain an original result that provides an analogue of Sarkozy's theorem in the finite field setting (showing that any subset […]