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ItemSome problems in additive combinatorics & analytic number theory(Georgia Institute of Technology, 2011-01-09) Croot, Ernest ; Georgia Institute of Technology. Office of Sponsored Programs ; Georgia Institute of Technology. School of Mathematics ; Georgia Institute of Technology. Office of Sponsored Programs
ItemNew Applications of the Polynomial Method to Problems in Combinatorics(Georgia Institute of Technology, 2016-10-13) Croot, Ernest ; Georgia Institute of Technology. School of MathematicsErnest Croot will discuss some new applications of the polynomial method to some classical problems in combinatorics, in particular the Cap-Set Problem. The Cap-Set Problem is to determine the size of the largest subset A of F_p^n having no three-term arithmetic progressions, which are triples of vectors x,y,z satisfying x+y=2z. I will discuss an analogue of this problem for Z_4^n and the recent progress on it due to myself, Seva Lev and Peter Pach; and will discuss the work of Ellenberg and Gijswijt, and of Tao, on the F_p^n version (the original context of the problem).