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Colloquium: Gilles Zemor (Université de Bordeaux) - "Additive Combinatorics in Field Extensions" | Einstein Institute of Mathematics

Colloquium: Gilles Zemor (Université de Bordeaux) - "Additive Combinatorics in Field Extensions"

Date: 
Thu, 22/03/201815:30-16:30
Location: 
Manchester Building (Hall 2), Hebrew University Jerusalem
Additive combinatorics enable one to characterize subsets S of elements in a group such that S+S has small cardinality. We are interested in linear analogues of these results, namely characterizing subspaces S in some algebras (mostly extension fields) such that the linear span of the set S^2 of products st, for s,t in S, has small dimension. We shall present a linear analogue of a theorem of Vosper which says that under the right conditions, a sufficiently small dimension for S^2 implies that S has a basis of elements in geometric progression. We shall also attempt to go beyond this theorem and claim that when the dimension of S^2 is sufficiently small, S must be close to a Riemann-Roch space of an algebraic curve of small genus.
Based on joint works with Christine Bachoc, Alain Couvreur and Oriol Serra.