M. Bays: The geometry of combinatorially extreme algebraic configurations
Thursday, 07.12.2017 11:00 im Raum SR 1D
Given a system of polynomial equations in m complex variables with solution set of dimension d, if we take finite subsets X_i of C each of size at most N, then the number of solutions to the system whose ith co-ordinate is in X_i is easily seen to be bounded as O(N^d).
We ask: when can we improve on the exponent d in this bound?
Hrushovski developed a formalism in which such questions become amenable to the tools of model theory, and in particular observed that incidence bounds of Szemeredi-Trotter type imply modularity of associated geometries. Exploiting this, we answer a (more general form of) our
question above. This is part of a joint project with Emmanuel Breuillard.
Angelegt am Thursday, 30.11.2017 14:43 von Martina Pfeifer
Geändert am Thursday, 30.11.2017 14:43 von Martina Pfeifer
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