Math CS Colloquium, Vincent Guingona (WES):"On Generalized Notions of Dimension"

Thursday, November 19, 2015
4:15 PM - 5:15 PM (ET)
Exley 121
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Han Li
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Abstract: In many areas of mathematics, there are various notions of dimension, like the dimension of a vector space, or the dimension of an algebraic variety over the complex field, or the dimension of a semi-algebraic set over the reals. What can we say about dimension in a general setting when looking at an arbitrary structure? In this talk, I discuss several notions of dimension for abstract structures, including dp-rank, o-minimal dimension, and Morley rank. Tying all of these dimension notions together is the notion of VC-density, which is a measure of the combinatorial complexity of set systems. I define VC-density, discuss how it relates (or conjecturally relates) to the other notions of dimension, and give open problems and partial solutions about computing VC-density in certain classes of structures.

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