The ACO Seminar (2010-2011)
, 3:30pm, Porter Hall 125C *** NON-STANDARD ROOM ***
, Univesity of Chicago
A substantial part of extremal combinatorics studies relations existing
between densities with which given (fixed size) combinatorial structures may
appear in unknown (and presumably very large) structures of the same type.
Using basic tools and concepts from algebra, analysis and measure theory, we
develop a general framework that allows to treat all problems of this sort
in an uniform way and reveal mathematical structure that is common for most
known arguments in the area. The backbone of this structure is made by commutative
algebras defined in terms of finite models of the associated first-order theory.
In this talk I will give a general impression of how things work in this
framework, and we will pay a special attention to concrete applications of our methods.
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