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Ramsey Theory: From Finite to Infinite

Yoni Marshall, Department of Mathematics, Washington University in St. Louis

March 28, 2011 - 10:00 am to 11:00 am
Location: Cupples I, Room 199 | Sponsor: Prof. Ron Freiwald

Senior Undergraduate Honors Thesis Presentation
Abstract: We will present a survey of some results in Ramsey Theory, ranging from classic theorems that form the basis of the field to recent results that apply combinatorial techniques to the theory of Banach Spaces. First we will present classical Ramsey Theory. Next we will present a discussion of how the results in finite Ramsey Theory carry over (or fail to carry over) to the infinite case, examining finite and infinite colorings of countable and uncountable sets. Finally, we will present an application of Ramsey-theoretic combinatorial technique to a class of Hilbert spaces, which was, somewhat surprisingly, recently used to answer an open question of Banach in functional analysis.


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