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53 KAM Mathematical Colloquium

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Prof. Ehud Friedgut

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Hebrew University, Jerusalem

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SOME APPLICATIONS OF FOURIER ANALYSIS IN COMBINATORICS

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February 2, 2005

Lecture room S5, II. floor
10:30 AM

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Abstract

Why do graph properties emerge so suddenly in random graphs when the edge probability changes slightly?
What is the largest number of triangles one can construct with one million edges? (an edge can be shared by
many triangles.) What are the optimal colorings of the graph of the $n$-fold product of a triangle?
And most importantly - what do these questions have to do with Fourier analysis? The answers
involve calculating partial derivatives, estimating different norms of certain functions,
and understanding the eigenvalues of certain matrices - in short, a delicious mixture of
mathematical flavors that arise when applying discrete Fourier analysis to combinatorial
questions.