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SUMMARY:ARC Colloquium: Gil Kalai\, Hebrew University of Jerusalem- Israel/Yale University - New Haven\, CT
DESCRIPTION:Title: Probability and Algorithms - Examples of open collaborative research over the Internet\nAbstract:\n I shall discuss examples of recent Internet research oriented math activities:\n 1) Polymath5 - Erdos discrepancy problem.\nThe problem is to find a function from the natural numbers to {-1\,1} such that the sum of values on any sequence of the form {a\,2\,3a\,...\,ra} is bounded. Erdos conjectured that no such function exists. It is still open even after many individual attempts and an attempt to solve it collectively in a polymath project.\nBackground: please look at this MO problem\nhttp://mathoverflow.net/questions/105383/the-behavior-of-a-certain-greedy-algorithm-for-erds-discrepancy-problem  (and the blog post linked there.)\n 2) The study of Mobius randomness over blogs and MathOverflow.\n A function defined on the natural number is Mobius-random if its correlation with the Mobius function tends to zero. The prime number theorem asserts that the constant one function is Mobius random. I will discuss the result by Ben Green that functions described by bounded depth circuits are Mobius-random.\nHere is one link\nMO posts: http://mathoverflow.net/questions/57543/walsh-fourier-transform-of-the-mobius-function\, which contains more links.\nI may briefly mention a couple more examples. One is my debate with Aram Harrow on the feasibility of quantum computers. It took place over the blog "Goedel's lost letter and NP=P" (The first post the last post ) and the other is probability-motivated questions regarding the computer game "angry birds".\nI will try to give some taste of the mathematical problems/issues and also a little taste of this way of "doing mathematics".\n \n \n
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