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COLLOQUIUM Jones’ Conjecture and Matsuda Branched Surfaces Dr. Douglas LaFountain Visiting Postdoc and Lecturer University of California, Berkeley Abstract Conjectures that are easy to state and yet difficult to prove provide wonderful grist for the mill of mathematics. In this talk we will discuss a 25-year-old conjecture of Vaughan Jones concerning topological links and closed braids, namely that the algebraic length of a braid at minimum index is a link invariant. We will present a new approach to this problem which reduces the original question to a more tractable conjecture concerning links projected onto a specific family of simple branched surfaces, providing hope for an affirmative resolution of the general problem. This is joint work with Hiroshi Matsuda and Bill Menasco; familiarity with the subject will not be required. Department of Mathematics Wednesday, February 29th, 2012 4:00 p.m. 204 Morgan Hall Refreshments will be served at 3:45 p.m.