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February 4: Nathanael Berestycki
Introduction to mixing times and the cutoff phenomenon
How many times should you shuffle a deck of cards so that its distribution is approximately uniform? This question can be formalised through the notion of mixing time for a Markov chain. Elementary theory tells us that, given an irreducible and aperiodic Markov chain on a
Lisa Piccirillo received the 2019 Michael H. Granof Award, which recognizes the outstanding Ph.D. dissertation of the year from any UT Austin department. Lisa's Ph.D. thesis, "Knot Traces and the Slice Genus”, written under the supervision of Prof. John Luecke, contains several remarkable results in knot theory, including the theorem that the Conway knot is not slice, i.e., it does not bound a smooth embedded disk in the 4-ball. The Conway knot is notoriously difficult to handle, and was the only knot of at most 12 crossings for which the slice property had not been decided.