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Abstract: Permutations are 1-1 maps from a set of n symbols {1,2,...,n} to itself. To begin this talk I will discuss how you multiply two permutations, and how each permutation has an inverse. In fact, permutations form a "group". Then we will discuss how the group of permutations can be generalized to the group of braids. There are only finitely many permutations for each integer n, but there are infinitely many braids.
The "word problem" is a fundamental algorithmic problem in infinite groups. We will discuss it via the example of the braid group. Then we will discuss one way to solve it. The solution shows that, in some ways, the connections between permutations and braids is very strong. At the end of the talk we will discuss how a new set of generators for the braid group can be used to give a very fast algorithm for solving the word problem.
Everyone is invited. A reception with refreshments for midshipmen will follow the talk.