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Caprice Stanley, Suzanne Crifo, NC State
April 23, 2018 | 3:00 pm - 4:00 pm EDT
Speaker 1: Caprice Stanley
Title: Markov Chain Mixing Time
Abstract: Informally a Markov chain is a memoryless stochastic process and its mixing time is the time required for the chain to be near its stationary distribution. Depending on the context, analysis of mixing time can be of great importance. For example, random walk-based algorithms for sampling should have fast mixing in order to be practical and efficient.
In this talk we carefully define these notions and describe some mixing time type problems. In particular we will look at families of Markov chains indexed by some set and show results about the mixing behavior of these chains as a function of the index. This talk will be accessible for general audiences.
Speaker 2: Suzanne Crifo
Title: Some Maximal Dominant Weights and Their Multiplicities for Affine Lie Algebra Representations
Abstract: Affine Lie algebras are infinite dimensional analogs of finite dimensional simple Lie algebras. In this talk we give background on these as well as their representations. The set of weights of a representation is an infinite set. However, the set of maximal dominant weights is a finite weight. Knowing this finite set of maximal dominant weights, we can determine other weights. We focus in detail on finding the maximal dominant weights for the affine Lie algebra B_n^{(1)} and give our results for other types.