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Dave Caldwell, University of DelawareDave Caldwell, University of DelawareEwing 336TBA12/4/2017 5:00:00 PM12/4/2017 6:00:00 PMFalse
Noah Forman, University of WashingtonNoah Forman, University of WashingtonEwing 336Title: Random walks on a space of trees with integer edge weights <br></br> Abstract: Consider the Markov process in the space of binary trees in which, at each step, you delete a random leaf and then grow a new leaf in a random location on the tree. This is applied in MCMC algorithms for phylogenetic inference. In 2000, Aldous conjectured that it should have a continuum analogue, which would be a continuum random tree-valued diffusion. We will discuss a family of projectively consistent Markov chains that are projections of this tree, and discuss how these representations can be passed to the continuum. This is joint work with Soumik Pal, Douglas Rizzolo, and Matthias Winkel. 11/27/2017 8:30:00 PM11/27/2017 9:30:00 PMFalse
Steve Melczer, University of PennsylvaniaSteve Melczer, University of PennsylvaniaEwing 336TITLE: Lattice Path Enumeration, Multivariate Singularity Analysis, and Probability Theory <br><br> ABSTRACT: The problem of enumerating lattice paths with a fixed set of allowable steps and restricted endpoint has a long history dating back at least to the 19th century. For several reasons, much research on this topic over the last decade has focused on two dimensional lattice walks restricted to the first quadrant, whose allowable steps are "small" (that is, each step has coordinates +/- 1, or 0). In this talk we relax some of these conditions and discuss recent work on walks in higher dimensions, with non-small steps, or with weighted steps. Particular attention will be given to the asymptotic enumeration of such walks using representations of the generating functions as diagonals of rational functions, through the theory of analytic combinatorics in several variables. Several techniques from computational and experimental mathematics will be highlighted, and open conjectures of a probabilistic nature will be discussed. 11/6/2017 8:30:00 PM11/6/2017 9:30:00 PMFalse
Chad Giusti, University of DelawareChad Giusti, University of DelawareEwing 336Title: A survey of stochastic topology Abstract: The study of probability distributions on matrices and graphs provide baseline tools for scientific inference about combinatorial models for complex systems. The recent development of effective computational tools in algebraic topology opens the door to a expanding this picture with a rich new family of models and measures: random simplicial complexes and (persistent) homology. We will survey the basic questions and some fundamental and recent results from this emerging field.10/30/2017 7:30:00 PM10/30/2017 8:30:00 PMFalse

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