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Series: Research Horizons Seminar

Series: Research Horizons Seminar

Series: Research Horizons Seminar

Series: Research Horizons Seminar

Series: Research Horizons Seminar

Series: Research Horizons Seminar

Series: Research Horizons Seminar

After briefly describing my research interests, I’ll speak on two results that involve points moving around on surfaces. The first result shows how to “hear the shape of a billiard table.” A point bouncing around a polygon encodes a sequence of edges. We show how to recover geometric information about the table from the collection of all such bounce sequences. This is joint work with Calderon, Coles, Davis, and Oliveira. The second result answers the question, “Given n distinct points in a closed ball, when can a new point be added in a continuous fashion?” We answer this question for all values of n and for all dimensions. Our results generalize the Brouwer fixed point theorem, which gives a negative answer when n=1. This is joint work with Chen and Gadish.

Series: Research Horizons Seminar

Integer sequences arise in a large variety of combinatorial problems as a way to count combinatorial objects. Some of them have nice formulas, some have elegant recurrences, and some have nothing interesting about them at all. Can we characterize when? Can we even formalize what is a "formula"? I will try to answer these questions
by presenting many examples, results and open problems.
Note: This is an introductory general audience talk unrelated to the colloquium.

Series: Research Horizons Seminar

In this talk, we describe transforming a theoretical algorithm from
structural graph theory into open-source software being actively used for
real-world data analysis in computational biology. Specifically, we apply
the r-dominating set algorithm for graph classes of bounded expansion in
the setting of metagenome analysis. We discuss algorithmic improvements
required for a practical implementation, alongside exciting preliminary
biological results (on real data!). Finally, we include a brief
retrospective on the collaboration process. No prior knowledge in
metagenomics or structural graph theory is assumed.
Based on joint work with T. Brown, D. Moritz, M. O’Brien, F. Reidl and T.
Reiter.

Series: Research Horizons Seminar

Random and irregular growth is all around us. We see it in the form of
cancer growth, bacterial infection, fluid flow through porous rock, and
propagating flame fronts. In this talk, I will introduce several
different models for random growth and
the different shapes that can arise from them. Then I will talk in more
detail about one model, first-passage percolation, and some of the main
questions that researchers study about it.