I am a graduate student in mathematics at Boston University. Before attending grad school, I taught math at public high schools in Chicago and Boston though Teach for America. I hold a B.A. in mathematics from Haverford College and a M.A in mathematics from Bryn Mawr College, both earned in 2002. Though my master's thesis was in algebraic topology, I have since become interested in evolutionary dynamics, diversity meausurement, information theory, and complex systems.
Evolutionary dynamics is the mathematical study of patterns that arise through evolutionary processes. Evolving organisms, behaviors, or ideas, can be modeled as agents who reproduce according to their ability to compete with others. The mathematical tools involved are game theory, dynamical systems, and stochastic processes. I am specifically interested in how cooperation can evolve through structured interactions between agents, and in the evolution of mutation rates.
I am also interested in mathematical notions of information and complexity. These ideas are very important for characterizing the behavior of complex systems in a mathematically general way. I am interested both in the abstract formality of these ideas and in their application to specific system such as ecological communities, where ideas from information theory can be used to quantify diversity.
Ben Allen, Mark Kon, Yaneer Bar-Yam. “A New Phylogenetic Diversity Measure Generlizing the Shannon Index and Its Application to Phyllostomid Bats.” American Naturalist, June 23, 2009. pdf
Benjamin Allen. "The Cateory-Theoretic Arithmetic of Information." on the ArXiv.
I maintain PLEKTIX, an expository blog on complex systems topics written for a general audience.
I taught a calculus course for social and life science majors at Boston University, summer 2007. I have also taught both algebra and geometry at the high school level, and assisted in calculus and applied math courses at Boston University.
Boston University Department of Mathematics and Statistics, 111 Cummington St, Boston, MA 02115.
Email: benallen (at) bu.edu