About Me

I am a posdoctoral research mathematician in the Program for Evolutionary Dynamics at Harvard University.  I hold a Ph.D. in mathematics from Boston University.  Before graduate school, I taught high school mathematics in Chicago and Boston.


Research Interests

The main goal of my research is to deepen the mathematical foundations of evolutionary theory.  I develop and investigate axiomatically-defined classes of stochastic evolutionary models.  The aim of this approach is to formalize general principles of evolution and prove them as mathematical theorems. 

I am particularly interested in the interplay of spatial or social structure and the evolution of social behavior.  While particular models have shown many interesting effects--notably, that spatial dispersal can promote cooperation--they have also revealed som puzzling discrepancies.  My research aims to resolve these discrepancies through a mathamtically general, axiomatically grounded approach.


My other interests in evolutionary dynamics include the evolution of mutation rates--both in toy models and in E. coli--and the somatic evolution of cancer.


Beyond evolutionary dynamics, I am interested in the power of information theory to quantify structure, coherence, and diversity in physical, biological, and social systems.  This thread of my research ranges from the concrete (developing information-theoretic measures of biodiversity) to the abstract (using category theory to formalize and abstract the mathematical foundations of information theory).


Publications

Benjamin Allen, Mark Kon, Yaneer Bar-Yam. A new phylogenetic diversity measure generalizing the Shannon index and its application to phyllostomid bats. American Naturalist vol. 174, no. 2, pp. 236-243.  [pdf Appendix]


Benjamin Allen, Arne Traulsen, Corina E. Tarnita, Martin A. Nowak.  How mutation affects evolutionary games on graphs.  Journal of Theoretical Biology in press. [pdf]


Benjamin Allen.  The category-thoeretic arithmetic of information.  Arxiv preprint. [pdf]


Blog

I am the author of Plektix, an expository blog on complex systems.