# 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.