“The lack of real contact between mathematics and biology is either a tragedy, a scandal or a challenge, it is hard to decide which.” - Gian Carlos Rota
My belief is that the lack of contact between biology and mathematics is a challenge and I hope to use this page to explore the frontiers of this interaction. In particular, how abstract mathematical ideas from algebraic topology, category theory, and beyond can be used to study biological systems and there dynamics. Many of these ideas are just beginning to emerge but provide interesting tools to problems we deal with in biology.The 'Notes' section is where the bulk of the ideas are. Intially, I plan on beginning with Persistent Homology (first draft is already uploaded) and then Discrete Morse Theory. These are rapidly developing areas of research and have already seen many applications. From there I hope to get to Sheaf theory and eventually Conley Index Theory and Discrete Hodge Theory. These notes will most likely keep evolving as I learn more and find more interesting applications.
The 'Snippets' section contains short notes on computational tools and methods that are revelant in biology.