When Information Theory Meets Algebra and Topology

In recent years, a few surprising connections have arisen between information theory, algebra, and topology. This talk is in a similar vein. We will discuss a certain correspondence between Shannon entropy and continuous functions on topological simplices that satisfy an equation akin to the Leibniz rule from Calculus. The correspondence relies heavily on a particular operad, which is an abstract tool with origins in algebraic topology. A broad goal for this talk is to unwind this result and to share why the confluence of these ideas is both unexpected yet intriguing.

Speaker Bio:

Headshot of SpeakerTai-Danae Bradley is currently a research mathematician at Sandbox AQ and a visiting professor of mathematics at The Master’s University where she helps run the Math3ma Institute. She finished her PhD in mathematics in spring 2020 at the CUNY Graduate Center under the supervision of John Terilla and spent some time as a postdoctoral researcher at X, the Moonshot Factory (Google X). Her research interests lie in the intersection of quantum physics, machine intelligence, and category theory.

Links:
https://www.sandboxaq.com/
https://www.masters.edu/
https://math3ma.institute/
https://qcpages.qc.cuny.edu/~jterilla/