
Now available: A Finite-Dimensional String 2-Group
I am currently an NSF postdoc at Harvard University and a C. L. E. Moore Instructor at MIT (on leave for the '09-'10 academic year). I graduated from UC Berkeley in 2009 under the guidance of my fantastic advisor, Peter Teichner.
Research: Three areas: Topology, Higher Categories, and Quantum Field Theory. I'm interested in the interactions of these subjects, and my research emphasizes how to exploit these interactions to learn something new and interesting. My Dissertation (Last updated May 16th, 2009) classified 2-dimensional extended topological field
theories in terms of generators and relations. In this context, a topological field theory
is a functor from a bordism category to some target category and an extended
field theory is a higher categorical version of this. Why use higher categories? They allow you to mathematically encode the locality of the theory, something which is predicted from the physical point of view and which is very helpful mathematically. Combining some algebraic results on symmetric monoidal bicategories with a generalization of Cerf
theory, I obtained an explicit generators and relations description of the
2-dimensional bordism bicategory, effectively classifying extended 2D TFTs with any
target bicategory. This has lead to new joint work with Christopher Douglas where we
extend these results to higher dimensions. I've given several talks on this work, and it was featured on John Baez's This Week's Finds in Mathematical Physics (Week 275). Another direction my research has turned of late is to the higher categorical geometry of the String group. I have given a construction of a finite dimensional model of the String group as a group object in the bicategory of Lie groupoids, left principal bibundles, and bibundle maps, which is now available as a preprint. This has lead to some new results in bicategorical homological algebra which I hope to write up soon. I hope this will lead to a better understanding of the geometry of string structures. Papers/Preprints:
| Some Activities: On occasion I post articles on the Secret Bloging Seminar, and sometimes I'm spotted on MathOverflow.
Dr. Christopher Schommer-Pries Selected Blog Posts: |
