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Christopher Schommer-Pries, Ph. D.




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:
  • "A Finite-Dimensional String 2-Group". This paper constructs a finite dimensional model of the String group as an central extension of 2-groups in smooth stacks. It also classifies a certain class of such extensions in terms of a cohomology theory of topological groups invented by G. Segal in the late 60's. 
  • Notes on Smooth Group Cohomology. These are some notes on Segal's derived functor cohomology of topological groups. The main new result is a short proof that Segal cohomology agrees with local cohomology for locally contractible paracompact groups, i.e. cohomology computed with cochains continuous in a neighborhood of the identity. The exact argument works equally well in the smooth setting. I claimed this statement as true in the above paper, but haven't found a direct proof in the literature. 
  • "The Classification of Two-Dimensional Extended Topological Field Theories" Ph.D. Dissertation. The title pretty much explains what's going on here. 
  • "Examples of Cayley 4-manifolds" Houston Journal of Mathematics 30 (2004), no. 1, 55--87.
    Joint with my undergraduate advisor Weiqing Gu.
  • "Exotic Holonomy and Symplectic Connections" . This is an expository term paper I wrote for Alan Weinstein's symplectic geometry class in the Fall of 2005.

Some Activities:
On occasion I post articles on the Secret Bloging Seminar, and sometimes I'm spotted on MathOverflow.














  • Office: 524 Harvard Science Center
  • Office Hours: By Appointment Only.
  • Phone: 617.495.1938
  • Email Address: schommerpries.chris.math@gmail
  • Snail Address: 
Dr. Christopher Schommer-Pries
Department of Mathematics
Harvard University
1 Oxford St.
Cambridge, MA 02138

Selected Blog Posts:



Subpages (4): Course Notes and Materials My Web Documents Recent and Upcoming Conferences Recent and Upcoming Talks

Attachments (6)

  • FiniteString2-Group-Arxiv.pdf - on Nov 13, 2009 7:05 AM by Chris Schommer-Pries (version 1)
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  • Schommer-Pries-Thesis.pdf - on Jun 17, 2009 9:20 AM by Chris Schommer-Pries (version 2 / earlier versions)
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  • Slides-Berkeley-4-29-09.pdf - on May 17, 2009 7:51 AM by Chris Schommer-Pries (version 1)
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  • Slides-MFO-6-11-09.pdf - on Jun 12, 2009 12:02 AM by Chris Schommer-Pries (version 1)
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  • Slides-MPIM-7-14-09.pdf - on Jul 14, 2009 7:12 AM by Chris Schommer-Pries (version 1)
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  • SmoothGroupCohomology11-17-09.pdf - on Nov 17, 2009 2:05 PM by Chris Schommer-Pries (version 1)
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