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.
On rare occasion I post articles on the Secret Bloging Seminar.Research: My research centers around three areas of mathematics: topology, higher
category theory, and quantum field theory. My Dissertation (Last updated May 16th, 2009) classified 2-dimensional extended topological field
theories in terms of generators and relations. 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. Combining some basic
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.
- 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
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.
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"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.
Selected Blog Posts: |
Attachments (6)
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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)
541k
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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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