nLab
Urs Schreiber
contact
The best way to contact me is by sending me an email at urs.schreiber@gmail.com
my position
I have my PhD in theoretical physics. Have been a postdoc in math and mathematical physics for four years at Hamburg University. Was based for a bit at MPI in Bonn and am now on a postdoc position in Ieke Moerdijk’s group in Utrecht.
my research
My research has to a large extent been motivated by thinking about mathematical model building in theoretical physics. With co-editors we are currently producing a book that should give a good sense of modern insights into the general abstract nonsense structure of the universe:
This is the kind of stuff that I am thinking about.
Something like a personal research wiki with more information on my personal research is beginning to develop at
More concretely, my research interest is in understanding the higher differential geometric and categorical structures underlying what should be called differential nonabelian cohomology: the theory of connections on principal bundles and their generalization to gerbes and principal ∞-bundles.
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ingredients – Structurally this involves ∞-stack (∞,1)-toposes (“derived stacks”) in a smooth context modeled by synthetic differential geometry. Technically it involves a theory of ∞-Lie theory that controls ∞-Lie groupoids and their infinitesimal approximation, ∞-Lie algebroids in terms of which one may conceive notions like Cartan-Ehresmann ∞-connections on principal ∞-bundles.
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applications – Such objects notably model higher order gauge fields in quantum field theory and string theory that have already been a main motivation for the development of generalized abelian differential cohomology by Hopkins, Singer, Freed and others. With Hisham Sati and Jim Stasheff we are working on showing that the fundamental picture involves differential refinements of the full (∞,1)-topos-theoretic refinement of abelian cohomology to what is called nonabelian cohomology.
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classical physics – We show for instance that the anomaly cancellation Green-Schwarz mechanism on which much of the original interest in string theory is based encodes twisted differential String- and Fivebrane structures: differential and twisted refinements of string structures in nonabelian cohomology.
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quantum physics – A good structural understanding of sigma-model background fields in twisted differential nonabelian cohomology should help to understand the systematic quantization of differential nonabelian cocycles to the corresponding sigma-model extended quantum field theories. Such a formalization of the path integral is perhaps one of the central outstanding tasks in the mathematical description of quantum field theory.
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exchange of thoughts
I enjoy exchanging thoughts on topics of interest for my research and always felt it would be a pity not to use the web for that purpose. To satisfy that need I use to
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discuss on the blog The n-Category Cafe
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work on the wiki The nLab (this wiki here).
Such research web interaction may still be unusual and has its pitfalls, but does serve a good purpose. Among various highly esteemed discussion partners scattered all over the world, I found at least three of my official collaborators – John Baez, David Roberts and Jim Stasheff – from such discussion on the web. In each case our first joint article was finished before we ever met in person.
While the nCafe blog has proven useful for exchange of thoughts and information, the nLab wiki was created with the idea that it would provide a useful space for effective joint technical work. For storing and developing material which is too personal or too tentative for the main Lab I am now using
This turns out to be also useful for distributed collaborative development and editing. While I seem to have an unusually low barrier (maybe too low) to exposing research material in public, I do also keep a
to which access is password protected. It may happen that some hyperlink that you come across here sends you to this private web. If you feel you do want to follow the link nevertheless, you need to send me an email and try to convince me that I share the password with you, as I do with my collaborators.