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Quantum Geometry Research Focus Group
Andrew Waldron and Derek Wise
U.C. Davis
20082009
This page lists activities of the 20089
RFG on quantum geometry.
What's the Quantum Geometry RFG about? Here's a blurb from our RFG proposal:
Quantum geometry arises from the realization that any truly fundamental theory of physics must reconcile quantum field theory with Einstein's geometric theory of gravity. Precisely how spacetime geometry is "quantized" is contentious; there are various approaches to quantum gravity—string theory, loop quantum gravity, and others—each with its own ideas of what "quantum geometry" should ultimately be like. While the path forward in fundamental physics is never completely certain, the study of quantum gravity and quantum geometry has led to a wealth of beautiful mathematics.
In particular, quantum geometry has interesting ties to differential geometry, combinatorics, number theory, operator algebras and noncommutative geometry, topological and conformal quantum field theories, quantum algebra, higher category theory, and lowdimensional topology.
The Quantum Geometry Research Focus Group
aims to make a broad survey of quantum gravity research living at the interface
of mathematics and theoretical physics.
Below are some of our activities.
Fall 2008
A graduate topics course on Gauge Theory and Gravity, with online lecture notes available (Tuesdays 2:103:30, Thursdays 1:102:30, MSB 3106)
Seminar / Reading Group series (Thursdays 3:104:30, MSB 2112)
 Discussion of the PonzanoRegge model of 3d quantum gravity
Some references:
 (10/23) A talk by Andrew Waldron on "Tractors, Mass and Weyl Invariance"

Andrew's slides

The related paper by Gover, Shaukat, and Waldron.
 (10/30) Shannon McCurdy and Anthony Tagliaferro (UC Berkeley) visit; Shannon gave a talk on on "The Star Product for Differential Forms on Symplectic Manifolds"

Shannon's slides

The related paper by McCurdy, Tagliaferro, and Zumino.
 (11/6) D. Wise  PonzanoRegge model discussion group
 (11/18) Mithat Unsal (Stanford/SLAC), Deformed Type IIB matrix models, lattice supersymmetry and twisting
 (12/4) Dmitri Fuchs, A Lie Algebra Cohomology Primer
Winter 2009
Meeting times:
Tuesdays 3:104:00 (MSB 2240  Except 20 Jan, TBD)
Thursdays 3:105:00 (MSB 2112)
The Thursday slot will be our main time for formal seminars. The additional hour on Tuesdays will typically be a more informal meeting, but will serve whatever purpose we need: reading/discussion group, background material related to an upcoming Thursday lecture, or sometimes an additional talk.
Minicourse by Derek Wise on InfiniteDimensional
Representations of 2Groups:
 Slides for first lecture, which introduced 2groups and "2linear algebra", or more precisely, KapranovVoevodsky 2vector spaces.
 Slides for second lecture, which introduced infinite dimensional "2Hilbert spaces" and representations of 2groups on those.
Minicourse by Albert Schwarz on Space and Time from Translation Symmetry.
(1/29) Catherine Williams (Stanford) Asymptotic behavior of marginally trapped tubes (slides)
Other seminars
Reading group
Spring 2009
Lecture by Marc Rieffel on Dirac operators on coadjoint orbits.
Many of us are attending the course by Steve Carlip in the physics department, on quantum gravity.
Tuesdays 3:10 MSB 2112: Reading group focusing on spin foam models, based on the paper by Baez: an introduction to spin foam models of BF theory and quantum gravity
Other seminars
Minicourse by Catherine Meusburger (U. Hamburg) on Observables in 3d quantum gravity (joint RFG activity with the Geometric Topology RFG)
If you have a UCD Math account, you can access some RFG resources and notes via the svn by navigating to wally/quantum_geometry.
© 20082009 Derek Wise & Andrew Waldron
Last update: 12 June 2009
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