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Quantum Geometry Research Focus Group

Andrew Waldron and Derek Wise
U.C. Davis

2008-2009

This page lists activities of the 2008-9 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 low-dimensional 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 2:10-3:30, Thursdays 1:10-2:30, MSB 3106)

Seminar / Reading Group series (Thursdays 3:10-4:30, MSB 2112)

Discussion of the Ponzano-Regge model of 3d quantum gravity
Some references:
- 0803.3319
- hep-th/0401076 gr-qc/0410141 hep-th/0502106
(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 -- Ponzano-Regge 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 3:10-4:00 (MSB 2240 -- Except 20 Jan, TBD)
Thursdays 3:10-5:00 (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 Infinite-Dimensional Representations of 2-Groups:

Slides for first lecture, which introduced 2-groups and "2-linear algebra", or more precisely, Kapranov-Voevodsky 2-vector spaces.
Slides for second lecture, which introduced infinite dimensional "2-Hilbert spaces" and representations of 2-groups 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