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This is an introduction to background independent quantum theories of gravity, with a focus on loop quantum gravity and related approaches. Basic texts: -Quantum Gravity, by Carlo Rovelli, Cambridge University Press 2005 -Quantum gravityy with a positive cosmological constant, Lee Smolin, hep-th/0209079 -Invitation to loop quantum gravity, Lee Smolin, hep-th/0408048 -Gauge fields, knots and gravity, JC Baez, JP Muniain Prerequisites: -undergraduate quantum mechanics -basics of classical gauge field theories -basic general relativity -hamiltonian and lagrangian mechanics -basics of lie algebras

This is an introduction to background independent quantum theories of gravity, with a focus on loop quantum gravity and related approaches. Basic texts: -Quantum Gravity, by Carlo Rovelli, Cambridge University Press 2005 -Quantum gravityy with a positive cosmological constant, Lee Smolin, hep-th/0209079 -Invitation to loop quantum gravity, Lee Smolin, hep-th/0408048 -Gauge fields, knots and gravity, JC Baez, JP Muniain Prerequisites: -undergraduate quantum mechanics -basics of classical gauge field theories -basic general relativity -hamiltonian and lagrangian mechanics -basics of lie algebras

Asymptotic statements like the almost-equi-partition law, the theorm of Shannon Mc -Millan-Breiman, the theorem of Sanov have all natural quantum analogs. They all talk about the thermodynamik limit of quantum spin systems. I will try to summarize these results and sketch the main ideas of proof.

I look at the information-processing involved in a quantum computation, in terms of the difference between the Boolean logic underlying a classical computation and the non-Boolean logic represented by the projective geometry of Hilbert space, in which the subspace structure of Hilbert space replaces the set-theoretic structure of classical logic. I show that the original Deutsch XOR algorithm, Simon's algorithm, and Shor's algorithm all involve a similar geometric formulation. In terms of this picture, I consider the question of where the speedup relative to classical algorithms comes from.

From Monday, January 30th to Thursday, February 2nd, Senarath (Shanta) de Alwis will give a four lecture mini-course on `Potentials for light moduli in N=1 supergravity and string theory'. In these lectures, Shanta will be describing some of the technical ingredients used in recent constructions of inflation in string theory. The lectures will be given at a level appropriate for advanced graduate students and will be held in the Bob Room at 11:00am each day. The topics to be covered include: Derivation of the potential for chiral scalars in N=1 supergravity; Weyl anomalies and the generation of non-perturbative terms in the superpotential; Derivation of moduli potentials from fluxes in type IIB and heterotic string theory; Derivation of potentials for light moduli by integrating out heavy moduli. Shanta is a faculty member in the Physics Department at the University of Colorado, Boulder who is spending his sabbatical year here at Perimeter.