Saturday, April 9, 2011

9:00 a.m.-5:30 p.m.

Social and Behavioral Sciences Gateway, Room 1517

Attendance is free, but registration with Patty Jones (patty.jones@uci.edu), preferably by April 1st, is appreciated.

9:00 Hans Halvorson (Princeton University): "Natural Structure on State Space"

Abstract: "Classical mechanics" is an umbrella term for several theories, including most notably Lagrangian and Hamiltonian mechanics. Are these the same two theories? According to the folklore, yes they are. According to philosophers Erik Curiel and Jill North, no they are not. But then Curiel and North render opposite judgments about which theory is more "fundamental" than the other. In this talk, we inject some precision into this discussion, in particular by explicating the notion of definable, or natural, structures within a category. As a side benefit, we defend Mac Lane's account of definability against a criticism of Hodges.

10:30 Coffee

11:00 Jos Uffink (University of Utrecht): "Lanford's Theorem and the Emergence of Irreversibility"

Abstract: It has been a long-standing problem in the foundations of statistical physics how a description of irreversible macroscopic phenomena, such as presented by the Boltzmann equation, can be reconciled with an underlying time-reversal invariant theory, such as,for example, classical mechanics. One of the most prominent attempt to provide such a reconciliation is by means of Lanford's theorem (1975) which allegedly shows that the Boltzmann equation emerges naturally from the underlying classical mechanical equations of motion for hard spheres in an appropriate limit, and for a limited time range. This beautiful result, however, still seems to leave open the question of how exactly the irreversibility, or violation of time-reversal invariance, emerges in this theorem. In this talk, presenting joint work with Giovanni Valente, I will review the variety of answers on this question in the literature on Lanford's theorem, and hope to provide a judgment on their merits.

12:30 Lunch

2:00 Miklós Rédei (London School of Economics): "How Local are Local Operations in Local Quantum Field Theory?"

Abstract: A notion called operational C*-separability of local C*-algebras (A(V1) and A(V2)) associated with spacelike separated spacetime regions V1 and V2 in a net of local observable algebras satisfying the standard axioms of local, algebraic relativistic quantum field theory is defined in terms of operations (completely positive unit preserving linear maps) on the local algebras A(V1) and A(V2). Operational C*- separability is interpreted as a "no-signaling" condition formulated for general operations, for which a straightforward no-signaling theorem is shown not to hold. By linking operational C*-separability of (A(V1), A(V2)) to the recently introduced operational C*-independence of (A(V1), A(V2)) it is shown that operational C*-separability typically holds for the pair (A(V1), A(V2)) if V1 and V2 are strictly spacelike separated double cone regions. The status in local, algebraic relativistic quantum field theory of a natural strengthening of operational C*-separability, i.e. operational W*-separability, is discussed and open problems about the relation of operational separability and operational independence are formulated.

3:30 Coffee

4:00 Robert Geroch (University of Chicago): "Computation"

Abstract: The talk with deal with some aspect of computation -- perhaps how computational efficiency is affected by allowing programs that employ random-number generators, or by disallowing programs for which there is no formal proof that the program actually computes the given problem.

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