Scientific Series

Chris Isham in pre-recorded video, with Andreas Doring fielding questions and clarifications. Like watching commentators Scott Hamilton and Katarina Witt analyze Kristi Yamaguchi\'s performance at the World Figure Skating Championships for CBS News, join us for something different in quantum foundations. Chris Isham parries the intricacies of topos theory; Andreas Doring shows us how to see the moves in slow motion. Bring your own popcorn and plenty of questions.

I will summarize current observational constraints in cosmology with emphasis on what we have learned about the properties of the primordial density perturbations. I will describe future directions including observations of high redshift neutral hydrogen through is 21 cm line.

Quantum measure theory describes quantum theory as a generalization of a classical stochastic process, which may be fruitful for quantum gravity. I will describe the approach, and show that, in the context of an EPRB setup with two distant experimenters, two alternative experiments, and two outcomes per experiment, any set of no signaling probabilities can be realized, albeit by violating a `strong positivity\' condition.

The talk concerns a generalization of the concept of a minimum uncertainty state to the finite dimensional case. Instead of considering the product of the variances of two complementary observables we consider an uncertainty relation involving the quadratic Renyi entropies summed over a full set of mutually unbiased bases (MUBs). States which achieve the lower bound set by this inequality were introduced by Wootters and Sussman, who proved existence for every prime power dimension, and by Appleby, Dang and Fuchs who showed that in prime dimension the fiducial vector for a for a symmetric informationally complete positive operator valued measure (SIC-POVM) covariant under the Weyl-Heisenberg group is a state of this kind. Subsequently Sussman proved existence for a class of odd prime power dimensions. The purpose of this talk is to complete the existence proof by showing that minimum uncertainty states exist in every prime power dimension, without exception. Along the way we establish a number of properties of the Clifford group, and Galois extension fields, which might be of some independent interest.

The Great Plague of London, which claimed the lives of one fifth of London\'s population in 1665, is one of the most famous epidemics of all time. We have recently digitized the mortality records for London during the Great Plague, yielding weekly data for each of the 130 parishes. I will describe the temporal and spatial dynamics of the plague, and discuss our efforts to estimate the transmissibility of the infectious agent. I will also briefly describe other projects in progress inspired by disease-specific mortality records for London over the past 650 years.

It is usually expected that nonrelativistic many-body Schroedinger equations emerge from some QFT models in the limit of infinite masses. For instance, from Yukawa\'s QFT, if the initial state contains 2 fermions, we expect to recover a 2-fermion nonrelativistic Schroedinger equation with 2-body Yukawa potential (in the limit of infinite fermion mass). I will give an easy (but still heuristic) derivation of this, based on the analysis of the corresponding Feynman diagrams and on the behaviour of the complete propagators for large spacetime distances. Then, I may outline another possible derivation based on the Schroedinger picture and dressed particles.

A single classical system is characterized by its manifold of states; and to combine several systems, we take the product of manifolds. A single quantum system is characterized by its Hilbert space of states; and to combine several systems, we take the tensor product of Hilbert spaces. But what if we choose to combine an infinite number of systems? A naive attempt to describe such combinations fails, for there is apparently no natural notion of an infinite product of manifolds; nor of an infinite tensor product of Hilbert spaces. But, at least in the quantum case, the situation is not as hopeless as it might appear. We argue that there does indeed exist a natural mathematical framework for combinations of infinite numbers of quantum systems.