Talks

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.

Probabilities and randomness arise whenever we're not sure what will happen next. They apply to everything from lottery jackpots to airplane crashes; email spam to insurance policies; medical studies to election polls. This exploration of odds and oddities will explain how a Probability Perspective can shed new light on many familiar situations in our everyday lives, and how computer algorithms which use randomness can be used to address problems in many branches of science.

Jeffrey Rosenthal is a professor in the Department of Statistics at the University of Toronto and examines odds and statistics in everyday life. His interest in probability theory began at an early age when, as a child, he enjoyed flipping coins, rolling dice and computing probabilities. He followed his passion and earned his BSc in Mathematics, Physics, and Computer Science from the University of Toronto at the age of 20; his PhD in Mathematics from Harvard University at the age of 24; and tenure in the Department of Statistics at the University of Toronto at the age of 29. He is also a fellow of the Institute for Mathematical Statistics.

Professor Rosenthal has been honoured with a Premier’s Research Excellence Award, the COPSS President’s Award from the Committee of Presidents of Statistical Societies, a Harvard University Teaching Award in 1991, an Arts and Science Outstanding Teaching Award in 1998 at the University of Toronto and the 2006 CRM-SSC Prize in Statistics. He is author of “Struck by Lightning, The Curious World of Probabilities” and A First Look a Rigorous Probability Theory. He also co-authored “Probability and Statistics: The Science of Uncertainty”.

Despite being born on Friday the thirteenth, Rosenthal considers himself a very fortunate person.

""It is a truth very certain that, when it is not in our power to determine what is true, we ought to follow what is most probable."" - Rene Descartes (1596-1650), French philosopher and mathematician

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.