June 20, 2018

2002-2003 Fields Institute AGM


Raymond Laflamme (University of Waterloo)
Quantum Computing
Advances in computing are revolutionizing our world. Present day computers advance at a rapid pace toward the barrier defined by the laws of quantum
physics. The quantum computation program short-circuits that constraint by exploiting the quantum laws to advantage rather than regarding them as obstacles. Quantum computer accepts any superposition of its inputs as an input, and processes the components simultaneously, performing a sophisticated interference experiment of classical inputs. This ``quantum parallelism'' allows one to explore exponentially many trial solutions with relatively modest means, and to select the correct one. This has a particularly dramatic effect on factoring of large integers, which is at the core of the present day encryption strategies (public key) used in diplomatic communication, and (increasingly) in business. As demonstrated approximately five years ago, quantum computers could yield the most commonly used encryption protocol obsolete. Since then, it was also realized that quantum computation can lead to breakthroughs elsewhere, including simulations of quantum systems, implementation of novel encryption strategies (quantum cryptography), as well as more mundane applications such as sorting. I will describe recent work done in quantum computation, in particular the discovery and implementation of methods to make quantum information robust against corruption, both in theory and experiments. I will end with speculations about the field.

Moshe Milevsky (Schulich School of Business, York University)
A Mathematical Analysis of Silly Investment Strategies
Financial advisors, brokers, planners, banks and fund companies continuously bombard the general public with investment advice on how to amass and accumulate wealth for retirement. Newspapers and magazines are filled with articles on which stocks to buy, which bonds to sell and which funds to hold. Unfortunately, most of this advice is grounded on faulty logic, questionable data and is often tainted by subtle conflicts of interest.

In this non-technical presentation I will review and discuss many of the commonly recommended investment strategies and illustrate why most of them do not stand-up to basic scrutiny when examined with some 'probabilistic' common sense.

I will conclude the talk with some thoughts on the need to encourage greater financial awareness and skepticism and the wider relationship of these skills to numerical literacy.

Juris Steprans (York University)
Set Theory and its Impact on Analysis
Many introductions to set theory mention the subject's roots in the work of Cantor on sets of uniqueness for the convergence of trigonometric series. The path that lead Cantor from these questions to the derived set operation and from there to the definition of the ordinals has been retread by various authors. However, the fact that contemporary set theorists have done some very exciting work in this same area is less well known. Indeed, the current interaction between set theory and analysis deserves to be more widely popularized and this talk will be a contribution in this direction. The subjects mentioned will include topics in the geometry of the plane, operators on Banach spaces, classification problems in abelian groups and some measure theory.

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