### Abstracts

**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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