# Mathematics

## Expanders, Group Theory, Arithmetic Geometry, Cryptography and Much More

Speaker:

Eyal Goran
Date:

Tue, Apr 6, 2010
Location:

University of Calgary, Calgary, Canada
CRG:

Number Theory (2010-2013) Abstract:

This is a lecture given on the occasion of the launch of the PIMS CRG in "L-functions and Number Theory".
The theory of expander graphs is undergoing intensive development. It finds more and more applications to diverse areas of mathematics. In this talk, aimed at a general audience, I will introduce the concept of expander graphs and discuss some interesting connections to arithmetic geometry, group theory and cryptography, including some very recent breakthroughs.

## Small Number Counts to 100

Speaker:

Veselin Jungic
Speaker:

Mark Maclean
Speaker:

Rena Sinclair
Date:

Sun, Nov 22, 2009
Location:

Simon Fraser University, Burnaby, Canada
Location:

University of British Columbia, Vancouver, Canada
Conference:

BIRS First Nations Math Education Workshop Abstract:

This short animation movie is a math education resource based on Aboriginal culture. For more information, visit: http://www.math.sfu.ca/~vjungic/SmallNumber.html
Special Thanks To:
Banff International Research Station for Mathematical Innovation and Discovery
Department of Mathematics, Simon Fraser University
Pacific Institute For Mathematical Sciences
Sean O'Reilly, Arcana Studios
The IRMACS Centre, Simon Fraser University

## Quantum Magic in Secret Communication

Speaker:

Gilles Brassard
Date:

Tue, Apr 6, 2010
Location:

University of Calgary, Calgary, Canada
CRG:

Mathematics of Quantum Information (2010-2013) Abstract:

In this talk, we shall tell the tale of the origin of Quantum Cryptography from the birth of the first idea by Wiesner in 1970 to the invention of Quantum Key Distribution in 1983, to the first prototypes and ensuing commercial ventures, to exciting prospects for the future. No prior knowledge in quantum mechanics or cryptography will be expected.

## Small Number Counts to 100 (Blackfoot)

Speaker:

Veselin Jungic
Speaker:

Mark Maclean
Speaker:

Rena Sinclair
Date:

Sun, Nov 22, 2009
Location:

Simon Fraser University, Burnaby, Canada
Location:

University of British Columbia, Vancouver, Canada
Conference:

BIRS First Nations Math Education Workshop Abstract:

This short animation movie is a math education resource based on Aboriginal culture. For more information, visit: http://www.math.sfu.ca/~vjungic/SmallNumber.html
This version of the video was recorded by Dr. Eldon Yellowhorn of the Pikani First Nation in Blackfoot.
Special Thanks To:
Banff International Research Station for Mathematical Innovation and Discovery
Department of Mathematics, Simon Fraser University
Pacific Institute For Mathematical Sciences
Sean O'Reilly, Arcana Studios
The IRMACS Centre, Simon Fraser University

## What I am Doing in Australia

Speaker:

Jonathan Borwein
Date:

Tue, May 17, 2011
Location:

IRMACS Center, Simon Fraser University
Conference:

JonFest 2011, Computation & Analytical Mathematics Conference Abstract:

Jonathan Borwein talks about his current research and the Priority Research Center for Computer Assisted Research Mathematics and its Applications (CARMA). Professor Borwein is both a Laureate Professor and the Director at CARMA which is located at the University of Newcastle in New South Wales, Australia.

## Cloaking and Transformation Optics

Speaker:

Gunther Uhlmann
Date:

Mon, Jul 6, 2009
Location:

University of New South Wales, Sydney, Australia
Conference:

1st PRIMA Congress Abstract:

We describe recent theoretical and experimental progress on making objects invisible to detection by electromagnetic waves, acoustic waves and quantum waves. Maxwell's equations have transformation laws that allow for design of electromagnetic materials that steer light around a hidden region, returning it to its original path on the far side. Not only would observers be unaware of the contents of the hidden region, they would not even be aware that something was being hidden. The object, which would have no shadow, is said to be cloaked. We recount the recent history of the subject and discuss some of the mathematical and physical issues involved, especially the use of singular transformations.

## Conformal Invariance and Universality in the 2D Ising Model

Speaker:

Stalislav Smirnov
Date:

Mon, Jul 6, 2009
Location:

University of New South Wales, Sydney, Australia
Conference:

1st PRIMA Congress Abstract:

It is conjectured that many 2D lattice models of physical phenomena (percolation, Ising model of a ferromagnet, self avoiding polymers, ...) become invariant under rotations and even conformal maps in the scaling limit (i.e. when "viewed from far away"). A well-known example is the Random Walk (invariant only under rotations preserving the lattice) which in the scaling limit converges to the conformally invariant Brownian Motion.
Assuming the conformal invariance conjecture, physicists were able to make a number of striking but unrigorous predictions: e.g. dimension of a critical percolation cluster is almost surely 91/48; the number of simple length N trajectories of a Random Walk is about N11/32·mN, with m depending on a lattice, and so on.
We will discuss the recent progress in mathematical understanding of this area, in particular for the Ising model. Much of the progress is based on combining ideas from probability, complex analysis, combinatorics.

## Lagrangian Floer Homology and Mirror Symmetry

Speaker:

Kenji Fukaya
Date:

Tue, Jul 7, 2009
Location:

University of New South Wales, Sydney, Australia
Conference:

1st PRIMA Congress Abstract:

This is a survey of Lagrangian Floer homology which I developed together with Y.G.-Oh, Hiroshi Ohta, and Kaoru Ono. I will focus on its relation to (homological) mirror symmetry. The topic discussed include

- Definition of filtered A infinity algebra associated to a Lagrangian submanifold and its categorification.
- Its family version and how it is related to mirror symmetry.
- Some example including toric manifold. Calculation in that case and how mirror symmetry is observed from calculation.

## Categorical Crepant Resolutions of Higher Dimensional Simple Singularities

Speaker:

Yujiro Kawamata
Date:

Tue, Jul 7, 2009
Location:

University of New South Wales, Sydney, Australia
Conference:

1st PRIMA Congress Abstract:

Simple singularities in dimension 2 have crepant resolutions and satisfy the McKay correspondence. But higher dimensional generalizations do not. We propose the categorical crepant resolutions of such singularities in the sense that the Serre functors act as fractional shifts on the added objects.

## Linearity in the Tropics

Speaker:

Federico Ardila
Date:

Tue, Jul 7, 2009
Location:

University of New South Wales, Sydney, Australia
Conference:

1st PRIMA Congress Abstract:

Tropical geometry studies an algebraic variety X by `tropicalizing' it into a polyhedral complex Trop(X) which retains much of the information about X. This technique has been applied successfully in numerous contexts in pure and applied mathematics.

Tropical varieties may be simpler than algebraic varieties, but they are by no means well understood. In fact, tropical linear spaces already feature a surprisingly rich and beautiful combinatorial structure, and interesting connections to geometry, topology, and phylogenetics. I will discuss what we currently know about them.

Tropical varieties may be simpler than algebraic varieties, but they are by no means well understood. In fact, tropical linear spaces already feature a surprisingly rich and beautiful combinatorial structure, and interesting connections to geometry, topology, and phylogenetics. I will discuss what we currently know about them.