# Mathematics

## Lagrangian Floer Homology and Mirror Symmetry

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.

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

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.

## Cloaking and Transformation Optics

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.

## What I am Doing in Australia

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.

- Read more about What I am Doing in Australia
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## Small Number Counts to 100 (Blackfoot)

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

## Small Number Counts to 100

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

- Read more about Small Number Counts to 100
- 3822 reads

## New geometric and functional analytic ideas arising from problems in symplectic geometry

The study of moduli spaces of holomorphic curves in symplectic geometry is the key ingredient for the construction of symplectic invariants. These moduli spaces are suitable compactifications of solution spaces of a first order nonlinear Cauchy-Riemann type operator. The solution spaces are usually not compact due to bubbling-off phenomena and other analytical difficulties.

## PIMS/UBC Math Department Grad Student/Postdoc Job Forum

PIMS hosted a forum for postdocs or graduate students applying for jobs this year or next. Attendees gained valuable and useful information about the job application process.

## Math Mania

Math Mania is a popular alternative math education event which PIMS runs in elementary schools. These are some photos taken at Ecole Glen in Coquitlam BC on Feb 16, 2011. Thank you to all the teachers, students and volunteers from Douglas college who participated!

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## PIMS Board Meeting - Fall 2011

The PIMS 2011 Fall board meeting was held at the University of Saskatchewan. In addition to the board meeting, board members toured the Canadian Light Source facility.