Mathematics

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

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

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.

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

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.