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.
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.
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.
The 2011 IGTC (International Graduate Training Centre) Summit was held as part of the Applied Mathematics Perspectives thematic program at the University of Victoria. There was a poster session, research discussion session where students and experts interacted, and an education session for IGTC students.
Some photos from the Hyperplane Arrangements and Applications conference which took place at UBC Vancouver, August 8-12. This conference was held in honour of Hiroaki Terao.
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.
The School schedule ran 4 days per week to give participants ample time for study, interaction with other students and discovering Vancouver and its surroundings. Many explored the old growth forests at Lighthouse Park and Lynn Canyon and Headwaters Parks on the North Shore. Those who enjoy more strenuous hiking discovered the beauty of the surrounding mountains and ocean on a number of organized hikes. This year we went to the top of Anvil Island which is only accessible by water taxi from Horseshoe Bay. The 2500 ft.
Despite its large sample efficiency, the truncated flat (TF) kernel estimator of long-run covariance matrices is seldom used, because it lacks the guaranteed positive semidefiniteness and sometimes performs poorly in small samples, compared to other familiar kernel estimators. This paper proposes simple modifications to the TF estimator to enforce the positive definiteness without sacrificing the large sample efficiency and make the estimator more reliable in small samples through better utilization of the bias-variance tradeoff. We study the large sample properties of the modified TF estimators and verify their improved small-sample performances by Monte Carlo simulations.