Mathematics

Geometry and analysis of low dimensional manifolds

Speaker: 
Gang Tian
Date: 
Sat, Aug 8, 2009
Location: 
University of New South Wales, Sydney, Australia
Conference: 
1st PRIMA Congress
Abstract: 

In this talk, I will start with a brief tour on geometrization of 3-manifolds. Then I will discuss recent progresses on geometry and analysis of 4-manifolds.

Class: 
Scientific
Subject: 
Mathematics

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.

Class: 
Scientific
Subject: 
Mathematics

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.

Class: 
Scientific
Subject: 
Mathematics

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

  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.
Class: 
Scientific
Subject: 
Mathematics

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.

Class: 
Scientific
Subject: 
Mathematics
Condensed Matter and Statistical Mechanics

Cloaking and Transformation Optics

Speaker: 
Gunther Uhlmann
Date: 
Mon, Jul 6, 2009 to Tue, Jul 7, 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.

Class: 
Scientific
Subject: 
Mathematics

What I am Doing in Australia

Speaker: 
Jonathan Borwein
Date: 
Wed, May 18, 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.

Class: 
Scientific
Subject: 
Mathematics
Numerical Analysis

Small Number Counts to 100 (Blackfoot)

Speaker: 
Veselin Jungic
Mark Maclean
Rena Sinclair
Date: 
Sun, Nov 22, 2009
Location: 
Simon Fraser University, Burnaby, Canada
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

Class: 
Educational
Subject: 
Mathematics

Small Number Counts to 100

Speaker: 
Veselin Jungic
Mark Maclean
Rena Sinclair
Date: 
Sun, Nov 22, 2009
Location: 
Simon Fraser University, Burnaby, Canada
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

Class: 
Educational
Subject: 
Mathematics

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

Speaker: 
Helmut Hofer
Date: 
Mon, Oct 23, 2006 to Tue, Oct 24, 2006
Location: 
PIMS, University of British Columbia
Conference: 
PIMS 10th Anniversary Lectures
Abstract: 

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.

Class: 
Scientific
Subject: 
Mathematics
Differential Geometry and Geometric Analysis
Functional Analysis

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