Scientific

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.

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.

On Long-Run Covariance Matrix Estimation with the Truncated Flat Kernel

Author: 
Shinichi Sakata
Date: 
Tue, Jun 3, 2008
Location: 
Simon Fraser University, Burnaby, Canada
Conference: 
PIMS Vancouver Econometrics Workshop
Abstract: 
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.
Notes: 

Modelling Aperiodic Solids: Concepts and Properties of Tilings and their Physical Interpretation

Author: 
Franz Gaehler
Date: 
Thu, Aug 1, 2002
Location: 
University of Victoria, Victoria, Canada
Conference: 
Aperiodic Order, Dynamical Systems, Operator Algebras and Topology
Abstract: 
Topics: Quasicrystals, Quasiperiodicity, Translation module, Repetitivity, Local Isomorphism, Mutual Local Derivability, Matching Rules, Covering Rules, Maximal Coverings
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