Scientific

Frozen Boundaries and Log Fronts

Speaker: 
Andrei Okounkov
Date: 
Mon, Oct 16, 2006
Location: 
University of British Columbia, Vancouver, Canada
Conference: 
PIMS 10th Anniversary Lectures
Abstract: 

In this talk, based on joint work with Richard Kenyon and Grisha Mikhalkin, Andrei Okounkov discusses a binary operation on plane curves which

  1. generalizes classical duality for plane curves and
  2. arises naturally in probabilistic context,

namely as a facet boundary in certain random surface models.

Class: 
Scientific
Subject: 
Algebraic Geometry

IGTC Summit, 2011

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.

Conference: 
2011 IGTC Summit
Applied Mathematics Perspectives
Date: 
Thu, Jul 14, 2011
Class: 
Scientific
Subject: 
Applied Mathematics
Environmental Science

Hyperplane Arrangements and Applications

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.

Conference: 
Hyperplane Arrangements and Applications
Date: 
Mon, Aug 8, 2011
Class: 
Scientific
Subject: 
Algebraic Geometry
Combinatorics
Algebra
Topology

Applied Mathematics Perspectives

Photos taken during the Applied Mathematics Perspectives workshops, July 12-17, 2011 at the University of British Columbia, Vancouver.

Conference: 
Applied Mathematics Perspectives
Date: 
Tue, Jul 12, 2011
Class: 
Scientific
Subject: 
Applied Mathematics

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.

Date: 
Sat, Oct 1, 2011
Class: 
Scientific
Subject: 
Mathematics
Applied Mathematics
Physics
Statistics
Nonlinear Sciences
Computer Science

Summer School in Probablility 2008

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.

Date: 
Wed, Jun 11, 2008
Class: 
Scientific
Subject: 
Mathematics
Probability

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: 
PDF icon sakata.pdf
Class: 
Scientific
Subject: 
Econometrics
Statistics Theory

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

Notes: 
PDF icon Gaehler_Franz_2.pdf
Class: 
Scientific
Subject: 
Condensed Matter and Statistical Mechanics
Topology

Cohomology of Quasiperiodic Tilings

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:

• Quasiperiodic tilings

• The hull of a tiling

• Approximation the hull by CW-spaces

• Application to canonical projection tilings

• Relation to matching rules

• Towards an interpretation

Notes: 
PDF icon Gaehler_Franz_1.pdf
Class: 
Scientific
Subject: 
Discrete Mathematics
Topology

Equidistribution and Primes

Author: 
Peter Sarnak
Date: 
Sat, Sep 1, 2007
Location: 
University of British Columbia, Vancouver, Canada
Conference: 
PIMS 10th Anniversary Lectures
Abstract: 

We begin by reviewing various classical problems concerning the existence of primes or numbers with few prime factors as well as some of the key developments towards resolving these long standing questions. Then we put the theory in a natural and general geometric context of actions on affine n-space and indicate what can be established there. The methods used to develop a combinational sieve in this context involve automorphic forms, expander graphs and unexpectedly arithmetic combinatorics. Applications to classical problems such as the divisibility of the areas of Pythagorean triangles and of the curvatures of the circles in an integral Apollonian packing, are given.

Notes: 
PDF icon Sarnak.pdf
Class: 
Scientific
Subject: 
Number Theory

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