## Scientific General Events

A one-day regional conference featuring five invited lectures with ample opportunity for interaction, discussion and socialization between participants.

- Pure mathematics; Applied mathematics & mathematical physics; Statistics; and Industrial & computational mathematics.
The Cascade Topology Seminar is a biennial gathering of topologists from the Pacific Northwest and Southwestern Canada.

The Hybridizable Discontinuous Galerkin Methods

This one-day conference builds on the success of the last five

"Combinatorics Day" events, all supported by PIMS. The purpose of the

"Combinatorics Day" is two-fold. First, to bring together people

working in different areas of combinatorics (primarily from Alberta

universities) to exchange ideas and to foster an environment for

cooperation. Second, to take advantage of the presence of many

prominent mathematicians at the Banff International Research Station

(BIRS) for a 5 day meeting on "Invariants of Incidence Matrices" from

March 29 to April 3, 2009.This is a unique opportunity, and will be great for graduate students

and Faculty from the three Alberta universities.The themes for the workshop are facts and uncertainties of climate change and its effects on coastal systems and marine safety, and the use of modern statistical tools to address some of these important issues.

This is a short course on

*Statistical Software and Extreme Value Analysis.*

Combinatorial Game Theory---games of pure strategy where there are no chance devices---had its beginnings in 1902 and a major breakthrough in the theory was enunciated in the books "On Numbers and Games", Conway, 1978, and "Winning Ways", Berlekamp, Conway & Guy, 1980. This part of the theory works well when the games break up into components. This talk will look at the players in the area over the last 100 years---some who got it right, some who got it wrong, and some who just missed. At the same time, I will introduce some of the main concepts of Combinatorial Game Theory. Only High School level math is required to understand most of the talk, although having played a few games of (any of) Chess, Checkers, Go, Amazons or Nim will help.

This conference is mainly supported by the Global Center of Excellence (GCOE). It is based on a joint research project between PIMS and Kyoto University.

For more information, visit the external site, by clicking here [dead link removed].

Sections of line bundles on moduli spaces of sheaves on rational surfaces and Le Potier's strange duality

A k-configuration is a finite collection of n points and n lines, such that each of the n points is on precisely k lines and each line contains precisely k points. Some relevant results were known long ago, but the recent years have seen a large number of new results and novel problems. The development of the ideas will be sketched and some of the outstanding open questions described. A 3-configuration with n = 15 is shown below.

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A graph is Hamilton-connected if for any two vertices u and v there is a Hamilton path whose terminal vertices are u and v. Similarly, a bipartite graph is Hamilton-laceable if for any two vertices u and v from distinct parts there is a Hamilton path with terminal vertices u and v. We present a survey of what is known about Hamilton-connected and Hamilton-laceable vertex-transitive graphs.

Recent Advances in Optimal Experimental Designs: A well-designed study is crucial for the success of any scientific investigation. Despite advances in optimal design theory in the last few decades, applications to find efficient designs in many biomedical studies have been sporadic. Part of the reason may be that the theory can be very complicated and the optimal design is not easily determined for a specific problem. I review the mathematical foundations and recent developments in optimal experimental designs. To promote optimal design ideas in scientific research and facilitate practitioners' access to optimal designs, I present a website that generates a variety of optimal designs freely and easily. The user first selects a suitable model from a list of statistical models on the website and an optimality criterion, and then inputs design parameters for his or her problem. The site returns the optimal design and the efficiency of any user-selected design. It is hoped that this site informs and enables practitioners to implement a more efficient design in their work.

Some of the core problems in low-dimensional topology involve algorithms to identify and compare topological spaces. However, where these algorithms exist, they are often infeasibly slow and difficult to implement.Here we outline the ways in which topological results can be blended with traditional computer science techniques to improve these algorithms. In particular, we examine (i) the enumeration of normal surfaces, a key component of several recognition algorithms, and (ii) building a census of triangulations, a requirement for identifying minimal representations of a topological space.

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