Scientific General Events
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.
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.
- PIMS Special Speaker-Problems in computational topology: Where pure mathematics meets computer science
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.
The PIMS Postdoc Day will take place on Saturday, October 25th. This will be a gathering of math postdocs with the goal of of discussing issues which are relevant to postdoctoral fellows such as:
- applying for tenure track jobs in Canada and the United States
- connecting to industry
We plan to have presentations on these topics, as well as discussions where you will be encouraged to actively participate. This is also a great opportunity to meet with other postdocs. Lunch will be provided for participants.
If you are a Math postdoc and would like to participate, please send an email to Ken Leung by clicking here, confirming your attendance, so that we may have an accurate head count for lunch. The participation deadline is October 22, 2008.
Location: West Mall Annex Room 110
The Atiyah-Singer index theorem, which directs tools from Hilbert space operator theory toward problems in topology and geometry, fits very naturally into the framework of Alain Connes' non-commutative geometry.In fact index theory is a central theme in non-commutativegeometry. In this lecture I shall describe a non-commutative-geometricapproach to the index theorem, due to Connes, as well as a recently proved index theorem for contact manifolds, due to Erik van Erp, that illustrates very well the usefulness of a non-commutative point of view.
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