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Seminars

• Fuzzy Ecological Communities
  Shirley Pledger
  Friday 19th March 2010 at 04:10 PM

    , LABY LT118 http://msor.victoria.ac.nz/Main/MSORColloquia

  In studies of ecological communities, a typical data set is a matrix with one row per species and one column per sample. The matrix may contain incidence data (presence/absence, binary data 1/0), or abundance data (count data, the number of individuals of each species at each site).

  Traditional analyses use multivariate methods such as multidimensional scaling, principal component analysis, cluster analysis, ordination, correspondence analysis, association analysis, and direct and indirect gradient analysis. These methods are essentially mathematical rather than statistical, and they provide dimension reduction and plots in low dimensions in order to illustrate the main features of the data.

  By introducing statistical mixture models, we may switch to fuzzy clustering, in which species and/or samples are allocated to groups probabilistically. Exploring these models, we obtain not only low-dimensional graphical results similar to those from traditional analyses, but also the benefits of available methods for comparing models, testing hypotheses and estimating parameters. For example, (i) if species are to be clustered into "functional groups" (occurring in similar habitats), how many clusters are indicated by the data? (ii) can the samples be ordered (using their species compositions) along a single axis, or are more dimensions needed to represent the patterns?

  Although the examples will be from community ecology, these models have applications in a wide range of disciplines.

  No detailed knowledge of mathematics, statistics or, indeed, ecology is required of the audience.

• The Governing PDE's for nonlinear materials science, conformal geometry and the Hilbert Smith Conjecture.
  Gaven Martin, Massey Albany
  Thursday 25th March 2010 at 02:00 PM

    Cotton Club, Cotton 350

  The governing equations for the theories of conformal geometry and non-linear materials science are basically the same and have been much studied for centuries. Despite some significant advances in the theory of these non-linear elliptic equations there is still much to be considered. Here we discuss a little of what is known about these equations leading to a fascinating connection with Hilbert's fifth problem on Lie groups (from his famous list of 23 such problems in 1900).

  This talk will cover a broad sweep of modern mathematical ideas and connections between Analysis, PDE, Geometry, Algebra and Group theory painted with a broad brush and with few technical details.

• Challenges for Math Teachers’ preparation. A perspective from Latin America
  Angel Ruiz,  Vice President of ICMI from Costa Rica
  Tuesday 30th March 2010 at 03:30 PM

    Cotton Club, Cotton 350

  A general proposal for  the initial preparation of Math Teachers (6 to   12 grades) within universities in Latin America. The talk  will explore the connections between pedagogy and math within the curriculum and will point out some characteristics math courses should have for the benefit of math educators. It includes a brief account of   the history and some theoretical issues around Math Education (New Math in Latin America and the world).

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