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Peter Cameron from Queen Mary, University of London is going to visit School of Mathematics of IPM during April 10-May 10, 2004.
During his visit, Prof. Cameron will present two lectures and will
conduct a short course in "Permutation groups" at IPM.
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General talk: The random graph and the Urysohn space
April 22, 10:00-12:00
Abstract:
Erdos and Renyi showed that there is a unique countable random graph (up to isomorphism). This graph has many remarkable properties: For example, it is universal for finite and countable graphs, and is homogeneous (any isomorphism between finite subgraphs extends to an automorphism). These two properties characterise it. Quite a lot is known about its automorphism group. Earlier, Urysohn had constructed a Polish space (a complete separable metric space) with similar homogeneity and universality properties. It took longer for mathematicians to become interested in this space; but there are now some results on its isometry group. For example, it has an isometry all of whose orbits are dense.
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Technical talk: Product action and counting matrices
April 28, 14:00-15:00
Abstract:
How many zero-one matrices are there with a given number of ones and
having no row or column consisting entirely of zeros? There are different
versions of this question, according as we allow or forbid repeated rows
or columns and whether we allow row and/or column permutations and/or
transposition of the matrix. Some of these problems can be interpreted
in other contexts, such as counting set systems by weight, or counting
orbits of certain direct products of permutation groups with the product
action. Most of these problems have not been solved, but there are some
results. For example, if row and column permutations are not permitted but
repeated rows and columns are allowed, the number is known both exactly
and asymptotically.
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Short Course: Permutation groups and classical groups
Abstract:
In the theory of permutation groups, there are two natural reductions which bring our attention to primitive permutation groups. The Classification of Finite Simple Groups, together with the O'Nan-Scott theorem, have allowed us to answer many questions about primitive groups using our knowledge of the simple groups (in particular, their maximal subgroups and their linear representations). In a sense, most of the finite simple groups are classical groups over finite fields, and studying them this way helps us to get the information we need.
| Information about the short course: |
| Time: 10:00-12:00, every Saturdays and Wednesdays |
| Starting Date: Wednesday, April 14, 2004 |
| Place: School of Mathematics, Niavaran Bldg., Niavaran Square, Tehran, Iran. |
Online Access to Lecture Notes of the Short Course: |
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Wednesday, April 14, 2004: Notes 1
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Saturday, April 17, 2004: Notes 2
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Wednesday, April 21, 2004: Notes 3
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Saturday, April 24, 2004: Notes 4
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Wednesday, April 28, 2004: Notes 5
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Saturday, May 1, 2004: Notes 6
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Wednesday, May 5, 2004: Notes 7
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Saturday, May 8, 2004: Notes 8
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See some photos |
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