Logic seminar: David Evans
| Dates: | 28 May 2025 |
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| Times: | 15:00 - 16:00 |
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| What is it: | Seminar |
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| Organiser: | Department of Mathematics |
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| Who is it for: | University staff, External researchers, Adults, Alumni, Current University students |
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Title: Permutation modules for omega-categorical structures.
Abstract: Suppose F is a field and W is a countable, omega-categorical structure with automorphism group G. Consider the F-vector space K = FW with basis W and G-action permuting W (extended linearly). We are interested in the following questions.
1) Does K have the ascending chain condition on G-invariant subspaces?
2) If F is finite and W is homogeneous in a finite relational language, does K have only finitely many G-invariant subspaces?
A negative answer to (2) would give a negative answer to: a question of Dugald Macpherson on closed normal subgroups of automorphism groups of finitely homogeneous structures, and a conjecture of Simon Thomas on reducts.
I will talk about some further context and older work on these questions and some ongoing recent work on (2) in the case where W is a Ramsey structure (that is, G is extremely amenable).
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Frank Adams 1
Alan Turing Building
Manchester
