Abstracts:
Aleksandra Kwiatkowska (UCLA). Speaker information
Title:Comeager conjugacy classes in automorphism groups and the pseudo-arc
Abstract: The pseudo-arc is an important example of a hereditary indecomposable compact and connected space. As proved by Irwin and Solecki, the pseudo-arc can be realized as a natural quotient of a certain projective Fraisse limit L. We show that the group of all automorphisms of L, Aut(L), has a comeager conjugacy class. This generalizes a very recent result due to Oppenheim, who showed that Aut(L) has a dense conjugacy class.
Miodrag Sokic (Caltech). Speaker information
Title: A generalization of the Partite Construction
Abstract: The Ramsey property for ordered graphs was proved independently by Nesetril-Rodl and Abramson-Harrington. The main ingredient of the Nesetril-Rodl proof is the so-called partite lemma, which shows that only specific objects, called transversals, have the Ramsey property. We give a generalization of this lemma by replacing transversal objects by arbitrary objects in the corresponding class of finite relational structures. In particular we consider relational classes obtained by adding unary relations or equivalence relations to structures. We obtain not only combinatorial results but we also give a topological interpretation of our results. We calculate the universal minimal flow for certain groups of automorphisms of countable structures.
Andrew Marks (Caltech).
Speaker information
Title: Borel combinatorics and the Borel cardinality of recursive isomorphism
Abstract: We use determinacy to settle several questions in Borel combinatorics related to colorings and matchings of n-regular graphs. We then describe how these results can be used to show that recursive isomorphism on 2
ω is not a universal countable Borel equivalence relation in a "nicely uniform" way.
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Organizers:
Alexander Kechris (Caltech).
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Itay Neeman (UCLA).
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Martin Zeman (UCI)
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Local Organizers:
Alexander Kechris (Caltech)
Robin Tucker-Drob (Caltech)
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