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Logic Seminar
2019-2020

 


Thursday, September 19

  • Logic Seminar
    Allison Y. Wang (Caltech)
    Hyperfiniteness and Ramsey notions of large
          2:00 -- 3:00 pm // Linde, Room 255

Abstract: We discuss the interactions of hyperfiniteness with notions of largeness on Ramsey spaces. In particular, we present a classical proof of Mathias's theorem that every countable Borel equivalence relation on the Ellentuck space is hyperfinite when restricted to some pure Ellentuck cube.
This is in joint work with A. Panagiotopoulos


Friday, October 18

  • Caltech-UCLA Logic Seminar
    Forte Shinko (Caltech)
    Quotients by countable subgroups are hyperfinite
          2:00 -- 3:30 pm //UCLA MS 6221

Abstract: Given a countable group Gamma, the outer automorphism group Out(Gamma) is either countable or of cardinality continuum. A finer and more suitable notion is to consider the Borel complexity of Out(Gamma) as a Borel equivalence relation. We show that in this context, Out(Gamma) is of rather low complexity, namely that it is a hyperfinite Borel equivalence relation. In general, we show that for any Polish group G and any countable normal subgroup Gamma, the quotient group G/Gamma is hyperfinite. This is joint work with Joshua Frisch


Tuesday, October 29

  • Logic Seminar
    Aristotelis Panagiotopoulos(Caltech)
    Automatic continuity for homeomorphism groups of compact manifolds,I
          3:00 -- 4:00 pm // Linde, Room 387

Abstract: In this talk we will go over the proof of the following theorem of Kathryn Mann: if Homeo(M) is the group of all homeomorphisms of a compact manifold M, endowed with the compact open topology, then every homomorphism from Homeo(M) to any separable topological group is necessarily continuous


Tuesday, November 5

  • Logic Seminar
    Aristotelis Panagiotopoulos(Caltech)
    Automatic continuity for homeomorphism groups of compact manifolds,II
          3:00 -- 4:00 pm // Linde, Room 387

Abstract: In this talk we will go over the proof of the following theorem of Kathryn Mann: if Homeo(M) is the group of all homeomorphisms of a compact manifold M, endowed with the compact open topology, then every homomorphism from Homeo(M) to any separable topological group is necessarily continuous


Tuesday, November 12

  •  Logic Seminar
    Forte Shinko (Caltech)
    Hyperfinite actions with the same invariant random subgroup
          3:00 -- 4:00 pm // Linde, Room 387

Abstract: Let Gamma be a countable group. The invariant random subgroup of a pmp action of Gamma on X is the measure on the space of subgroups of Gamma obtained by pushing forward the measure on X via the map sending x to its stabilizer. A result of Elek states that if two pmp actions of Gamma have the same invariant random subgroup and one is hyperfinite, then they are strongly equivalent, so in particular they are both hyperfinite. We present a proof due to Giraud.








Contact information: A. Kechris, kechris@caltech.edu
Previous seminars

2013-2014

2014-2015

2015-2016

2016-2017

2017-2018

2018-2019