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Logic
Seminar 
Thursday,
September 19
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
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
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
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
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 
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