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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.


Tuesday, November 26

  •  Logic Seminar
    Peter Burton (University of Texas at Austin)
      Flexible stability and nonsoficity
          3:00 -- 4:00 pm // Linde, Room 387

Abstract: It is a well known open problem to determine if every group is sofic. A sofic group $G$ is said to be flexibly stable if every sofic approximation to $G$ can converted to a sequence of disjoint unions of Schreier graphs by modifying an asymptotically vanishing proportion of edges. We will discuss a joint result with Lewis Bowen that if $\mathrm{PSL}_d(\mathbb{Z})$ is flexibly stable for some $d \geq 5$ then there exists a group which is not sofic.



Tuesday, December 10

  •  Logic Seminar
    Dana Bartosova (University of Florida)
        Questions about phase spaces of minimal Boolean flows    
          2:30 -- 3:30 pm // Linde, Room 387

Abstract: By a flow, we mean a continuous action of a topological groups $G$ on a compact Hausdorff space $X$. We refer to $X$  as the phase space of the flow. We are primarily interested in minimal flows, that is, flows with no non-trivial proper closed invariant subset. Among minimal flows, there exists a maximal one called the universal minimal flow, $M(G),$ which admits a continuous homomorphism onto every minimal flow. When $G$ is non-Archimedean, that is, it admits a neighbourhood basis of the identity of open subgroups, then $M(G)$ is $0$-dimensional. These are exactly groups of automorphisms of first-order structures with the topology of pointwise convergence. If $M(G)$ is $0$-dimensional, we can think dually in terms of its algebra of clopen subsets.  We summarize which algebras are known to appear as phase spaces of universal minimal flows and we pose questions about the unknown.



Friday, January 10

  • Caltech-UCLA Logic Seminar
    Ronnie Chen (UIUC)
    A universal characterization of standard Borel spaces
          2:00 -- 3:30 pm //UCLA MS 6221

Abstract: We show that the category of standard Borel spaces is the free
or "universal" category equipped with some familiar set operations of
countable arity (e.g., products) obeying some simple compatibility
conditions (e.g., products distribute over disjoint unions).  In this
talk, we will discuss the precise formulation of this result, its
connection with the amalgamation property for $\kappa$-complete Boolean
algebras, and its proof using methods from categorical logic.


Wednesday, February 5

  •  Logic Seminar
    Forte Shinko (Caltech)
    Weak containment of subgroups
          2:00 -- 3:00 pm // Linde, Room 387

Abstract: Given a countable group Gamma, there is a compact space of subgroups Sub(Gamma), which is equipped with the Gamma-action via conjugation. We study the notion of weak containment on this space, namely when one subgroup is contained in the orbit closure of another, which is related to weak containment of quasi-regular unitary representations of Gamma. In particular, we will consider necessary and sufficient conditions for the existence of dense orbits.


Wednesday, February 12

  •  Logic Seminar
    Shaun Allison (Carnegie Mellon University)
         Title: Non-Archimedean tsi Polish groups, and obstructions to Borel reducibility
        2:00 -- 3:00 pm // Linde, Room 387

Abstract



n this talk, we show that any generically E_

Wednesday, February 19

  •  Logic Seminar
    Jack H. Lutz (Iowa State University)
         Title: Passing Hilbert's Final Test
        2:00 -- 3:00 pm // Linde, Room 387

Abstract


Wednesday, April 8

  •  Logic Seminar (online)
    Aristotelis Panagiotopoulos (Caltech)
         Dynamical obstructions for classification by TSI group actions
        12:00 -- 1:00 pm

Abstract. A big part of mathematical activity revolves around classification problems. However, not every classification problem has a satisfactory solution, and some classification problems are more complicated than others. Dynamical properties such as generic ergodicity and turbulence are crucial in the development of a rich complexity theory for classification problems. In this talk we will review some of the existing anti-classification techniques and we will introduce a new obstruction for classification by orbit equivalence relations of TSI Polish groups; a topological group is TSI if it admits a compatible two side invariant metric. We will then  show that the Wreath product of any two non-compact subgroups of $S_{\infty}$ admits an action whose orbit equivalence relation is generically ergodic with respect to orbit equivalence relations of TSI group actions.


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

2013-2014

2014-2015

2015-2016

2016-2017

2017-2018

2018-2019