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Seminar 
Tuesday,
October 3
Tuesday,
October 17
Tuesday,
October 24
A
recursion theoretic property of
analytic equivalence relations
Tuesday,
October 31
Tuesday,
November 7
3:00  4:00 pm // Mathematics, Room 131 Abstract: Let L be a countable language, let I be an isomorphismtype of countable Lstructures and let a be an oracle. We say that I is "astrange" if it contains a recursiveina structure and its Scott rank is exactly omega_1^a. Such structures exist but there are no known natural examples. Theorem(AD): If C is a collection of aleph_1 isomorphismtypes of countable structures, then for a Turing cone of a's, no member of C is astrange. Tuesday,
November 14
3:00  4:00 pm // Mathematics, Room 131 Abstract: In
this talk, based on joint work with Daniel Drimbe
and Adrian Ioana, will focus on an operator
algebraic criterion sufficient for deducing measure
equivalence of countable groups in the sense of
Gromov. In particular, we will give a tool for
determining when measure equivalence between
$\Gamma_1 \times \Gamma_2$ and $\Lambda_1 \times
\Lambda_2$ can be upgraded to measure equivalence
between the factors, as is the case in a well known
result of Monod and Shalom. The motivation is to
bring to bear the power of Sorin Popa's
deformation/rigidity theory, but no familiarity with
that theory will be assumed.
Tuesday,
November 21
3:00  4:00 pm // Mathematics, Room 131 Abstract: A sequence $(z_n)$ in the unit disc is called an interpolating sequence for $H^\infty$ if for every bounded sequence of complex values $(w_n)$, there exists a bounded analytic function $f$ in the disc such that $f(z_n) = w_n$ for all $n$. Such sequences were characterized by Lennart Carleson. I will talk about a generalization of Carleson's theorem to other classes of functions. The proof of this result uses the solution of the KadisonSinger problem due to Marcus, Spielman and Srivastava. This is joint work with Alexandru Aleman, John McCarthy and Stefan Richter. Tuesday,
November 28
Tuesday, December 5
Monday,
January 8
2:00  3:00 pm // Mathematics, Room 131
Wednesday,
January 17
Abstract: For any Polish space $X$ it is wellknown that the CantorBendixson rank provides a coanalytic rank on $F_{\aleph_0}(X)$ if and only if $X$ is a sigmacompact. In the case of $\omega^\omega$ one may recover a coanalytic rank on $F_{\aleph_0}(\omega^\omega)$ by considering the CantorBendixson rank of the induced trees instead. We shall generalize this idea to arbitrarily Polish spaces and thereby construct a family of coanalytic ranks on $F_{\aleph_0}(X)$ for any Polish space $X$. We study the behaviour of this family and compare the obtained ranks to the original CantorBendixson rank. The main results are characterizations of the compact and sigmacompact Polish spaces in terms of this behavior. Monday,
January 22
Abstract: In a recent Annals paper, Conley and Miller showed that any basis for the countable Borel equivalence relations strictly above E_0 in measure reducibility is uncountable. This is the first in a series of talks where we will provide an overview of this result.

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