Seminar Calendar
for events the day of Friday, September 24, 2010.

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Friday, September 24, 2010

Graduate Analysis Seminar
1:00 pm   in 241 Altgeld Hall,  Friday, September 24, 2010
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Submitted by savsec2.
Noel DeJarnette (UIUC Math)
Characterizations of Sobolev Spaces on Metric Measure Spaces
Abstract: The classical definition of Sobolev spaces is strongly associated with the Euclidean structure of the underlying domain. This may cause difficulty when replacing the domain with a metric space equipped with a Borel measure. We will introduce a few different characterizations to Sobolev spaces on metric measure spaces and show in what general settings these definitions are equivalent.

Model Theory and Descriptive Set Theory Seminar
4:00 pm   in 345 Altgeld Hall,  Friday, September 24, 2010
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Submitted by phierony.
Aaron Hill (UIUC Math)
Rank-1 transformations as homeomorphisms of Cantor space
Abstract: An important class of measure-preserving transformations of a Lebesgue space is the class of Rank-1 transformations. We will discuss the notion of rank-1 and describe how any totally ergodic, Rank-1 transformation can be naturally viewed as a homeomorphism of a Cantor space. We will then show that the centralizer of such a homeomorphism (in the group of all homeomorphisms of Cantor space) consists only of the powers of that homeomorphism. This is analogous to a theorem of Jonathon King, who proved that the centralizer of any rank-1 transformation (in the group of all measure-preserving transformations) equals the closure of its powers in the usual (weak) topology. This is the second of two talks. The first one is given in the Logic Seminar on Tuesday September 21st.