Events for 09/09/2016 from all calendars

Algebra and Combinatorics Seminar

Time: 3:00PM - 3:50PM

Location: BLOC 628

Speaker: Andrew Bridy, Texas A&M University

Title: Automatic Sequences and Curves over Finite Fields

Abstract: An amazing theorem of Christol states that a power series over a finite field is an algebraic function if and only if its coefficient sequence can be produced by a finite automaton, which is a limited model of a computer with no memory. The proof is straightforward, but it hides information about the representation theory of semigroups associated to automata, which are naturally realized as operators on the differentials of an algebraic curve. I make this explicit by proving a precise link between the complexity of the automaton and the geometry of the curve.

Linear Analysis Seminar

Time: 4:00PM - 5:00PM

Location: BLOC 220

Speaker: David Blecher, University of Houston

Title: Von Neumann algebraic Hardy spaces, quantum measure theory, and peak sets

Abstract: This talk has three related parts. In the first we discuss peak sets, classical and noncommutative. These will be important particularly in the second part, where we describe some recent progress on (Arveson's) noncommutative Hardy spaces--for general von Neumann algebras (joint with Louis Labuschagne). We use Haagerup's reduction theory to generalize Ueda's peak set theorem and its several striking consequences such as uniqueness of predual, an F and M Riesz theorem, a Gleason-Whitney theorem, etc. The third part flows out of, but is partly independent of, the second, and is joint work with Nik Weaver. We discuss some aspects of quantum measure theory, and quantum cardinals. Some of the proofs make use of Farah and Weaver's theory of quantum filters to investigate states on von Neumann algebras which are not normal but have other natural continuity properties. These are then applied to characterize the von Neumann algebras for which Ueda's peak set theorem holds.