Operator Algebras and Dynamics Seminars
Fall 2015
All talks are from 3:454:45 p.m. in the Seminar room, unless otherwise specified.

Dec14

UHF Factors, Dynamical Properties, and a Theorem of PowersProf. Mitch BakerUSNATime: 03:45 PM
View Abstract
We present an old result proved by Powers and used in his famous paper on UHF algebras in order to compare the concepts of ergodicity and strong mixing in Dynamical Systems to a kind of asymptotic factorization of states in a noncommutative setting.

Dec07

Integrable Measure Equivalence and Quasiisometric Rigidity of Nilpotent GroupsMichael CantrellUniversity of Illinois, ChicagoTime: 03:45 PM
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Integrable measure equivalence is an equivalence relation on countable groups that is finer than measure equivalence. While all amenable groups form one ME class, they split in to infinitely many IME classes. Our main result is that the IME classes of nilpotent groups are quite rigid. This generalizes/implies a seminal result of Pansu on the quasiisometric rigidity of nilpotent groups, answers a question of Austin, and yields a cocycle analog of Pansu's Rademachertype differentiation theorem for nilpotent groups. Our ergodictheoretic approach differs from previous approaches to QI rigidity, and our main tool is a nilpotentvalued ergodic theorem.

Nov02

A rigidity theorem for generalized odometers. Part IIKostya MedynetsUnited States Naval Academy
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We show that generalized odometers are continuously orbit equivalent if and only if the sequences of finiteindex subgroups defining the systems are virtually isomorphic. For minimal equicontinuous $Z^d$systems the continuous orbit equivalence implies that the acting groups have finite index subgroups (having the same index) whose actions are piecewise conjugate. This result extends M.~Boyle's flipconjugacy theorem originally established for $\Z$actions. As a corollary we obtain a dynamical classification of the restricted isomorphism between generalized BunceDeddens $C*$algebras. We also show that the full group associated with a generalized odometer is amenable if and only if the acting group is amenable.

Oct26

A rigidity theorem for generalized odometers. Part IKostya MedynetsUnited States Naval AcademyTime: 03:45 PM
View Abstract
We show that generalized odometers are continuously orbit equivalent if and only if the sequences of finiteindex subgroups defining the systems are virtually isomorphic. For minimal equicontinuous $Z^d$systems the continuous orbit equivalence implies that the acting groups have finite index subgroups (having the same index) whose actions are piecewise conjugate. This result extends M.~Boyle's flipconjugacy theorem originally established for $\Z$actions. As a corollary we obtain a dynamical classification of the restricted isomorphism between generalized BunceDeddens $C*$algebras. We also show that the full group associated with a generalized odometer is amenable if and only if the acting group is amenable.

Oct19

Dispersing billiards and the heat equationPeter NandoriUniversity of MarylandTime: 03:45 PM
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Dispersing billiard or Sinai billiard is one of the very few physical systems where chaos is well understood (see the laudation for Sinai's Abel prize in 2014). In the talk, I will briefly review the fascinating story of dispersing billiards. Then I will report on some endeavors for deriving heat equation from large billiard type systems in two toy models: for the distribution of mass when energy is fixed (joint work with D. Dolgopyat) and the evolution of the energy when mass is fixed (joint work with P. Balint, T. Gilbert, I.P. Toth, D. Szasz).

Oct05

Sofic Shifts and Finite State CodesMIDN James TalisseTime: 03:45 PM
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We present a necessary and sufficient condition for transforming a sofic shift into the full shift. In particular, if the entropy of the sofic shift is greater than or equal to the entropy of the full shift then such a transformation exists, which we call a finitestate code. Additionally a specific algorithm is developed for establishing finitestate codes. This has fundamental applications in data storage.

Sep28

Dynamics of Some Substitution SystemsKelly B. YanceyUniversity of Maryland, College ParkTime: 03:45 PM
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In this talk we will discuss substitution dynamical systems and some of their dynamical properties. Specifically we will talk about when they display the property of rigidity. Certain classes of interval exchange transformations will also be discussed in relation to substitutions. We will focus on 3IETs.

Aug31

Tensor Products of C(X)Algebras over C(X)Vrej ZarikianUSNATime: 03:45 PM