A symbolic representation of Anosov-Katok Diffeomorphisms IV

Speaker: 

Matt Foreman

Institution: 

UC Irvine

Time: 

Tuesday, April 14, 2015 - 1:00pm to 2:00pm

Location: 

RH 440R

I present joint work with B. Weiss that describes a concrete operation on words that allows one to generate symbolic representations of Anosov-Katok diffeomorphisms. We show that each A-K diffeomorphism can be represented this way and that each symbolic system generated by this operation can be realized as an A-K diffeomorphism.

A symbolic representation of Anosov-Katok Diffeomorphisms III

Speaker: 

Matt Foreman

Institution: 

UC Irvine

Time: 

Tuesday, March 3, 2015 - 1:00pm to 2:00pm

Location: 

RH 440R

I present joint work with B. Weiss that describes a concrete operation on words that allows one to generate symbolic representations of Anosov-Katok diffeomorphisms. We show that each A-K diffeomorphism can be represented this way and that each symbolic system generated by this operation can be realized as an A-K diffeomorphism.

Consequences of the existence of ample generics and automorphism groups of homogeneous metric structures

Speaker: 

Maciej Malicki

Institution: 

Department of Mathematics and Mathematical Economics, Warsaw School of Economics

Time: 

Tuesday, March 10, 2015 - 1:00pm to 2:00pm

Host: 

Location: 

RH 440R

Inspired by a recent work of Marcin Sabok, we define a criterionfor a homogeneous metric structure X that implies that its automorphism group Aut(X) satisfies all the main consequences of the existence of ample generics: it has the small index property, the automatic continuity property, and uncountable cofinality for non-open subgroups. Then we verify it for the Urysohn space, the Lebesgue probability measure algebra, and the Hilbert space, regarded as metric structures, thus proving that their automorphism groups share these properties. We also formulate a condition for X which implies that every homomorphism of Aut(X) into a separable group with a left-invariant, complete metric, is trivial, and we verify it for the Urysohn space, and the Hilbert space.

Diophantine properties of elements of SO(3)

Speaker: 

Ryan Broderick

Institution: 

UC Irvine

Time: 

Tuesday, February 10, 2015 - 1:00pm to 2:00pm

Location: 

RH 440R

A real number x is called diophantine if its distance to rationals p/q is large relative to q -- more precisely, if for every d > 0 there is a positive C such that for every reduced rational p/q, we have |x - p/q| > Cq^{-2-d}, or equivalently |qx-p| > Cq^{-1-d}. Almost all reals have this property. Furthermore, almost every pair (x_1, x_2) has the property that for every d > 0 there is a C such that |q_1x_1+q_2x_2 -p| > C||q||^{-2(1+d)} for all p, q_1, q_2. In this talk, we discuss a noncommutative analog of this property for elements of SO(3). Namely, a pair (A,B) is called diophantine if there exists a constant D such that for every positive integer n and every reduced word W of length n in A, B, A^{-1}, B^{-1}, we have ||W - E|| > D^{-n}, where E is the identity matrix. It is conjectured that almost every such pair (in the sense of Haar measure) is diophantine. We will present a paper of Kaloshin and Rodnianski, in which the weaker bound D^{-n^2} is obtained.

Pages

Subscribe to RSS - Dynamical Systems