Student Dynamics Archives for Academic Year 2012


Organizational Meeting

When: Tue, September 4, 2012 - 3:30pm
Where: Math 1308


An Introduction to C*-algebras in Dynamics

When: Tue, September 18, 2012 - 3:30pm
Where: Math 1308
Speaker: Mike Kreisel (UMD) -

Why do dynamicists care about C*-algebras?

When: Tue, September 25, 2012 - 3:30pm
Where: Math 1308
Speaker: Scott Schmieding (University of Maryland - College Park) -

Why Do Dynamicists Care About C*-algebras II: The Reckoning

When: Tue, October 2, 2012 - 3:30pm
Where: Math 1308
Speaker: Scott Schmieding (UMD) -

Evolution of the shape of asymptotic convex hull of the rapidly exploring random tree

When: Tue, October 9, 2012 - 3:30pm
Where: Math 1308
Speaker: Maxim Arnold (University of Illinois at Urbana-Champaign) -
Abstract: Rapidly exploring Random Trees (RRT) have become
increasingly popular as a way to explore high-dimensional spaces for
problems in robotics, motion planning, virtual prototyping,
computational biology, and other fields. It was established that the
vertex distribution converges in probability to the sampling
distribution. It was also noted that there is a "Voronoi bias" in the
tree growth because the probability that a vertex is selected is
proportional to the volume of its Voronoi region. I shall explain the
evolution of the shape of convex hull of RRT when the size of the
search space is increased.

Introduction to Automorphisms of Shifts

When: Tue, October 23, 2012 - 3:30pm
Where: Math 1308
Speaker: Brendan Berg (UMD)


Dynamics on Isolated Invariant Sets (Preliminary Oral Exam)

When: Mon, November 5, 2012 - 3:00pm
Where: MTH 1308
Speaker: Scott Schmieding (University of Maryland)

Bohr Sets of Integers and Combinatorial Number Theory

When: Tue, November 20, 2012 - 3:30pm
Where: MTH 1308
Speaker: Hillel Furstenberg (Hebrew University) -

Quasicrystals in Dynamics

When: Tue, November 27, 2012 - 3:30pm
Where: Math 1308
Speaker: Mike Kreisel (UMD) -

Classification of beta-shifts (Special Extra Session)

When: Tue, January 29, 2013 - 11:00am
Where: Math 3206
Speaker: Rune Johansen (University of Copenhagen)


Global observables and infinite mixing

When: Tue, January 29, 2013 - 3:30pm
Where: Math 1308
Speaker: Marco Lenci, Universita' di Bologna, Italy
Abstract: Finding a satisfactory definition of mixing for dynamical systems
preserving an infinite measure (in short, infinite mixing) is an
important open problem. Virtually all the definitions that have been
attempted so far use ’local observables’, that is, functions that
essentially only “see” finite portions of the phase space. We
introduce the concept of ’global observable’, a function that gauges a
certain quantity throughout the phase space. This concept is based on
the notion of infinite-volume average, which plays the role of the
expected value of a global observable. Endowed with these notions,
which are to be specified on a case-by-case basis, we give a number of
definitions of infinite mixing. These fall in two categories:
global-global mixing, which expresses the “decorrelation” of two
global observables, and global-local mixing, where a global and a
local observable are considered instead. Time permitting, we will see
how these definitions respond on some examples of
infinite-measure-preserving dynamical systems.

Organizational Meeting

When: Tue, February 5, 2013 - 3:30pm
Where: Math 1308


Quasicrystals, Dynamical Systems, and Topology for Aperiodic Sets

When: Tue, February 12, 2013 - 3:30pm
Where: MATH 1308
Speaker: Scott Schmieding (UMD)

Quasicrystals, Dynamical Systems, and Topology for Aperiodic Sets: Part 2

When: Tue, February 19, 2013 - 3:30pm
Where: MATH 1308
Speaker: Scott Schmieding (UMD)

Gap Labelling for Quasicrystals Part 1: Crystals

When: Tue, February 26, 2013 - 3:30pm
Where: MATH 1308
Speaker: Mike Kreisel (UMD)

Gap Labelling for Quasicrystals Part 2

When: Tue, March 5, 2013 - 3:30pm
Where: Math 1308
Speaker: Mike Kreisel

An introduction to beta-shifts

When: Tue, March 26, 2013 - 3:30pm
Where: Math 1308
Speaker: Brendan Berg (UMD)

Homeomorphic measures on a Cantor set

When: Tue, April 2, 2013 - 3:30pm
Where: MATH 1308
Speaker: Olena Karpel (Institute for Low Temperature Physics, Kharkov, Ukraine)
Abstract: Two measures \mu and \nu on a topological space X are called homeomorphic if there exists a homeomorphism f of X such that \mu(A) = \nu(f(A)) for every Borel subset A. We are interested in the problem of classification of Borel probability and infinite measures on a Cantor set with respect to a homeomorphism.

For a wide class of probability measures which E. Akin called good, a criterion of being homeomorphic is known. A full non-atomic measure \mu is good if whenever U, V are clopen sets with \mu(U) < \mu(V), there exists a clopen subset W of V such that \mu(W) = \mu(U). For the class of good probability measures, the set S(\mu) of values of measure \mu on all clopen subsets of X is a complete invariant.

We consider ergodic probability and infinite invariant measures for aperiodic substitution dynamical systems. S. Bezuglyi, J.Kwiatkowski, K.Medynets and B.Solomyak showed that these measures can be described as ergodic measures on non-simple stationary Bratteli diagrams invariant with respect to the cofinal (tail) equivalence relation. We also consider a wide class of infinite measures on a Cantor set. We find necessary and sufficient condition for good measures to be homeomorphic. It turns out, that for good infinite measures, the set S(\mu) is not a complete invariant, we find a new invariant which is complete.

Entropy on Groups

When: Tue, April 16, 2013 - 3:30pm
Where: Math 1308
Speaker: Scott Schmieding (UMD)

Exponential decay of correlations for dispersing planar billiards with corner points

When: Tue, April 23, 2013 - 3:30pm
Where: Math 1308
Speaker: Jacopo De Simoi (Università di Roma - Tor Vergata)