http://www-math.umd.edu/research/seminars.html http://www-math.umd.edu/research/seminars.html Tue, 04 Sep 2012 15:30:00 EDT Where: Math 1308

]]> http://www-math.umd.edu/research/seminars.html Tue, 18 Sep 2012 15:30:00 EDT Where: Math 1308
Speaker: Mike Kreisel (UMD) -
]]> http://www-math.umd.edu/research/seminars.html Tue, 25 Sep 2012 15:30:00 EDT Where: Math 1308
Speaker: Scott Schmieding (University of Maryland - College Park) -
]]> http://www-math.umd.edu/research/seminars.html Tue, 02 Oct 2012 15:30:00 EDT Where: Math 1308
Speaker: Scott Schmieding (UMD) -
]]> http://www-math.umd.edu/research/seminars.html Tue, 09 Oct 2012 15:30:00 EDT 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.
]]> http://www-math.umd.edu/research/seminars.html Tue, 23 Oct 2012 15:30:00 EDT Where: Math 1308
Speaker: Brendan Berg (UMD)

]]> http://www-math.umd.edu/research/seminars.html Mon, 05 Nov 2012 15:00:00 EST Where: MTH 1308
Speaker: Scott Schmieding (University of Maryland)
]]> http://www-math.umd.edu/research/seminars.html Tue, 20 Nov 2012 15:30:00 EST Where: MTH 1308
Speaker: Hillel Furstenberg (Hebrew University) -
]]> http://www-math.umd.edu/research/seminars.html Tue, 27 Nov 2012 15:30:00 EST Where: Math 1308
Speaker: Mike Kreisel (UMD) -
]]> http://www-math.umd.edu/research/seminars.html Tue, 29 Jan 2013 11:00:00 EST Where: Math 3206
Speaker: Rune Johansen (University of Copenhagen)

]]> http://www-math.umd.edu/research/seminars.html Tue, 29 Jan 2013 15:30:00 EST 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.
]]> http://www-math.umd.edu/research/seminars.html Tue, 05 Feb 2013 15:30:00 EST Where: Math 1308

]]> http://www-math.umd.edu/research/seminars.html Tue, 12 Feb 2013 15:30:00 EST Where: MATH 1308
Speaker: Scott Schmieding (UMD)
]]> http://www-math.umd.edu/research/seminars.html Tue, 19 Feb 2013 15:30:00 EST Where: MATH 1308
Speaker: Scott Schmieding (UMD)
]]> http://www-math.umd.edu/research/seminars.html Tue, 26 Feb 2013 15:30:00 EST Where: MATH 1308
Speaker: Mike Kreisel (UMD)
]]> http://www-math.umd.edu/research/seminars.html Tue, 05 Mar 2013 15:30:00 EST Where: Math 1308
Speaker: Mike Kreisel
]]> http://www-math.umd.edu/research/seminars.html Tue, 26 Mar 2013 15:30:00 EDT Where: Math 1308
Speaker: Brendan Berg (UMD)
]]> http://www-math.umd.edu/research/seminars.html Tue, 02 Apr 2013 15:30:00 EDT 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.
]]> http://www-math.umd.edu/research/seminars.html Tue, 16 Apr 2013 15:30:00 EDT Where: Math 1308
Speaker: Scott Schmieding (UMD)
]]> http://www-math.umd.edu/research/seminars.html Tue, 23 Apr 2013 15:30:00 EDT Where: Math 1308
Speaker: Jacopo De Simoi (Università di Roma - Tor Vergata)
]]>