Texas A&M University, Department of Mathematics
Special Year on
Asymptotic
Group Invariants and their Applications
Fall Workshop 1, November 6, 2004
Schedule
317 Milner Hall, Texas A&M
University, College Station TX
- 10:00 - 10:50
Speaker: Tullio Ceccherini-Silberstein of
Universitá
del
Sannio, Benevento, Italy
Title: Cellular automata,
subshifts and amenable groups. Abstract.
- 11:05 - 11:55
Speaker: Filippo Tolli of Universitá di Roma Tre
Title: Spectral analysis of
finite Markov chains with spherical symmetries. Abstract.
- 12:10 - 12:30
Speaker: Ievgen Bondarenko of Texas A&M University
Title: Schreier graphs of
iterated monodromy groups of sub-hyperbolic quadratic polynomials. Abstract.
- 12:30 - 2:00 Lunch Break
- 2:00 - 2:45
Speaker: Zoran Sunik of Texas A&M University
Title: Growth of
Grigorchuk groups. Abstract.
- 3:00 - 3:20
Speaker: Dmytro Savchuk of Texas A&M University
Title: Some graphs of
Schreier type related to the Thompson group. Abstract.
- 3:30 - 3:50
Speaker: Yevgen Muntyan of Texas A&M University
Title: The Bellaterra
automaton group. Abstract.
Organizers: Rostislav
Grigorchuk, Gilles Pisier and Zoran Sunik of Texas A&M University
Abstracts
Ievgen
Bondarenko of Texas A&M University
Schreier graphs of
iterated monodromy groups of sub-hyperbolic quadratic polynomials
An efficient method is proposed for calculating the orbital contracting
coefficient of these groups. An efficient method is given for finding
the growth of diameters of Schreier graphs on levels. We will provide
the boundaries, where the growth degrees of orbital Schreier graphs are
located. Interesting examples of Schreier graphs are considered.
Tullio
Ceccherini-Silberstein of Universitá
del
Sannio, Benevento, Italy
Cellular automata, subshifts and
amenable groups
We discuss the notions of cellular automata and subshifts over a
finitely generated group: several examples will be presented. We then
focus our attention on the so-called "Garden of Eden Theorem" asserting
the equivalence between (1) surjectivity, (2) preinjectivity and (3)
entropy-preserving for the corresponding local maps when the group is
amenable.
Yevgen Muntyan
of Texas A&M University
The Bellaterra automaton group
A 3-state automaton generating the free product Z_2*Z_2*Z_2 is
described.
Dmytro Savchuk
of Texas A&M University
Some graphs of Schreier type related
to the Thompson group
The Schreier graph of the Thompson group F with respect to the
stabilizer of 1/2 is constructed. Its relation to the action of F on
L_2([0,1]) is considered.
Zoran Sunik
of Texas A&M University
Growth of
Grigorchuk groups
New upper bounds on the growth of groups of Grigorchuk type are
provided. The bounds are obtained by estimates on the shortening
coefficients achieved in the decomposition of the elements during the
portrait construction.
Filippo Tolli
of Universitá di Roma Tre, Italy
Spectral analysis of
finite Markov chains with spherical symmetries
Let G be a finite group
acting on a finite set X and let A_1, A_2, ... ,A_N be the orbits of G
on X. Under the hypothesis that each (G,A_i) is a Gel'fand pair we
analyze the structure of the G-invariant operators on X. In particular
we show how the computation of the spectrum of a large class of
G-invariant random walks on certain posets can be reduced to the
analysis of some tridiagonal matrices. This latter problem is solved by
a suitable sine or cosine transform.