Within the program

Prof. Benjamin Steinberg

Abstract:

If T is a transducer such that each state computes an invertible function from A*->A*, then one can generate a group from the states of the automata. We give an introduction to some of the techniques and basic results in the subject. The first two lectures will establish the basic theory. The last lecture will survey some of the applications of the theory without proofs.

3rd lecture

Boardroom of the Department of Mathematics and Statistics (08-2015)

Mon May 4 12-14

Tue May 5 16-18

Wed May 6 11-13

Several items of relevant literature:

Grigorchuk, R. I.; Nekrashevich, V. V.; Sushchanskii, V. I.;

Automata, dynamical systems, and groups. (Russian. Russian summary)

Tr. Mat. Inst. Steklova 231 (2000), Din. Sist., Avtom. i Beskon. Gruppy, 134--214;

translation in Proc. Steklov Inst. Math. 2000, no. 4 (231), 128--203

www.math.tamu.edu/~grigorch/publications/PSIM128.PS

Nekrashevych, Volodymyr; Self-similar groups. Mathematical Surveys and

Monographs, 117. American Mathematical Society, Providence, RI, 2005.

Grigorchuk, Rostislav; Sunic, Zoran; Self-similarity and branching in

group theory. Groups St. Andrews 2005. Vol. 1, 36--95, London Math. Soc.

Lecture Note Ser., 339, Cambridge Univ. Press, Cambridge, 2007.

Silva, P. V.; Steinberg, B.; On a class of automata groups generalizing lamplighter

groups. Internat. J. Algebra Comput. 15 (2005), no. 5-6, 1213--1234.

www.fc.up.pt/cmup/preprints/2003-30.ps

Students are asked to enroll that course by writing an email to nebolova@sci.muni.cz

with her/his full name and the identification number.