The conference “Algebras, Representations and Applications” was held in Mare-
sias, Brazil on August 26 - September 1, 2007. It had 124 participants from 23
countries. The conference was organized by the Department of Mathematics of the
University of S˜ ao Paulo to celebrate the 60th birthday of Ivan Shestakov.
Ivan Pavlovich Shestakov was born in a small village in Eastern Siberia. He
distinguished himself early in the mathematical olympiads and as a teenager was
invited to the special physical and mathematical boarding school at the Academic
Town of Novosibirsk. His masters thesis “On a Class of Non-commutative Jordan
Ring” was awarded the Medal of the Academy of Science of USSR for students.
Soon after having obtained the BC and PhD degrees at the Novosibirsk State
University under the supervision of A.I. Shirshov and K.A. Zhevlakov he became
a leading force in the area of nonassociative algebra and carried the torch of the
Novosibirsk Nonassociative School.
From 1993 to 1998 Ivan held visiting positions at the Universities of Oviedo
and Logro˜ no in Spain. In 1999 he accepted a position of Professor Titular at the
University of S˜ ao Paulo and moved to Brazil.
In 2002 Ivan Shestakov and his former student Ualbai Umirbaev proved the long
standing Nagata Conjecture on the existence of wild automorphisms in polynomial
algebras. For this remarkable work the authors were awarded the Moore prize of
This volume contains selected papers contributed by the participants in the
conference. We gratefully acknowledge that the conference would not be possible
without the generous ﬁnancial support from CAPES, CNPq, FAPESP, Instituto
Millenium and the Institute of Mathematics and Statistics of the University of S˜ao
Our special thanks are to Christine Thivierge of the AMS for her invaluable
help during the preparation of this volume and to many anonymous referees whose
deep remarks greatly improved the manuscripts.