Artículos con la etiqueta ‘Group Theory (math.GR)’

A report on Tarski’s decidability problem

Por • 29 ene, 2014 • Category: Educacion

This paper contains a list of crucial mistakes and counterexamples to some of the main statements in the paper «Elementary theory of free nonabelian groups» by O. Kharlampovich and A. Myasnikov, which was published in the Journal of Algebra in June 2006.

Mathematics discovered, invented, and inherited

Por • 13 sep, 2013 • Category: Ambiente

Abstract: The classical platonist/formalist dilemma in philosophy of mathematics can be expressed in lay terms as a deceptively naive question: is mathematics discovered or invented? Using an example from my own mathematical life, I argue that there is also a third way: mathematics can also be inherited — and in the process briefly discuss a remarkable paper by W. Burnside of 1900.

Growth in groups: ideas and perspectives

Por • 12 mar, 2013 • Category: Opinion

This is a survey of methods developed in the last few years to prove results on growth in non-commutative groups. These techniques have their roots in both additive combinatorics and group theory, as well as other fields. We discuss linear algebraic groups, with SL_2(Z/pZ) as the basic example, as well as permutation groups. The emphasis lies on the ideas behind the methods.