Permutation Groups (16w5087)

The Banff International Research Station will host the "Permutation Groups" workshop from November 13th to November 18th, 2016.

Permutation groups are a mathematical approach to analysing structures by studying
the rearrangements of the elements of the structure that preserve it. Finite permutation
groups are primarily understood through combinatorial methods, while concepts from logic and
topology come to the fore when studying infinite permutation groups. These two branches of
permutation group theory are not completely independent however because techniques from algebra and
geometry may be applied to both, and ideas transfer from one branch to the other. This workshop
will bring together researchers on both finite and infinite permutation groups to share techniques and
recent advances.

The permutation groups act on discrete structures such as graphs or incidence geometries
comprising points and lines, and many of the same intuitions apply whether the structure is
finite or infinite. Matrix groups are also an important source of both finite and infinite
permutation groups, and the constructions used to produce the geometries on which they act
in each case are similar.

Counting arguments are important when studying finite permutation groups but cannot be
used to the same effect with infinite permutation groups. Progress comes instead by using
techniques from model theory and descriptive set theory. Another approach to infinite
permutation groups is through topology and approximation. In this approach, the infinite
permutation group is locally the limit of finite permutation groups and results from the
finite theory may be brought to bear.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT).