This award supports speakers and participants in the conference "Groups and Computation: Interactions between Geometric Group Theory, Computability and Computer Science," to be held at the Stevens Institute of Technology in Hoboken NJ, June 26-30, 2017. The conference will bring together experts in geometric group theory, computability theory and computer science to discuss recent developments and interactions between these subjects, and to create a roadmap for future cooperation. The junior faculty, postdocs, and graduate students attending the conference will benefit from interacting with senior researchers in several disciplines and establishing valuable professional connections and collaborations. In addition to the regular scientific program, the conference will feature a presentation and a discussion on Wikipedia editing in Mathematics, including a practical how-to guide and demonstration.
Interaction with computation permeated the development of geometric group theory, from the work of Max Dehn in the 1910s, through the work of Turing in 1930s, the Novikov-Boone Theorem in the 1950s and the theory of word-hyperbolic and automatic groups in the 1990s, to the present day. Now group theorists are interested not just in decidability of various problems but in specific low-complexity estimates. Various data compression techniques (such as straight-line programs, power circuits, etc.) have found amazing applications to group-theoretic decision problems. In turn, geometric group theory has repaid in kind and produced powerful ideas that have found applications in computer science and computability theory. Thus, the notion of "generic-case complexity" as a way of capturing the practical behavior of an algorithm on "most" inputs (and distinct from average-case complexity) was born in geometric group theory. This notion has led to the development of the theory of coarse and generic computability in computational complexity, which is now transforming that subject. The ideas of CAT(0) cubical geometry, coming from geometric group theory, are finding useful applications in computational topology, robotics, and computer science. The conference aims to take stock of these developments and map possible future venues of interaction between geometric group theory, computer science and computability theory.
More detailed information can be found at the conference website, http://web.stevens.edu/algebraic/Schupp/
