Topological algebra / geometric group theory

I am a Lecturer in Mathematics at Coventry University.  The majority of my research involves applying algebraic and combinatorial ideas from the theory of operads to geometric group theory.  See the research section below for a more detailed explanation of this.

Research

For my PhD thesis I described a classifying space for the group of symmetric automorphisms of a free product.  The classifying space can be interpreted as a moduli space of cactus products and the homology of this space splits over the set of planted forests.  I have also worked in the past on cohomology theories of algebras over an operad, in particular I have described the Hodge decomposition in this context.  Current research directions include:
  1. Computing the homology/homotopy type of the space of Euclidean circles embedded in 3-space.
  2. Homological stability for the automorphism group the free product of n copies of a group G, for any G.
  3. Computing relations between Morita cycles in the homology of outer automorphism group of the free groups.
     

Publications

My thesis "Automorphisms of free products of groups" can be downloaded here.

Accepted:

  • Davidsen, Jorn; Griffin, James. 2010 Volatility of unevenly sampled fractional Brownian motion: An application to ice core records. Physical Review E, 81 (1), 016107. 1-9. 10.1103/PhysRevE.81.016107
  • Griffin, James. Diagonal complexes and the integral homology of the automorphism group of a free product, to appear in Proc. LMS, available at arXiv:1011.6038
  • (joint with Gaël Collinet and Aurélien Djament) Stabilité homologique pour les groupes d'automorphismes des produits libres, to appear in Int. Math. Res. Not., available at arXiv:1109.2686.
  • (joint with Vladimir Dotsenko) Cacti and filtered distributive laws, to appear in Alg. and Geom. Topology, available at arXiv:1109.5354

Submitted:

  • Operadic comodules and (co)homology theories, available at arxiv:1403.4831
In preparation:
  • Configurations of separated planes in hyperbolic space.
  • Homological stability of automorphisms of free products.