I am currently a postdoc at the University of Glasgow. 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.
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:
- Computing the homology/homotopy type of the space of Euclidean circles embedded in 3-space. I conjecture that the homology splits over planted forests.
- Generalising Outer space from the outer automorphism group of a free group to that of a free product (this is related to, but different from the work of Guirardel and Levitt). I aim to use this to prove homological stability for the automorphism group the free product of n copies of a group G, for any G.
- Computing relations between Morita cycles in the homology of outer automorphism group of the free groups.
My thesis "Automorphisms of free products of groups" can be downloaded here
- 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, arXiv:1109.5354
- An operadic approach to the algebraic Hodge decomposition.