Nicholas Georgiou, Heilbronn Research Fellow, Department of Mathematics, University of Bristol

Heilbronn Research Fellow, Department of Mathematics, University of Bristol, 2005–2011

Areas of interest: Probabilistic combinatorics and partial orders; modular decomposition and its connection to the Reconstruction Conjecture

Publications:

The simple harmonic urn, Annals of Probability 39 (2011), no. 6, 2119–2177. Also available on the arXiv. Joint with: Edward Crane, Stanislav Volkov, Andrew Wade and Robert Waters.
Continuum limits for classical sequential growth models, Random Structures and Algorithms 36 (2010), no. 2, 218–250. Preprint available. Joint with Graham Brightwell.
On a universal best choice algorithm for partially ordered sets, Random Structures and Algorithms 32 (2008), no. 3, 263–273. Preprint available. Joint with: Małgorzata Kuchta, Michał Morayne and Jarosław Niemiec.
Embeddings and other mappings of rooted trees into complete trees, Order 22 (2005), no. 3, 257–288. Preprint available.
The random binary growth model, Random Structures and Algorithms 27 (2005), no. 4, 520–552. Preprint available (note the change in title).

Current research: (under construction - more to appear here soon!)

Antichains in the k-dimensional random order, collaborative research project with Ed Crane. We held a related workshop in July 2011, funded by the Bristol Mathematics department's GRASP initiative, attended by Cedric Boutillier, Graham Brightwell, Malwina Luczak and Peter Winkler.
Subcritically indecomposable graphs and reconstruction, collaborative research with Robert Brignall. We're investigating the structure of indecomposable graphs (where indecomposable means with respect to modular decomposition) that have the property that very few of the vertex-deleted subgraphs (subgraphs obtained by deleting a single vertex) are indecomposable.
Modular decomposition and the Reconstruction Conjecture, joint with Robert Brignall and Rob Waters. We started this project in the hope of proving that decomposable graphs are reconstructible. We didn't quite get there, but proved that a reasonably large family of decomposable graphs are reconstructible.

Thesis:
My thesis, Random Structures for Partially Ordered Sets, comprises two parts: in the first I studied random models that produce partial orders sequentially; in the second I studied a correlation of embeddings of rooted trees. The main results were subsequently published in my first two papers, and one section was expanded on in my "Continuum limits..." paper with Graham Brightwell, my PhD supervisor.