Special Seminar (past)

A workshop on different aspects of deformation theory in various fields

Exhibitors will be here along with recruiters from different sectors. There will also be panel talks. For further information see http://www.careers.ox.ac.uk/wp-content/uploads/2012/02/JobsForMathematic... and in particular last year brochure for the event at http://www.careers.ox.ac.uk/wp-content/uploads/2012/04/MathsPrintII.pdf

Nodes in complex networks organize into communities of nodes that share a common property, role or function, such as social communities, functionally related proteins, or topically related webpages. Identifying such communities is crucial to the understanding of the structural and functional roles of networks.

Current work on overlapping community detection (often implicitly) assumes that community overlaps are less densely connected than non-overlapping parts of communities. This is unnatural as it means that the more communities nodes share, the less likely it is they are linked. We validate this assumption on a diverse set of large networks and find an increasing relationship between the number of shared communities of a pair of nodes and the probability of them being connected by an edge, which means that parts of the network where communities overlap tend to be more densely connected than the non-overlapping parts of communities.

Existing community detection methods fail to detect communities with such overlaps. We propose a model-based community detection method that builds on bipartite node-community affiliation networks. Our method successfully detects overlapping, non-overlapping and hierarchically nested communities. We accurately identify relevant communities in networks ranging from biological protein-protein interaction networks to social, collaboration and information networks. Our results show that while networks organize into overlapping communities, globally networks also exhibit a nested core-periphery structure, which arises as a consequence of overlapping parts of communities being more densely connected.

This meeting will mark the 80th birthday of Sir Roger Penrose. Twistor theory is one of his most remarkable discoveries and continues to have applications across pure mathematics and mathematical physics. This meeting will focus on some recent developments with speakers both on geometry and physics.

Speakers:

• Nima Arkani-Hamed (IAS, Princeton): Scattering without space-time
• Mike Eastwood (ANU): CR geometry and conformal foliations
• Nigel Hitchin (Oxford): Twistors and Octonions
• Andrew Hodges (Oxford): Polytopes and amplitudes
• Claude LeBrun (SUNY Stony Brook): On Hermitian, Einstein 4-Manifolds
• David Skinner (Perimeter Institute): Scattering amplitudes from holomorphic linking in twistor space
• Paul Tod (Oxford): Conformal cyclic cosmology

Registration will start at 1.30pm on the 21st with the first lecture at 2.15pm. The meeting will finish by 4.30pm on the 22nd. See the programme for more details.

There will be a reception at 6.30pm on the 21st July (Wadham College) followed by dinner at 7.15 in Wadham College.