Past Special Seminar

13 April 2012
Jure Leskovec

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.

6 March 2012
Gil Cavalcanti

We show how the reduction procedure for generalized Kahler  
structures can be used to recover Hitchin's results about the  
existence of a generalized Kahler structure on the moduli space of  
instantons on bundle over a generalized Kahler manifold. In this setup  
the proof follows closely the proof of the same claim for the Kahler  
case and clarifies some of the stranger considerations from Hitchin's  

24 February 2012
Kobi Kremnizer

In recent years, surprising connections between type theory and homotopy theory have been discovered. In this talk I will recall the notions of intensional type theories and identity types. I will describe "infinity groupoids", formal algebraic models of topological spaces, and explain how identity types carry the structure of an infinity groupoid. I will finish by discussing categorical semantics of intensional type theories.

The talk will take place in Lecture Theatre B, at the Department of Computer Science.

3 February 2012
Samson Abramsky

The seminar will take place in Lecture Theatre A, Department of Computer Science.


Contextuality and non-locality are features of quantum mechanics which stand in sharp contrast to the realistic picture underlying classical physics. We shall describe a unified geometric perspective on these notions in terms of *obstructions to the existence of global sections*. This allows general results and structural notions to be uncovered, with quantum mechanics appearing as a special case. The natural language to use here is that of sheaves and presheaves; and cohomological obstructions can be defined which witness contextuality in a number of salient examples.

This is joint work with Adam Brandenburger

and Shane Mansfield and Rui Soares Barbosa

20 January 2012
Bob Coecke

We will demonstrate the following. Category theory, usually conceived as some very abstract form of metamathematics, is present everywhere around us. Explicitly, we show how it provides a kindergarten version of quantum theory, an how it will help Google to understand sentences rather than words.

Some references are:

-[light] BC (2010) "Quantum picturalism". Contemporary Physics 51, 59-83. arXiv:0908.1787 
-[a bit heavier] BC and Ross Duncan (2011) "Interacting quantum observables: categorical algebra and diagrammatics". New Journal of Physics 13, 043016. arXiv:0906.4725
-[light] New Scientist (8 December 2010) "Quantum links let computers understand language".
-[a bit heavier] BC, Mehrnoosh Sadrzadeh and Stephen Clark (2011) "Mathematical foundations for a compositional distributional model of meaning". Linguistic Analysis - Lambek Festschrift. arXiv:1003.439

21 July 2011
22 July 2011

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.


  • 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.