This will be a review of recent work that obtains amplitudes at strong coupling from certain minimal surfaces in AdS.
9:50am Welcome \\
10:00am Malcolm McCulloch (Engineering, Oxford), "Dual usage of land: Solar power and cattle grazing"; \\
10:45am Jonathan Moghal (Materials, Oxford), “Anti-reflectance coatings: ascertaining microstructure from optical properties”; \\
11:15am (approx) Coffee \\
11:45am Agnese Abrusci (Physics, Oxford), "P3HT based dye-sensitized solar cells"; \\
12:15pm Peter Foreman (Destertec UK), "Concentrating Solar Power and Financial Issues" \\
1:00pm Lunch.
One may answer a question of Macintyre by showing that there are recursive existentially closed dimension groups. One may build such groups having most of the currently known special properties of finitely generic dimension groups, though no finitely generic dimension group is arithmetic.
We report the numerical realization and demonstration of robustness of certain 2-component structures in Bose-Einstein Condensates in 2 and 3 spatial dimensions with non-trivial topological charge in one of the components. In particular, we identify a stable symbiotic state in which a higher-dimensional bright soliton exists even in a homogeneous setting with defocusing interactions, as a result of the effective potential created by a stable vortex in the other component. The resulting vortex-bright solitary waves, which naturally generalize the recently experimentally observed dark-bright solitons, are examined both in the homogeneous medium and in the presence of parabolic and periodic external confinement and are found to be very robust.
We discuss a class of high-order spectral-Galerkin surface integral algorithms with specific focus on simulating the scattering of electromagnetic waves by a collection of three dimensional deterministic and stochastic particles.
The talk concerns experiments that study strategic thinking by eliciting subjects’ initial responses to series of different but related games, while monitoring and analyzing the patterns of subjects’ searches for hidden but freely accessible payoff information along with their decisions.
This talk will largely be a survey and so will gloss over technicalities. After introducing the basics of the theory of the étale fundamental group I will state the theorems and conjectures related to Grothendieck's famous "anabelian" letter to Faltings. The idea is that the geometry and arithmetic of certain varieties is in some sense governed by their non-abelian (anabelian) fundamental group. Time permitting I will discuss current work in this area, particularly the work of Minhyong Kim relating spaces of (Hodge, étale) path torsors to finiteness theorems for rational points on curves leading to a conjectural proof of Faltings' theorem which has been much discussed in recent years.
What do historians of mathematics do? What sort of questions do they ask? What kinds of sources do they use? This series of four informal lectures will demonstrate some of the research on history of mathematics currently being done in Oxford. The subjects range from the late Renaissance mathematician Thomas Harriot (who studied at Oriel in 1577) to the varied and rapidly developing mathematics of the seventeenth century (as seen through the eyes of Savilian Professor John Wallis, and others) to the emergence of a new kind of algebra in Paris around 1830 in the work of the twenty-year old Évariste Galois.
Each lecture will last about 40 minutes, leaving time for questions and discussion. No previous knowledge is required: the lectures are open to anyone from the department or elsewhere, from undergraduates upwards.
Consider the following simple question:
Is there a subcategory of Top that is dually equivalent to Lat?
where Top is the category of topological spaces and continuous maps and Lat is the category
of bounded lattices and bounded lattice homomorphisms.
Of course, the question has been answered positively by specializing Lat, and (less
well-known) by generalizing Top.
The earliest examples are of the former sort: Tarski showed that every complete atomic
Boolean lattice is represented by a powerset (discrete topological space); Birkhoff showed
that every finite distributive lattice is represented by the lower sets of a finite partial order
(finite T0 space); Stone generalized Tarski and then Birkhoff, for arbitrary Boolean and
arbitrary bounded distributive lattices respectively. All of these results specialize Lat,
obtaining a (not necessarily full) subcategory of Top.
As a conceptual bridge, Priestley showed that distributive lattices can also be dually
represented in a category of certain topological spaces augmented with a partial order.
This is an example of the latter sort of result, namely, a duality between a category of
lattices and a subcategory of a generalization of Top.
Urquhart, Hartung and Hartonas developed dualities for arbitrary bounded lattices in
the spirit of Priestley duality, in that the duals are certain topological spaces equipped with
additional structure.
We take a different path via purely topological considerations. At the end, we obtain
an affirmative answer to the original question, plus a bit more, with no riders: the dual
categories to Lat and SLat (semilattices) are certain easily described subcategories of Top
simpliciter. This leads directly to a very natural topological characterization of canonical
extensions for arbitrary bounded lattices.
Building on the topological foundation, we consider lattices expanded with quasioperators,
i.e., operations that suitably generalize normal modal operatos, residuals, orthocomplements
and the like. This hinges on both the duality for lattices and for semilattices
in a natural way.
This talk is based on joint work with Peter Jipsen.
Date: May 2010.
1
In this talk we will first survey results which guarantee the existence of
spanning subgraphs in dense graphs. This will lead us to the proof of the
bandwidth-conjecture by Bollobas and Komlos, which states that any graph
with minimum degree at least $(1-1/r+\epsilon)n$ contains every r-chromatic graph
with bounded maximum degree and sublinear bandwidth as a spanning subgraph.
We will then move on to discuss the analogous question for a host graph that
is obtained by starting from a sparse random graph G(n,p) and deleting a
certain portion of the edges incident at every vertex.
This is joint work with J. Boettcher, Y. Kohayakawa and M. Schacht.
In the first half of the talk we explain - in very broad terms - how the objects defined in the previous meetings are linked with each other. We will motivate this 'big picture' by briefly discussing class field theory and the Artin conjecture for L-functions. In the second part we focus on a particular aspect of the theory, namely the L-function preserving construction of elliptic curves from weight 2 newforms via Eichler-Shimura theory. Assuming the Modularity theorem we obtain a proof of the Hasse-Weil conjecture.