Forthcoming Seminars

Mon, 18/01/2010
12:00 		Daniel Thompson (Queen Mary, UL) String Theory Seminar Add to calendar L3
T-Duality Invariant String Theory at the Quantum Level
In this talk I will be discussing some reformulations of string theory which promote T-duality to the level of a manifest symmetry namely Hull's Doubled Formalism and Klimcik and Severa's  Poisson-Lie T-duality.   Such formalisms double the number of fields but also incorporate some chirality-like constraint. Invoking this constraint leads one to consider sigma-models which, though duality invariant, do not possess manifest Lorentz Invariance.   Whilst such formalisms make sense at a classical level their quantum validity is less obvious.  I address this issue by examining the renormalization of these duality invariant sigma models.  This talk is based upon both forthcoming work and recent work in arXiv:0910.1345 [hep-th] and its antecedents arXiv:0708.2267, arXiv:0712.1121.
Mon, 18/01/2010
14:15 		Claus Koestler (Carlton University Ottawa) Stochastic Analysis Seminar Add to calendar Eagle House
Symetries and Independence in Noncommutative Probability
The subject of distributional symmetries and invarianceprinciples yields deep results on the structure of the underlying randomobjects. So it is of general interest to investigate if such an approach turnsout to be also fruitful in the quantum world. My talk will report recentprogress in the transfer of de Finetti's pioneering work to noncommutativeprobability. More precisely, an infinite sequence of random variables isexchangeable if its distribution is invariant under finite permutations. The deFinetti theorem characterizes such sequences as conditionally i.i.d. Recentlywe have proven a noncommutative analogue of this celebrated theorem. We willdiscuss the new symmetries `braidability'and `quantum exchangeability' emerging from our approach.In particular, this brings our approach in close contact with Jones' subfactortheory and Voiculescu's free probability. Finally we will address that ourmethods give a new proof of Thoma's theorem on the general form of charactersof the infinite symmetric group. Quite surprisingly, Thoma's theorem turns outto be the spectral analysis of the tail algebra coming from a certainexchangeable sequence of transpositions. This is in part joint work with RolfGohm and Roland Speicher. REFERENCES:[1] C. Koestler. A noncommutative extended de Finettitheorem 258 (2010) 1073-1120.[2] R. Gohm & C. Kostler. Noncommutativeindependence from the braid group $ \mathbb{B}_\infty $. Commun. Math. Phys.289(2) (2009), 435-482.[3] C. Koestler & R. Speicher. A noncommutative deFinetti theorem:Invariance under quantum permutations is equivalent tofreeness with amalgamation. Commun. Math. Phys. 291(2) (2009), 473-490.[4] R. Gohm & C. Koestler: An application ofexchangeability to the symmetric group $ \mathbb{S}_\infty $. Preprint.
Mon, 18/01/2010
14:15 		Nicholas Manton (Cambridge) Geometry and Analysis Seminar Add to calendar L3
Hyperbolic Vortices
TBA
Mon, 18/01/2010
15:35 		Pierre Tarres (University of Oxford) Stochastic Analysis Seminar Add to calendar Eagle House
To Be Announced
TBA
Mon, 18/01/2010
15:45 		Professor Graem Segal (Oxford) Topology Seminar Add to calendar L3
Wick Rotation in Quantum Field Theory
Physical space-time is a manifold with a Lorentzianmetric, but the more mathematical treatments of the theory usually prefer toreplace the metric with a positive - i.e. Riemannian - one. The passage fromLorentzian to Riemannian metrics is called 'Wick rotation'. In my talk I shallgive a precise description of what is involved, and shall explain some of itsimplications for physics. 
Mon, 18/01/2010
16:00 		Timothy Trudgian (Oxford) Junior Number Theory Seminar Add to calendar SR1
An Round-Up of the Circle Problem
How many integer-points lie in a circle of radius $ \sqrt{x} $? A poor man's approximation might be $ \pi x $, and indeed, the aim-of-the-game is to estimate
$$P(x) = \sharp\{(m, n) \in\mathbb{Z}: \;\; m^{2} + n^{2} \leq x\} -\pi x,$$
Once one gets the eye in to show that $ P(x) = O(x^{1/2}) $, the task is to graft an innings to reduce this bound as much as one can. Since the cricket-loving G. H. Hardy proved that $ P(x) = O(x^{\alpha}) $ can only possible hold when $ \alpha \geq 1/4 $ there is some room for improvement in the middle-order. In this first match of the Junior Number Theory Seminar Series, I will present a summary of results on $ P(x) $.
Mon, 18/01/2010
17:00 		Henrik Shahgholian (KTH Stockholm) Partial Differential Equations Seminar Add to calendar Gibson 1st Floor SR
Obstacle type problems : An overview and some recent results
In this talk I will present recent developments of the obstacle type problems, with various applications ranging from: Industry to Finance, local to nonlocal operators, and one to multi-phases. The theory has evolved from a single equation
$$ \Delta u = \chi_{u > 0}, \qquad u \geq 0 $$
to embrace a more general (two-phase) form
$$ \Delta u = \lambda_+ \chi_{u>0} - \lambda_- \chi_{u<0} $$
with $ \lambda_\pm $ reasonably smooth functions (down to Dini continuous). Astonishing results of Yuval Peres and his collaborators has shown remarkable relationships between obstacle problem and various forms of random walks, including Smash sum of Diaconis-Fulton (Lattice sets), and there is more to come. The two-phase form (and its multi-phase form) has been under investigation in the last 10 years, and interesting recoveries has been made about the behavior of the free boundaries in such problems. Existing methods has so far only allowed us to consider $ \lambda_\pm>0 $. The above problem changes drastically if one allows $ \lambda_\pm $ to have the incorrect sign (that appears in composite membrane problem)! In part of my talk I will focus on the simple unstable case
$$ \Delta u = - \chi_{u>0} $$
and present very recent results (Andersson, Sh., Weiss) that classifies the set of singular points ($ \{u=\nabla u =0\} $) for the above problem. The techniques developed recently by our team also shows an unorthodox approach to such problems, as the classical technique fails. At the end of my talk I will explain the technique in a heuristic way.
Tue, 19/01/2010
12:00 		Piotr T Chrusciel (Oxford) Relativity Seminar Add to calendar L3
The Cauchy problem for the vacuum Einstein equations on a light-cone
I will present existence and uniqueness results for theCauchy problem as in the title.
Tue, 19/01/2010
14:00 		Dr Orly Alter (University of Texas at Austin) Computational Mathematics and Applications Add to calendar 3WS SR
Discovery of Mechanisms from Mathematical Modeling of DNA Microarray Data by Using Matrix and Tensor Algebra: Computational Prediction and Experimental Verification
Future discovery and control in biology and medicine will come from the mathematical modeling of large-scale molecular biological data, such as DNA microarray data, just as Kepler discovered the laws of planetary motion by using mathematics to describe trends in astronomical data. In this talk, I will demonstrate that mathematical modeling of DNA microarray data can be used to correctly predict previously unknown mechanisms that govern the activities of DNA and RNA. First, I will describe the computational prediction of a mechanism of regulation, by using the pseudoinverse projection and a higher-order singular value decomposition to uncover a genome-wide pattern of correlation between DNA replication initiation and RNA expression during the cell cycle. Then, I will describe the recent experimental verification of this computational prediction, by analyzing global expression in synchronized cultures of yeast under conditions that prevent DNA replication initiation without delaying cell cycle progression. Finally, I will describe the use of the singular value decomposition to uncover "asymmetric Hermite functions," a generalization of the eigenfunctions of the quantum harmonic oscillator, in genome-wide mRNA lengths distribution data. These patterns might be explained by a previously undiscovered asymmetry in RNA gel electrophoresis band broadening and hint at two competing evolutionary forces that determine the lengths of gene transcripts.
Tue, 19/01/2010
14:30 		Peter Keevash (QMUL) Combinatorial Theory Seminar Add to calendar L3
Shadows and intersections: stability and new proofs
We give a short new proof of a version of the Kruskal-Katona theorem due to Lovász. Our method can be extended to a stability result, describing the approximate structure of configurations that are close to being extremal, which answers a question of Mubayi. This in turn leads to another combinatorial proof of a stability theorem for intersecting families, which was originally obtained by Friedgut using spectral techniques and then sharpened by Keevash and Mubayi by means of a purely combinatorial result of Frankl. We also give an algebraic perspective on these problems, giving yet another proof of intersection stability that relies on expansion of a certain Cayley graph of the symmetric group, and an algebraic generalisation of Lovász’s theorem that answers a question of Frankl and Tokushige.
Tue, 19/01/2010
15:45 		Damiano Testa (Oxford) Algebraic and Symplectic Geometry Seminar Add to calendar L3
Big rational surfaces
The Cox ring of a variety is an analogue of the homogeneous coordinate ring of projective space. Cox rings are not defined for every variety and even when they are defined, they need not be finitely generated. Varieties for which the Cox ring is finitely generated are called Mori dream spaces and, as the name suggests, they are particularly well-suited for the Minimal Model Program. Such varieties include toric varieties and del Pezzo surfaces. I will report on joint work with T. Várilly and M. Velasco where we introduce a class of smooth projective surfaces having finitely generated Cox ring. This class of surfaces contains toric surfaces and (log) del Pezzo surfaces.
Tue, 19/01/2010
16:00 		Dawid Kielak (Oxford) Junior Geometric Group Theory Seminar Add to calendar SR1
CAT(0) spaces and their boundaries
We will look at CAT(0) spaces, their isometries and boundaries (defined through Busemann functions).
Tue, 19/01/2010
17:00 		Paul Lescot (University of Rouen) Algebra Seminar Add to calendar L2
Prime ideals and spectra of B1-algebras
Wed, 20/01/2010
10:10 		Dr Chris Farmer (OCCAM) OCCAM Literature Seminar Add to calendar OCCAM Common Room (RI2.28)
“Why 2-point statistics are sufficient for image analysis and synthesis"
The paper for this first session is "Every discrete, finite image is uniquely determined by its dipole histogram" by Charles Chubb and John I. Yellott
Wed, 20/01/2010
11:30 		Peter Neumann (University of Oxford) Algebra Kinderseminar Add to calendar ChCh, Tom Gate, Room 2
Synchronizing groups and irreducible modules over the field of size two
Thu, 21/01/2010
11:00 		Will Anscombe (Oxford) Advanced Logic Class Add to calendar SR2
Existentially Definable Subsets of Henselian Fields
TBA
Thu, 21/01/2010
13:30 		Steven Rayan (Oxford) Junior Geometry and Topology Seminar Add to calendar SR1
Co-Higgs bundles I: spectral curves
PLEASE NOTE THE CHANGE OF TIME FOR THIS WEEK: 13.30 instead of 12. In the first of two talks, I will simultaneously introduce the notion of a co-Higgs vector bundle and the notion of the spectral curve associated to a compact Riemann surface equipped with a vector bundle and some extra data. I will try to put these ideas into both a historical context and a contemporary one. As we delve deeper, the emphasis will be on using spectral curves to better understand a particular moduli space.
Thu, 21/01/2010
14:00 		Prof. Ernesto Estrada (University of Strathclyde) Computational Mathematics and Applications Add to calendar Rutherford Appleton Laboratory, nr Didcot
An excursion through the world of complex networks guided by matrix theory
A brief introduction to the field of complex networks is carried out by means of some examples. Then, we focus on the topics of defining and applying centrality measures to characterise the nodes of complex networks. We combine this approach with methods for detecting communities as well as to identify good expansion properties on graphs. All these concepts are formally defined in the presentation. We introduce the subgraph centrality from a combinatorial point of view and then connect it with the theory of graph spectra. Continuing with this line we introduce some modifications to this measure by considering some known matrix functions, e.g., psi matrix functions, as well as new ones introduced here. Finally, we illustrate some examples of applications in particular the identification of essential proteins in proteomic maps.

For any corrections/updates to these listings, please contact seminars [-at-] maths [dot] ox [dot] ac [dot] uk.

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