Forthcoming Seminars
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Thu, 12/05/2011 11:00 |
B.Zilber (Oxford) |
Advanced Class Logic  |
L3 |
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Thu, 12/05/2011 13:00 |
Ferhana Ahmad |
Mathematical Finance Internal Seminar |
DH 1st floor SR |
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Thu, 12/05/2011 13:00 |
David Hume (University of Oxford) |
Junior Geometry and Topology Seminar |
SR1 |
| Mikhail Borovoi's theorem states that any simply connected compact semisimple Lie group can be understood (as a group) as an amalgam of its rank 1 and rank 2 subgroups. Here we present a recent extension of this, which allows us to understand the same objects as a colimit of their rank 1 and rank 2 subgroups under a final group topology in the category of Lie groups. Loosely speaking, we obtain not only the group structure uniquely by understanding all rank 1 and rank 2 subgroups, but also the topology. The talk will race through the elements of Lie theory, buildings and category theory needed for this proof, to leave the audience with the underlying structure of the proof. Little prior knowledge will be assumed, but many details will be left out. | |||
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Thu, 12/05/2011 14:00 |
Prof Andrew Cliffe (University of Nottingham) |
Computational Mathematics and Applications |
Rutherford Appleton Laboratory, nr Didcot |
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This seminar will be held at the Rutherford Appleton Laboratory near Didcot. Abstract: Numerical calculations of laminar flow in a two-dimensional channel with a sudden expansion exhibit a symmetry-breaking bifurcation at Reynolds number 40.45 when the expansion ratio is 3:1. In the experiments reported by Fearn, Mullin and Cliffe [1] there is a large perturbation to this bifurcation and the agreement with the numerical calculations is surprisingly poor. Possible reasons for this discrepancy are explored using modern techniques for uncertainty quantification. When experimental equipment is constructed there are, inevitably, small manufacturing imperfections that can break the symmetry in the apparatus. In this work we considered a simple model for these imperfections. It was assumed that the inlet section of the channel was displaced by a small amount and that the centre line of the inlet section was not parallel to the centre line of the outlet section. Both imperfections were modelled as normal random variables with variance equal to the manufacturing tolerance. Thus the problem to be solved is the Navier-Stokes equations in a geometry with small random perturbations. A co-ordinate transformation technique was used to transform the problem to a fixed deterministic domain but with random coefficient appearing in the transformed Navier-Stokes equations. The resulting equations were solved using a stochastic collocation technique that took into account the fact that the problem has a discontinuity in parameter space arising from the bifurcation structure in the problem. The numerical results are in the form of an approximation to a probability measure on the set of bifurcation diagrams. The experimental data of Fearn, Mullin and Cliffe are consistent with the computed solutions, so it appears that a satisfactory explanation for the large perturbation can be provided by manufacturing imperfections in the experimental apparatus. The work demonstrates that modern methods for uncertainty quantification can be applied successfully to a bifurcation problem arising in fluid mechanics. It should be possible to apply similar techniques to a wide range of bifurcation problems in fluid mechanics in the future. References: [1] R M Fearn, T Mullin and K A Cliffe Nonlinear flow phenomena in a symmetric sudden expansion, J. Fluid Mech. 211, 595-608, 1990. |
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Thu, 12/05/2011 14:30 |
Alison Parker (Leeds) |
Representation Theory Seminar |
L3 |
In joint work with Karin Baur (ETH, Zurich) and Karin Erdmann (Oxford),
we study certain Delta-filtered modules for the Auslander
algebra of k[T]/T^n\rtimes C_2 where C_2 is the cyclic group
of order two.
The motivation of this lies in the problem of describing the  -orbit
structure for the action of a parabolic subgroup of a linear algebraic
group on its nilradical \mathfrak{n}. In general, there are
infinitely P-orbits in \mathfrak{n} and it is a “wild” problem to describe them.
However, in the case of a parabolic subgroup of SL_N, there
exists a bijection between P-orbits in the nilradical and
certain (Delta-filtered) modules for the Auslander algebra of k[T]/T^n,
due to work of Hille and Rohrle and Brustle et al..
Under this bijection, the Richardson orbit (i.e. the
dense orbit) corresponds to the Delta-filtered module without
self-extensions.
It has remained an open problem to describe such
a correspondence for other classical groups. |
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Thu, 12/05/2011 16:00 |
Nikolai Brilliantov (University of Leicester) |
Differential Equations and Applications Seminar |
DH 1st floor SR |
| We develop a theory of impact of viscoelastic spheres with adhesive interactions. We assume that the collision velocities are not large to avoid the fracture and plastic deformation of particles material and microscopic relaxation time is much smaller than the collision duration. The adhesive interactions are described with the use of Johnson, Kendall and Roberts (JKR) theory, while dissipation is attributed to the viscoelastic behavior of the material. For small impact velocities we apply the condition of a quasi-static collision and obtain the inter-particle force. We show that this force is a sum of four components, having in addition to common elastic, viscous and adhesive force, the visco-adhesive cross term. Using the derived force we compute the coefficient of normal restitution and consider the application of our theory to the collisions of macro and nano-particles. | |||
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Thu, 12/05/2011 16:00 |
Daniel Bertrand (Paris) |
Logic Seminar Number Theory Seminar |
L3 |
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The points in question can be found on any semi-abelian surface over an elliptic curve with complex multiplication. We will show that they provide counter-examples to natural expectations in a variety of fields : Galois representations (following K. Ribet's initial study from the 80's), Lehmer's problem on heights, and more recently, the relative analogue of the Manin-Mumford conjecture. However, they do support Pink's general conjecture on special subvarieties of mixed Shimura varieties.
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Thu, 12/05/2011 16:00 |
Daniel Bertrand (Paris) |
Number Theory Seminar |
L3 |
| The points in question can be found on any semi-abelian surface over an elliptic curve with complex multiplication. We will show that they provide counter-examples to natural expectations in a variety of fields : Galois representations (following K. Ribet's initial study from the 80's), Lehmer's problem on heights, and more recently, the relative analogue of the Manin-Mumford conjecture. However, they do support Pink's general conjecture on special subvarieties of mixed Shimura varieties. | |||
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Thu, 12/05/2011 17:15 |
Professor Hans Föllmer (Humboldt Universität zu Berlin) |
Nomura Lecture |
Examination Schools |
| Over the last decades, advanced probabilistic methods have played an increasing role in Finance, both in Academia and in the financial industry. In view of the recent financial crisis it has been asked to which extent "misplaced reliance on sophisticated maths" has been part of the problem. We will focus on the foundational issue of model uncertainty, also called "Knightian uncertainty". This will be illustrated by the problem of quantifying financial risk. We discuss recent advances in the theory of convex risk measures and a corresponding robustification of classical problems of optimal portfolio choice, where model uncertainty is taken into account explicitly. Biography: Hans Follmer is Professor Emeritus of Mathematics at Humboldt-Universitat zu Berlin, Andrew D. White Professor-at-Large at Cornell University, and Visiting Professor at the National University of Singapore. Before joining Humboldt University in 1994, he has been professor at the universities of Frankfurt and Bonn and at ETH Zurich. Hans Follmer is widely known for his contributions to probability theory and mathematical finance. He received numerous awards, including the Prix Gay-Lussac/Humboldt of the French Government, the Georg-Cantor medal of the German Mathematical Society, and a honorary degree of the University Paris-Dauphine. He is a member of the Berlin-Brandenburgische Akademie der Wissenschaften, the German National Academy of Sciences Leopoldina, and the European Academy of Sciences Academia Europaea. | |||
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Fri, 13/05/2011 00:00 |
Mathematical Biology and Ecology Seminar |
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Fri, 13/05/2011 11:15 |
Various |
OCCAM Special Seminar |
OCCAM Common Room (RI2.28) |
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Mon, 16/05/2011 12:00 |
Tom Bridgeland (Oxford) |
String Theory Seminar |
L3 |
| This talk will be about spaces of stability conditions. I will start by recalling Mike Douglas' original work on Pi-stability for D-branes, and go on to explain a couple of of the main open questions in the subject. The second half of the talk will focus on an illustrative example, namely the case of the local projective plane. | |||
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Mon, 16/05/2011 14:15 |
Monique Pontier (Inst. Math. De Toulouse (IMT)) |
Stochastic Analysis Seminar |
Oxford-Man Institute |
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The paper analyses structural models for the evaluation of risky debt following H.E. LELAND [2], with an approach of optimal stopping problem (for instance cf. N. EL KAROUI [1]) and within a more general context: a dividend is paid to equity holders, moreover a different tax schedule is introduced, depending on the firm current value. Actually, an endogenous default boundary is introduced and a nonlinear convex tax schedule allowing for a possible switching in tax benefits. The aim is to find optimal capital structure such that the failure is delayed, meaning how to decrease the failure level VB, anyway preserving D debtholders and E equity holders’interests: for the firm VB is needed as low as possible, for the equity holder, an optimal equity is requested, finally an optimal coupon C is asked for the total value. Keywords: corporate debt, optimal capital structure, default, |
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Mon, 16/05/2011 14:15 |
Rafe Mazzeo (Stanford) |
Geometry and Analysis Seminar |
L3 |
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Mon, 16/05/2011 15:45 |
Jean-Francois Chassagneux (Université d'Evry-Val-d 'Essonne) |
Stochastic Analysis Seminar |
Oxford-Man Institute |
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Mon, 16/05/2011 15:45 |
Jessica Banks (Oxford) |
Topology Seminar |
L3 |
| We give an introduction to the Kakimizu complex of a link, covering a number of recent results. In particular we will see that the Kakimizu complex of a knot may be locally infinite, that the Alexander polynomial of an alternating link carries information about its Seifert surfaces, and that the Kakimizu complex of a special alternating link is understood. | |||
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Mon, 16/05/2011 16:00 |
James Haydon (UCL) |
Junior Number Theory Seminar |
SR1 |
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Mon, 16/05/2011 17:00 |
Mariarosaria Padula (Universita di Ferrara) |
Partial Differential Equations Seminar |
Gibson 1st Floor SR |
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Given a film of viscous heavy liquid with upper free boundary over an inclined plane, a steady laminar motion develops parallel to the flat bottom ofthe layer. We name this motion Poiseuille Free Boundary PFBflow because of its (half) parabolic velocity profile. In flowsover an inclined plane the free surface introduces additionalinteresting effects of surface tension and gravity. These effectschange the character of the instability in a parallel flow, see{Smith} [1]. \parBenjamin [2], and Yih [3], have solved the linear stabilityproblem of a uniform film on a inclined plane. Instability takesplace in the form of an infinitely long wave, howeversurface waves of finite wavelengths are observed, see e.g.Yih [3]. Up to date direct nonlinear methods for the study ofstability seem to be still lacking.Aim of this talk is the investigation of nonlinear stability ofPFB providing a rigorous formulation of the problem by theclassical direct Lyapunov method assuming periodicity in theplane, when above the liquid there is a uniform pressure due tothe air at rest, and the liquid is moving with respect to the air.Sufficient conditions on the non dimensional Reynolds, Webernumbers, on the periodicity along the line of maximum slope, onthe depth of the layer and on the inclination angle are computedensuring Kelvin-Helmholtz nonlinear stability. We usea modified energy method, cf. [4],[5], which providesphysically meaningful sufficient conditions ensuring nonlinearexponential stability. The result is achieved in the class ofregular solutions occurring in simply connected domains havingcone property.\parNotice that the linear equations, obtained by linearization of ourscheme around the basic Poiseuille flow, do coincide with theusual linear equations, cf. {Yih} [3]. References [1] M.K. Smith, The mechanism for the long-waveinstability in thin liquid films J. Fluid Mech., 217,1990, pp.469-485. [2] Benjamin T.B., Wave formation in laminar flow down aninclined plane, J. Fluid Mech. 2, 1957, 554-574. [3] Yih Chia-Shun, Stability of liquid flow down aninclined plane, Phys. Fluids, 6, 1963, pp.321-334. [4] Padula M., On nonlinear stability of MHD equilibriumfigures, Advances in Math. Fluid Mech., 2009, 301-331. [5] Padula M., On nonlinear stability of linear pinch,Appl. Anal. 90 (1), 2011, pp. 159-192. |
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Tue, 17/05/2011 12:00 |
Jamie Vicary (Comlab) |
Quantum Field Theory Seminar |
L3 |
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I will present some new results on classifying 123 TQFTs, |
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Tue, 17/05/2011 14:15 |
Prof. David Andrews (AOPP (Oxford University)) |
Geophysical and Nonlinear Fluid Dynamics Seminar |
Dobson Room, AOPP |
