Past Seminars
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Mon, 29/04 15:00 |
Willi Jaeger (Heidelberg University) |
Partial Differential Equations Seminar  |
Gibson 1st Floor SR |
| Modelling reactive flows, diffusion, transport and mechanical interactions in media consisting of multiple phases, e.g. of a fluid and a solid phase in a porous medium, is giving rise to many open problems for multi-scale analysis and simulation. In this lecture, the following processes are studied: diffusion, transport, and reaction of substances in the fluid and the solid phase, mechanical interactions of the fluid and solid phase, change of the mechanical properties of the solid phase by chemical reactions, volume changes (“growth”) of the solid phase. These processes occur for instance in soil and in porous materials, but also in biological membranes, tissues and in bones. The model equations consist of systems of nonlinear partial differential equations, with initial-boundary conditions and transmission conditions on fixed or free boundaries, mainly in complex domains. The coupling of processes on different scales is posing challenges to the mathematical analysis as well as to computing. In order to reduce the complexity, effective macroscopic equations have to be derived, including the relevant information from the micro scale. In case of processes in tissues, a homogenization limit leads to an effective, mechanical system, containing a pressure gradient, which satisfies a generalized, time-dependent Darcy law, a Biot-law, where the chemical substances satisfy diffusion-transport-reaction equations and are influencing the mechanical parameters. The interaction of the fluid and the material transported in a vessel with its flexible wall, incorporating material and changing its structure and mechanical behavior, is a process important e.g. in the vascular system (plague-formation) or in porous media. The lecture is based on recent results obtained in cooperation with A. Mikelic, M. Neuss-Radu, F. Weller and Y. Yang. | |||
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Mon, 29/04 14:15 |
PENG HU (University of Oxford) |
Stochastic Analysis Seminar |
Oxford-Man Institute |
| Abstract: The aim of this lecture is to give a general introduction to the theory of interacting particle methods and an overview of its applications to numerical finance. We survey the main techniques and results on interacting particle systems and explain how they can be applied to deal with a variety of financial numerical problems such as: pricing complex path dependent European options, computing sensitivities, American option pricing or solving numerically partially observed control problems. | |||
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Mon, 29/04 14:15 |
Subhojoy Gupta (Aarhus) |
Geometry and Analysis Seminar |
L3 |
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Mon, 29/04 14:00 |
Weike Wang (Shanghai Jiao Tong University) |
OxPDE Special Seminar |
Gibson 1st Floor SR |
| In this talk, we will introduce how to apply Green's function method to get pointwise estimates for solutions of the Cauchy problem of nonlinear evolution equations with dissipative structure. First of all, we introduce the pointwise estimates of the time-asymptotic shape of the solutions of the isentropic Navier-Stokes equations and exhibit the generalized Huygen's principle. Then, for other nonlinear dissipative evolution equations, we will introduce some recent results and give brief explanations. Our approach is based on the detailed analysis of the Green's function of the linearized system and micro-local analysis, such as frequency decomposition and so on. | |||
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Mon, 29/04 12:30 |
Peter Carr (NYU and Morgan Stanley) |
Nomura Seminar |
Oxford-Man Institute |
| The Ross Recovery Theorem gives sufficient conditions under which the market’s beliefs can be recovered from risk-neutral probabilities. His approach places mild restrictions on the form of the preferences of the representative investor. We present an alternative approach which has no restrictions beyond preferring more to less, Instead, we restrict the form and risk-neutral dynamics of John Long’s numeraire portfolio. We also replace Ross’ finite state Markov chain with a diffusion with bounded state space. Finally, we present some preliminary results for diffusions on unbounded state space. In particular, our version of Ross recovery allows market beliefs to be recovered from risk neutral probabilities in the classical Cox Ingersoll Ross model for the short interest rate. | |||
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Mon, 29/04 12:00 |
Rhys Davies (Oxford) |
String Theory Seminar |
L3 |
| I will discuss a class of isolated singularities, given by finite cyclic quotients of a threefold node (conifold), which arise naturally in compact Calabi-Yau threefolds. These singularities admit projective crepant resolutions, and thereby give rise to topological transitions between compact Calabi-Yau spaces. Among the interesting properties of such 'hyperconifold transitions' is that they can change the fundamental group, and are related by mirror symmetry to familiar conifold transitions. Having established these mathematical properties, I will briefly discuss some applications, as well as the physics of type IIB string theory compactified on a space with a hyperconifold singularity. | |||
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Fri, 26/04 16:00 |
Mete Soner (ETH Zurich) |
Nomura Seminar |
L1 |
| The original transport problem is to optimally move a pile of soil to an excavation. Mathematically, given two measures of equal mass, we look for an optimal bijection that takes one measure to the other one and also minimizes a given cost functional. Kantorovich relaxed this problem by considering a measure whose marginals agree with given two measures instead of a bijection. This generalization linearizes the problem. Hence, allows for an easy existence result and enables one to identify its convex dual. In robust hedging problems, we are also given two measures. Namely, the initial and the final distributions of a stock process. We then construct an optimal connection. In general, however, the cost functional depends on the whole path of this connection and not simply on the final value. Hence, one needs to consider processes instead of simply the maps S. The probability distribution of this process has prescribed marginals at final and initial times. Thus, it is in direct analogy with the Kantorovich measure. But, financial considerations restrict the process to be a martingale Interestingly, the dual also has a financial interpretation as a robust hedging (super-replication) problem. In this talk, we prove an analogue of Kantorovich duality: the minimal super-replication cost in the robust setting is given as the supremum of the expectations of the contingent claim over all martingale measures with a given marginal at the maturity. This is joint work with Yan Dolinsky of Hebrew University. | |||
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Fri, 26/04 14:00 |
Dr Hugo van den Berg (University of Warwick) |
Mathematical Biology and Ecology Seminar |
L1 |
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Fri, 26/04 10:00 |
Charles Offer (Thales UK) |
Industrial and Interdisciplinary Workshops |
DH 3rd floor SR |
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Please note the change of venue! Suppose there is a system where certain objects move through a network. The objects are detected only when they pass through a sparse set of points in the network. For example, the objects could be vehicles moving along a road network, and observed by a radar or other sensor as they pass through (or originate or terminate at) certain key points in the network, but which cannot be observed continuously and tracked as they travel from one point to another. Alternatively they could be data packets in a computer network. The detections only record the time at which an object passes by, and contain no information about identity that would trivially allow the movement of an individual object from one point to another to be deduced. It is desired to determine the statistics of the movement of the objects through the network. I.e. if an object passes through point A at a certain time it is desired to determine the probability density that the same object will pass through a point B at a certain later time. The system might perhaps be represented by a graph, with a node at each point where detections are made. The detections at each node can be represented by a signal as a function of time, where the signal is a superposition of delta functions (one per detection). The statistics of the movement of objects between nodes must be deduced from the correlations between the signals at each node. The problem is complicated by the possibility that a given object might move between two nodes along several alternative routes (perhaps via other nodes or perhaps not), or might travel along the same route but with several alternative speeds. What prior knowledge about the network, or constraints on the signals, are needed to make this problem solvable? Is it necessary to know the connections between the nodes or the pdfs for the transition time between nodes a priori, or can this be deduced? What conditions are needed on the information content of the signals? (I.e. if detections are very sparse on the time scale for passage through the network then the transition probabilities can be built up by considering each cascade of detections independently, while if detections are dense then it will presumably be necessary to assume that objects do not move through the network independently, but instead tend to form convoys that are apparent as a pattern of detections that persist for some distance on average). What limits are there on the noise in the signal or amount of unwanted signal, i.e. false detections, or objects which randomly fail to be detected at a particular node, or objects which are detected at one node but which do not pass through any other nodes? Is any special action needed to enforce causality, i.e. positive time delays for transitions between nodes? |
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Thu, 25/04 16:00 |
Teruyoshi Yoshida (Cambridge) |
Number Theory Seminar |
L3 |
| One of the most subtle aspects of the correspondence between automorphic and Galois representations is the weight part of Serre conjectures, namely describing the weights of modular forms corresponding to mod p congruence class of Galois representations. We propose a direct geometric approach via studying the mod p cohomology groups of certain integral models of modular or Shimura curves, involving Deligne-Lusztig curves with the action of GL(2) over finite fields. This is a joint work with James Newton. | |||
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Thu, 25/04 16:00 |
Angel Ramos (Universidad Complutense de Madrid) |
Industrial and Applied Mathematics Seminar |
Gibson Grd floor SR |
| In this talk we will discuss the mathematical modelling of the performance of Lithium-ion batteries. A mathematical model based on a macro-homogeneous approach developed by John Neuman will be presented. The uniqueness and existence of solution of the corresponding problem will be also discussed. | |||
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Thu, 25/04 14:00 |
Dr Tobias Berka (University of Cambridge) |
Computational Mathematics and Applications |
Rutherford Appleton Laboratory, nr Didcot |
| Very-large scale data analytics are an alleged golden goose for efforts in parallel and distributed computing, and yet contemporary statistics remain somewhat of a dark art for the uninitiated. In this presentation, we are going to take a mathematical and algorithmic look beyond the veil of Big Data by studying the structure of the algorithms and data, and by analyzing the fit to existing and proposed computer systems and programming models. Towards highly scalable kernels, we will also discuss some of the promises and challenges of approximation algorithms using randomization, sampling, and decoupled processing, touching some contemporary topics in parallel numerics. | |||
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Thu, 25/04 13:00 |
Mathematical Finance Internal Seminar |
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Thu, 25/04 12:00 |
Konstantinos Koumatos (OxPDE, University of Oxford) |
OxPDE Lunchtime Seminar |
Gibson 1st Floor SR |
We derive geometrically linear elasticity theories as  -limits of rescaled nonlinear multi-well energies satisfying a weak coercivity condition, in the sense that the standard quadratic growth from below of the energy density  is replaced by the weaker p-growth far from the energy wells, where $1 |
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Wed, 24/04 16:00 |
Dimitrina Stavrova (Leicester) |
Analytic Topology in Mathematics and Computer Science |
L3 |
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Wed, 24/04 16:00 |
Dimitrina Stavrova (Leicester) |
Analytic Topology in Mathematics and Computer Science |
L3 |
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Wed, 24/04 16:00 |
(Various) (University of Oxford) |
Junior Geometric Group Theory Seminar |
SR2 |
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Wed, 24/04 11:30 |
David Hume ((Oxford University))) |
Algebra Kinderseminar |
Queen's College |
| Following the recent paper of Ogasa, we attempt to construct Boy's surface using only paper and tape. If this is successful we hope to address such questions as: Is that really Boy's surface? Why should we care? Do we have any more biscuits? | |||
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Tue, 23/04 17:00 |
David Edwards (Oxford) |
Functional Analysis Seminar |
L3 |
| We consider a vector lattice L of bounded real continuous functions on a topological space X that separates the points of X and contains the constant functions. A notion of tightness for linear functionals is defined, and by an elementary argument we prove with the aid of the classical Riesz representation theorem that every tight continuous linear functional on L can be represented by integration with respect to a Radon measure. This result leads incidentally to an simple proof of Prokhorov’s existence theorem for the limit of a projective system of Radon measures. | |||
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Tue, 23/04 15:45 |
Richard Rimanyi (University of North Carolina) |
Algebraic and Symplectic Geometry Seminar |
L3 |
| Consider non-negative integers assigned to the vertexes of an oriented graph. To this combinatorial data we associate a so-called quiver representation. We will study the geometry and the algebra of this representation, when the underlying un-oriented graph is of Dynkin type ADE. A remarkable object we will consider is Kazarian's equivariant cohomology spectral sequence. The edge homomorphism of this spectral sequence defines the so-called quiver polynomials. These polynomials are generalizations of remarkable polynomials in algebraic combinatorics (Giambelli-Thom-Porteous, Schur, Schubert, their double, universal, and quantum versions). Quiver polynomials measure degeneracy loci of maps among vector bundles over a common base space. We will present interpolation, residue, and (conjectured) positivity properties of these polynomials. The quiver polynomials are also encoded in the Cohomological Hall Algebra (COHA) associated with the oriented graph. This is a non-commutative algebra defined by Kontsevich and Soibelman in relation with Donaldson-Thomas invariants. The above mentioned spectral sequence has a structure identity expressing the fact that the sequence converges to explicit groups. We will show the role of this structure identity in understanding the structure of the COHA. The obtained identities are equivalent to Reineke's quantum dilogarithm identities associated to ADE quivers and certain stability conditions. | |||
