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New York : American Mathematical Society Physical description. Includes bibliographical references pages Geometry, Differential.
Related item. Online version:: Eisenhart, Luther Pfahler, b.
Non-Riemannian geometry. New York, American Mathematical Society, Bibliography text. Holdings information at the University of Bristol Libraries Live circulation data is not available. Back to results Back to item. University of Aberdeen Libraries. Implications for quantum gravity will be described. After some preliminaries on financial mathematics, I will discuss how a large financial market can be modeled via a stochastic evolution equation in an infinite dimensional space.
In the context of such a model, the issue of hedging can be studied in terms of a martingale representation theorem.
The specific topic of hedging exotic equity derivatives with a portfolio of variance swaps will be treated as an example. This work is joint with Francois Berrier. Much of our understanding of nonlinear systems revolves around what the system 'settles down to' at long times, and how this changes qualitatively as we vary control parameters. The payoff for understanding the generic qualitative changes 'bifurcations' that occur is that often the same bifurcations appear in mathematical models and experiments with very different physics.
I will illustrate this idea by discussing the large collection of nonlinear dissipative systems for example, from fluid mechanics which, when subjected to uniform external forcing, produce counterintuitively spatially-localised responses. In the simplest case, the set of localised equilibrium states and they're not solitons in the classical sense has a nice structure and a convincing theoretical explanation, but it's also clear that this is only the tip of the iceberg.
Riemannian holonomy groups and calibrated geometry. Dominic Joyce. Notes for graduate lecture course, MT Preliminary version, still under construction . The holonomy group Hol(g) of a Riemannian n-manifold (M, g) is a global invariant which measures the constant tensors on the manifold. It is a Lie subgroup of.
Lately people have been asking questions of the sort "How can one define an approximate X, to what extent does it resemble an actual X, and is this useful? I will attempt to say what this has to do with finding prime numbers in particular patterns, for example arithmetic progressions such as 5,11,17,23, It is well-known that through stereographic projection, one can put a complex coordinate z on a spherical surface.
Felix Klein studied the complex coordinates of the vertices, edge centres and face centres of each platonic solid this way, and found that they are the roots of rather simple polynomials in z. Related to these Klein polynomials there are some further, rational functions of z ratios of polynomials , which have the same symmetries as the platonic solids. Recently, it has been discovered that various model physical systems, in chemistry, condensed matter, nuclear and particle physics, have smooth structures with the same symmetries as platonic solids. The Klein polynomials and related rational functions are very useful for describing them mathematically.
The talk will end with a brief discussion of a model for atomic nuclei in which the protons and neutrons are regarded as close enough together to partially merge into a symmetric structure of this type, called a Skyrmion. Various small nuclei, up to carbon and a bit larger, have been modelled this way.
Modern number theory as unifying factor for mathematics.
Number theorists use in their research almost all areas of pure mathematics, and several fundamental developments in number theory serve as a unifying force in mathematics. I will present several recent instances of fruitful interplay between number theory and algebra, geometry, topology, functional analysis and emerging new links to quantum physics.
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Bifurcation theory for localised states Much of our understanding of nonlinear systems revolves around what the system 'settles down to' at long times, and how this changes qualitatively as we vary control parameters. An lot is and is to the fair sources. Contact the Duke WordPress team. J69 Ships in 10 to 15 business days. Starting with the basic geometry of connections, curvature, complex and Kahler structures suitable for beginning graduate students, the text covers seminal results such as Yau's proof of the Calabi Conjecture, and takes the reader all the way to the frontiers of current research in calibrated geometry, giving many open problems.
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