Mathematics has an essential role to play at the EPFL because of the range of application of its ideas and methods, which is leading to an increasing use of mathematical models by scientists and engineers.

The mathematical fields of potential interest at EPFL are diverse, thus underlining the need to maintain strong research groups across the range of fundamental and applicable mathematics; the resulting interactions can stimulate fundamental and applied mathematical research, as well as being of direct benefit to other domains.

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How high is high dimensional?

What does high dimensional mean? How high is “high dimensional”? In this lecture I will give a rather personal view of how our ideas of high dimensionality have changed, with particular reference to recent developments in Quasi-Monte Carlo (QMC) methods for high-dimensional integration.

By: Prof. Ian H. Sloan (UNSW Australia - The University of New South Wales)

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Gravitational Waves and Black Holes - the Legacy of General Relativity

While the Newtonian theory of gravity is similar to electrostatics, the field equations in both cases being elliptic, Einstein's general relativity is more similar to Maxwell's electromagnetic theory, the field equations in both cases being of hyperbolic character. A consequence of this fact is the presence in general relativity of gravitational waves, which are analogous to electromagnetic waves. Due however to the nonlinear nature of Einstein's equations, a long time elapsed before the theory of gravitational waves reached a satisfactory level of understanding. Another fundamental feature of general relativity is that gravitational collapse leads to the formation of spacetime regions which are inaccessible to observation from infinity, the black holes. In the last two years, on several occasions, wave trains have been detected generated by binary black holes which inspiral and coalesce. In my lecture, I shall describe the basic concepts, give an outline of their historical development, and discuss how the theory connects to the recent observations.