For many applications in science and engineering, the ability to efficiently and accurately approximate solutions to elliptic PDEs dictates what physical phenomena can be simulated numerically.  In this seminar, we present a high-order accurate discretization technique for variable coefficient PDEs with smooth coefficients.  The technique comes with a nested dissection inspired direct solver that scales linearly or nearly linearly with respect to the number of unknowns.  Unlike the application of nested dissection methods to classic discretization techniques, the constant prefactors do not grow with the order of the discretization.  The discretization is robust even for problems with highly oscillatory solutions.  For example, a problem 100 wavelengths in size can be solved to 9 digits of accuracy with 3.7 million unknowns on a desktop computer.  The precomputation of the direct solver takes 6 minutes on a desktop computer.  Then applying the computed solver takes 3 seconds.  The recent application of the algorithm to inverse media scattering also will be presented.

Proteomics is seen as the next logical step after genomics to understand life processes at the molecular level. With increasing capabilities of modern mass spectrometers the deep proteome (>8000 proteins detected) has become widely accessible, only to be replaced recently by the "Ultra-deep proteome" with ~14000 proteins detected in a single cell line. Furthermore, new data search algorithms and sample preparation methods allow not only to achieve comprehensive sequence coverage for the majority of proteins, but also to detect protein variations and single amino acid polymorphisms in proteins, further linking genomic variation to protein phenotypes. The combination of genomic and proteomic information on individual (patient) level could mark the beginning of the "Post-Proteomic Era".

Please register via https://www.eventbrite.co.uk/e/qbiox-colloquium-trinity-term-2017-ticke…

In 2016, Habegger and Pila published a proof of the Zilber-Pink conjecture for curves in abelian varieties (all defined over $\mathbb{Q}^{\rm alg}$). Their article also contained a proof of the same conjecture for a product of modular curves that was conditional on a strong arithmetic hypothesis. Both proofs were extensions of the Pila-Zannier strategy based in o-minimality that has yielded many results in this area. In this talk, we will explain our generalisation of the strategy to the Zilber-Pink conjecture for any Shimura variety. This is joint work with J. Ren.

 Locality is not expected to be a fundamental aspect of a full theory of quantum gravity; it should be emergent in an appropriate semiclassical limit.  In the context of general holography, I'll define a new construct - the causal state - which provides a necessary and sufficient condition for a boundary state to have a holographic semiclassical dual causal geometry (and thus be "local").  This definition illuminates some general features of holographic quantum gravity: for instance, I'll show that the emergence of locality is "all or nothing" in the sense that it exhibits features of quantum error correction and quantum secret sharing.  In the special case of AdS/CFT, I'll also argue that the causal state is the natural boundary dual to the so-called causal wedge of a region.