General Audience Maths Edinburgh Seminars
Speakers from the School of Mathematics will explain their research to a general mathematical audience, including mature undergraduates, postgraduates, postdocs and staff. Each session will contain two 25 minutes talks.
This talk introduces linear programming (LP) via the human diet problem. After giving a brief history of the simplex method for solving LP problems, the diet problem in the animal feed formulation industry is described. This yields an insight into the challenge and value of solving large-scale LP problems.
Diffusion maps is a popular framework based upon diffusion processes for finding meaningful geometric descriptions of data sets. In this talk, I will explain how this method can be used to define collective reaction coordinates in molecular dynamics.
Algebraic varieties are solutions of a system of polynomial equations in the affine or in the projective space. They are very fundamental objects and have been studied since ancient times.
In this talk, I will give a gentle introduction to the Minimal Model Program, one of the main tool in the classification of higher dimensional algebraic varieties.
In this talk, we present a Bayesian framework for semi-supervised binary classification on graphs. We develop several Bayesian models through the construction of a Gaussian prior from the graph Laplacian. Connections to the Ginzburg-Landau model are also made through the notion of a push-forward of the Gaussian prior under the double-well thresholding. We introduce efficient MCMC methods designed for large data sets to effectively sample from the posterior distribution for large scale problems. Through a variety of numerical experiments, we demonstrate the ability to perform uncertainty quantification by sampling from the posterior distribution. In particular, we observe empirically that the posterior mean and variance aligns well with certain external notions of uncertainty.
In this talk, we will show a very general version of a trust-region algorithm for unconstrained optimization problems. The idea is to extract only the important conditions that a model should have in order to successfully prove convergence of the algorithm. The described algorithm can then be used in a derivative-free implementation.
Mathematical and computer modelling is widely used to support decisions in energy systems planning and in development of government energy policy. This talk will explore key issues in the use of modelling for decision support (with the help of a few experts from history), and give a flavour of what we at Edinburgh are doing about these.
Abstract: The expansion history of the Universe encodes information about the matter and energy content on large scales and hence is a key observable for cosmological models. Starting with Edwin Hubble in 1929, astronomers have been improving their measurement of the expansion history for nearly a century. We describe some of the mathematics and statistics underlying these measurements and the most recent result - the first ever measurement of the expansion rate of the Universe using gravitational waves. The latter was made possible by combined gravitational wave and electromagnetic observations of the binary neutron star merger GW170817 discovered by LIGO in August 2017.