This week is a women's only week in which we are joined by the Mirzakhani society, the society for undergraduate women in maths, for lunch.
We are very excited to have another session with invited speakers joining us for the lunch next week. Annika Heckel, Frances Kirwan and Marc Lackenby will all be joining us for a panel discussion on balancing family with academia. All are welcome to join us and to ask questions.
We hope to see many of you at the lunch - Monday 1-2pm Quillen Room (N3.12).
The Sun has been emitting light and illuminating the Earth for more than four billion years. By analyzing the properties of solar light we can infer a wealth of information about what happens on the Sun. A particularly fascinating (and often overlooked) property of light is its polarization state, which characterizes the orientation of the oscillation in a transverse wave. By measuring light polarization, we can gather precious information about the physical conditions of the solar atmosphere and the magnetic fields present therein.
The Oxford-Princeton Workshops on Financial Mathematics & Stochastic Analysis have been held approximately every eighteen months since 2002, alternately in Princeton and Oxford. They bring together leading groups of researchers in, primarily, mathematical and computational finance from Oxford University and Princeton University to collaborate and interact. The series is organized by the Oxford Mathematical and Computational Finance Group, and at Princeton by the Department of Operations Research and Financial Engineering and the Bendheim Center for Finance.
The classical Dirac operator is part of an osp(1|2) realisation inside the Weyl-Clifford algebra which is Pin-invariant. This leads to a multiplicity-free decomposition of the space of spinor-valued polynomials in irreducible modules for this Howe dual pair. In this talk we review an abstract generalisation A of the Weyl algebra that retains a realisation of osp(1|2) and we determine its centraliser algebra explicitly. For the special case where A is a rational Cherednik algebra, the centralizer algebra provides a refinement of the previous decomposition whose analogue was no longer irreducible in general. As an example, for the group S3 in specific, we will examine the finite-dimensional irreducible modules of the centraliser algebra.
He calls it a "crazy idea." Then again, he points out, so is the idea of inflation as a way of explaining the beginnings of our Universe.
The problem of optimisation – that is, finding the maximum or minimum of an ‘objective’ function – is one of the most important problems in computational mathematics. Optimisation problems are ubiquitous: traders might optimise their portfolio to maximise (expected) revenue, engineers may optimise the design of a product to maximise efficiency, data scientists minimise the prediction error of machine learning models, and scientists may want to estimate parameters using experimental data.
Fermat’s two-squares theorem is an elementary theorem in number theory that readily lends itself to a classification of the positive integers representable as the sum of two squares. Given this, a natural question is: what is the minimal number of squares needed to represent any given (positive) integer? One proof of Fermat’s result depends on essentially a buffed pigeonhole principle in the form of Minkowski’s Convex Body Theorem, and this idea can be used in a nearly identical fashion to provide 4 as an upper bound to the aforementioned question (this is Lagrange’s four-square theorem). The question of identifying the integers representable as the sum of three squares turns out to be substantially harder, however leaning on a powerful theorem of Dirichlet and a handful of tricks we can use Minkowski’s CBT to settle this final piece as well (this is Legendre’s three-square theorem).
