In this joint work with D. Ciubotaru, we introduce the notion of local and global indices of Dirac operators for a rational Cherednik algebra H, with underlying reflection group G. In the local theory, I will report on some relations between the (local) Dirac index of a simple module in category O, the graded G-character and the composition series polynomials for standard modules. In the global theory, we introduce an "integral-reflection" module over which we define and compute the index of a (global) Dirac operator and show that the index is independent of the parameters. If time permits, I will discuss some local-global relations.

In this lecture Persi Diaconis will take a look at some of our most primitive images of chance - flipping a coin, rolling a roulette wheel and shuffling cards - and via a little bit of mathematics (and a smidgen of physics) show that sometimes things are not very random at all. Indeed chance is sometimes confused with frequency and this confusion caries over to a confusion between chance and evidence. All of which explains our wild misuse of probability and statistical models.

Persi Diaconis is world-renowned for his study of mathematical problems involving randomness and randomisation. He is the co-author of 'Ten Great Ideas about Chance (2017) and is the Mary V. Sunseri Professor of Statistics and Mathematics at Stanford University. 

Please email @email to register.

Watch live:

https://www.facebook.com/OxfordMathematics
https://livestream.com/oxuni/PersiDiaconis

The Oxford Mathematics Public Lectures are generously supported by XTX Markets.

Outer Space is an important object in Geometric Group Theory and can be described from two viewpoints: as a space of marked graphs and a space of actions on trees. The latter viewpoint can be used to prove that Outer Space is contractible; and this fact together with some arguments using the first viewpoint enables us to say something about the Outer Automorphism group of a free group - I will sketch both these proofs.

This talk will introduce the notion of categorical rigidity and the automorphism class group of a category. We will proceed with calculations for several important categories, hopefully illuminating the inverse relationship between the automorphisms of a category and the extent to which the structure of its objects is determined categorically. To conclude, some discussion of what progress there is on currently open/unknown cases.

Elastic gridshells arise from the buckling of an initially planar grid of rods. Architectural elastic gridshells first appeared in the 1970’s. However, to date, only a limited number of examples have been constructed around the world, primarily due to the challenges involved in their structural design. Yet, elastic gridshells are highly appealing: they can cover wide spans with low self-weight, they allow for aesthetically pleasing shapes and their construction is typically simple and rapid. A more mundane example is the classic pasta strainer, which, with its remarkably simple design, is a must-have in every kitchen.

This talk will focus on the geometry-driven nature of elastic gridshells. We use a geometric model based on the theory of discrete Chebyshev nets (originally developed for woven fabric) to rationalize their actuated shapes. Validation is provided by precision experiments and rod-based simulations. We also investigate the linear mechanical response (rigidity) and the non-local behavior of these discrete shells under point-load indentation. Combining experiments, simulations, and scaling analysis leads to a master curve that relates the structural rigidity to the underlying geometric and material properties. Our results indicate that the mechanical response of elastic gridshells, and their underlying characteristic forces, are dictated by Euler's elastica rather than by shell-related quantities. The prominence of geometry that we identify in elastic gridshells should allow for our results to transfer across length scales: from architectural structures to micro/nano–1-df mechanical actuators and self-assembly systems.

[[{"fid":"51243","view_mode":"small_image_100px_h","fields":{"format":"small_image_100px_h","field_file_image_alt_text[und][0][value]":"","field_file_image_title_text[und][0][value]":""},"type":"media","attributes":{"class":"media-element file-small-image-100px-h"}}]]

Medical imaging is a key diagnostic tool, and is paramount for disease detection and for patient monitoring during ongoing care. Often, to reduce the amount of radiation that a patient is subjected to, there is a strong incentive to consider image reconstruction from incomplete sets of measurements, and so the imaging process is formulated as a compressed sensing problem.

In this talk, we will focus on compressed sensing for digital tomosynthesis (DTS), in which three-dimensional images are reconstructed from a set of two-dimensional X-ray projections. We first discuss a reconstruction approach for static bodies, with a particular interest in the choice of basis for the image representation. We will then focus on the need for accurate image reconstructions when the body of interest is not stationary, but is undergoing simple motion, discussing two different approaches for tackling this dynamic problem.