The idea of isotropic localization is to substitute an algebro-geometric object (motive)
by its “local” versions, parametrized by finitely generated extensions of the ground field k. In the case of the so-called “flexible” ground field, the complexity of the respective “isotropic motivic categories” is similar to that of their topological counterpart. At the same time, new features appear: the isotropic motivic cohomology of a point encode Milnor’s cohomological operations, while isotropic Chow motives (hypothetically) coincide with Chow motives modulo numerical equivalence (with finite coefficients). Extended versions of the isotropic category permit to access numerical Chow motives with rational coefficients providing a new approach to the old questions related to them. The same localization can be applied to the stable homotopic category of Morel- Voevodsky producing “isotropic” versions of the topological world. The respective isotropic stable homotopy groups of spheres exhibit interesting features.

The aim of this talk is to describe joint work with Gergely Berczi using a recent extension to non-reductive actions of geometric invariant theory, and its links with moment maps in symplectic geometry, to study hyperbolicity of generic hypersurfaces in a projective space. Using intersection theory for non-reductive GIT quotients applied to  compactifications of bundles of invariant jet differentials over complex manifolds leads to a proof of the Green-Griffiths-Lang conjecture for a generic projective hypersurface of dimension n whose degree is greater than n^6. A recent result of Riedl and Yang then implies the Kobayashi conjecture for generic hypersurfaces of degree greater than (2n-1)^6.

https://arxiv.org/pdf/1906.11251.pdf

This session will discuss how Douglas Hartree and Arthur Porter used Meccano — a child’s toy and an engineer’s tool — to build an analogue computer, the Hartree Differential Analyser in 1934. It will explore the wider historical and social context in which this model computer was rooted, before providing an opportunity to engage with the experiential aspects of the 'Kent Machine,' a historically reproduced version of Hartree and Porter's original model, which is also made from Meccano.

The 'Kent Machine' sits at a unique intersection of historical research and educational engagement, providing an alternative way of teaching STEM subjects, via a historic hands-on method. The session builds on the work and ideas expressed in Otto Sibum's reconstruction of James Joule's 'Paddle Wheel' apparatus, inviting attendees to physically re-enact the mathematical processes of mechanical integration to see how this type of analogue computer functioned in reality. The session will provide an alternative context of the history of computing by exploring the tacit knowledge that is required to reproduce and demonstrate the machine, and how it sits at the intersection between amateur and professional science.