Oxford University

Symplectic cohomology is a Floer cohomology invariant of compact symplectic manifolds 
with contact type boundary, or of open symplectic manifolds with a certain geometry 
at the infinity. It is a graded unital K-algebra related to quantum cohomology, 
and for cotangent bundle, it recovers the homology of a loop space. During the talk 
I will define symplectic cohomology and show some of the results on its (non) vanishing. 
Time permitting, I will also mention natural TQFT algebraic structure on it.

The Grojnowski-Nakajima theorem states that the direct sum of the homologies of the Hilbert schemes on n points on an algebraic surface is an irreducible highest weight representation of an infinite-dimensional Heisenberg superalgebra. We present an idea to rederive the Grojnowski-Nakajima theorem using Halpern-Leistner's categorical Kirwan surjectivity theorem and Joyce's theorem that the homology of a moduli space of sheaves is a vertex algebra. We compute the homology of the moduli stack of perfect complexes of coherent sheaves on a smooth quasi-projective variety X, identify it as a (modified) lattice vertex algebra on the Lawson homology of X, and explain its relevance to the aforementioned problem.

We give an alternative, statistical physics based proof of the Ω(d2^{-d}) lower bound for the maximum sphere packing density in dimension d by showing that a random configuration from the hard sphere model has this density in expectation. While the leading constant we achieve is not the best known, we do obtain additional geometric information: we prove a lower bound on the entropy density of sphere packings at this density, a measure of how plentiful such packings are. This is joint work with Felix Joos and Will Perkins.

This is the first part of a discussion of  Ezra Miller's paper https://arxiv.org/abs/1709.08155.

The number of solutions of a given algebro-geometric configuration, when it is finite, does not change upon a small perturbation of the parameters; this persists 
even upon specializations that change the topology.    The precise formulation of this principle of Poncelet and Schubert   required, i.a., the notions of   algebraically closed fields, flatness, completenesss, multiplicity.     I will explain a model-theoretic version, presented in   quite different terms.  It applies notably to difference equations involving the Galois-Frobenius automorphism $x^p$, uniformly in a prime $p$.   In fixed positive characteristic, interesting technical problems arise that I will discuss if time permits.  

We are all familiar with the need for continuum mechanics-based models in physical applications. In this case, we are interested in large-scale water-wave problems, such as coastal flows and dam breaks.
When modelling these problems, we inevitably wish to solve them on a finite domain, and require boundary conditions to do so. Ideally, we would recreate the semi-infinite nature of a coastline by allowing any generated waves to flow out of the domain, as opposed to them reflecting off the far-field boundary and disrupting the remainder of our simulation. However, applying an appropriate boundary condition is not as straightforward as we might think.
In this talk, we aim to evaluate alternatives to so-called 'active boundary condition' absorption. We will derive a toy model of a shallow-water wavetank, and consider the implementation and efficacy of two 'passive' absorption techniques.
 

A theorem of Gromov states that the number of generators of the fundamental group of a manifold with nonnegative 
curvature is bounded by a constant which only depends on the dimension of the manifold. The main ingredient 
in the proof is Toponogov’s theorem, which roughly speaking says that the triangles on spaces with positive 
curvature, such as spheres, are thick compared to triangles in the Euclidean plane. In the talk I shall explain 
this more carefully and deduce Gromov’s result.

Andrew Hodges, University of Oxford, author of "Alan Turing: The Enigma” on 'Alan Turing: soft machine in a hard world.’

http://www.turing.org.uk/index.html

This event is free but you need to register:

https://www.eventbrite.co.uk/e/the-history-of-computing-beyond-the-comp… 2018

Forecasting a diagnosis of Alzheimer’s disease is a promising means of selection for clinical trials of Alzheimer’s disease therapies. A positive PET scan is commonly used as part of the inclusion criteria for clinical trials, but PET imaging is expensive, so when a positive scan is one of the trial inclusion criteria it is desirable to avoid screening failures. In this talk I will describe a scheme for pre-selecting participants using statistical learning methods, and investigate how brain regions change as the disease progresses.  As a means of generating features I apply the Chen path signature. This is a systematic way of providing feature sets for multimodal data that can probe the nonlinear interactions in the data as an extension of the usual linear features. While it can easily perform a traditional analysis, it can also probe second and higher order events for their predictive value. Combined with Lasso regularisation one can auto detect situations where the observed data has nonlinear information.