Let f be the planar Bargmann-Fock field, i.e. the analytic Gaussian field with covariance kernel exp(-|x-y|^2/2). We compute the critical point for the percolation model induced by the level sets of f. More precisely, we prove that there exists a.s. an unbounded component in {f>p} if and only if p<0. Such a percolation model has been studied recently by Beffara-Gayet and Beliaev-Muirhead. One important aspect of our work is a derivation of a (KKL-type) sharp threshold result for correlated Gaussian variables. The idea to use a KKL-type result to compute a critical point goes back to Bollobás-Riordan. This is joint work with Alejandro Rivera.

Let n be a positive integer. In this talk we provide a recipe to 
construct full orbit sequences in the affine n-dimensional space over a 
finite field. For n=1 our construction covers the case of the well 
studied pseudorandom number generator ICG.

This is a joint work with Federico Amadio Guidi.

The 5th Oxford Neuron and Brain Mechanics Workshop will take place on 22 and 23 March 2018, in St Hugh’s College, Oxford. The event includes international and UK speakers from a wide variety of disciplines, collectively working on Traumatic Brain Injury, Brain Mechanics and Trauma, and Neurons research.

The aim is to foster new collaborative partnerships and facilitate the dissemination of ideas from researchers in different fields related to the study of brain mechanics, including pathology, injury and healing.

Focussing on a multi-disciplinary and collaborative approach to aspects of brain mechanics research, the workshop will present topics from areas including Medical, Neuroimaging, Neuromechanics and mechanics, Neuroscience, Neurobiology and commercial applications within medicine.

This workshop is the latest in a series of events established by the members of the International Brain Mechanics and Trauma Lab (IBMTL) initiative *(www.brainmech.ox.ac.uk) in collaboration with St Hugh’s College, Oxford.

Speakers

Professor Lee Goldstein MD, Boston University
Professor David Sharp, Imperial College London
Dr Ari Ercole, University of Cambridge
Professor Jochen Guck, BIOTEC Dresden
Dr Elisa Figallo, Finceramica SPA
Dr Mike Jones, Cardiff University
Professor Ellen Kuhl, Stanford University
Mr Tim Lawrence, University of Oxford
Professor Zoltan Molnar, University of Oxford
Dr Fatiha Nothias, University Pierre & Marie Curie
Professor Stam Sotiropoulos, University of Nottingham
Professor Michael Sutcliffe, University of Cambridge
Professor Alain Goriely, University of Oxford
Professor Antoine Jérusalem, University of Oxford

Everybody is welcome to attend but (free) registration is required.

https://www.eventbrite.co.uk/e/5th-oxford-international-workshop-on-neu…

Students and postdocs are invited to exhibit a poster.

For further information on the workshop, or exhibiting a poster, please contact: @email

The workshop is generously supported by the ERC’s ‘Computational Multiscale Neuron Mechanics’ grant (COMUNEM, grant # 306587) and St Hugh’s College, Oxford.

The International Brain Mechanics and Trauma Lab, based in Oxford, is an international collaboration on projects related to brain mechanics and trauma. This multidisciplinary team is motivated by the need to study brain cell and tissue mechanics and its relation with brain functions, diseases or trauma.

After reviewing old work with Teitelbaum, in which we constructed the character variety X of the additive group o_L in a finite extension L/Q_p and established the Fourier isomorphism for the distribution algebra of o_L, I will briefly report on more recent work with Berger and Xie, in which we establish the theory of (\varphi_L,\Gamma_L)-modules over X and relate it to Galois representations. Then I will discuss an ongoing project with Venjakob. Our goal is to use this theory over X for Iwasawa theory.

I will discuss a wonderful structure theorem for finitely generated group containing a codimension one polycyclic-by-finite subgroup, due to Martin Dunwoody and Eric Swenson. I will explain how the theorem is motivated by the torus theorem for 3-manifolds, and examine some of the consequences of this theorem.

The aim of applied topology is to use and develop topological methods for applied mathematics, science and engineering. One of the main tools is persistent homology, an adaptation of classical homology, which assigns a barcode, i.e., a collection of intervals, to a finite metric space. Because of the nature of the invariant, barcodes are not well adapted for use by practitioners in machine learning tasks. We can circumvent this problem by assigning numerical quantities to barcodes, and these outputs can then be used as input to standard algorithms. I will explain how we can use tropical-like functions to coordinatize the space of persistence barcodes. These coordinates are stable with respect to the bottleneck and Wasserstein distances. I will also show how they can be used in practice.

Topological data analysis (TDA) is a robust field of mathematical data science specializing in complex, noisy, and high-dimensional data.  While the elements of modern TDA have existed since the mid-1980’s, applications over the past decade have seen a dramatic increase in systems analysis, engineering, medicine, and the sciences.  Two of the primary challenges in this field regard modeling and computation: what do topological features mean, and are they computable?  While these questions remain open for some of the simplest structures considered in TDA — homological persistence modules and their indecomposable submodules — in the past two decades researchers have made great progress in algorithms, modeling, and mathematical foundations through diverse connections with other fields of mathematics.  This talk will give a first perspective on the idea of matroid theory as a framework for unifying and relating some of these seemingly disparate connections (e.g. with quiver theory, classification, and algebraic stability), and some questions that the fields of matroid theory and TDA may mutually pose to one another.  No expertise in homological persistence or general matroid theory will be assumed, though prior exposure to the definition of a matroid and/or persistence module may be helpful.

Let L be a lattice in R^n and let Z in R^(m+n) a parameterized family of subsets Z_T of R^n. Starting from an old result of Davenport and using O-minimal structures, together with Martin Widmer, we proved for fairly general families Z an estimate for the number of points of L in Z_T, which is essentially best possible.
After introducing the problem and stating the result, we will present applications to counting algebraic integers of bounded height and to Manin’s Conjecture.