Oxford Mathematics Open Day Live Stream - 3 July
On 3 July we shall we live streaming our Open Day for prospective applicants as part of our going Behind the Scenes' at Oxford Mathematics. This is our way of making the Open Day 'open' to everyone, wherever you are.
The running order:
10.00am - James Munro introduces you to Mathematics at Oxford
10.30am - Vicky Neale on Pure Mathematics at Oxford
11.00am - Dominic Vella on Applied Mathematics at Oxford
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Certain inflammatory and infectious diseases, including atherosclerosis and tuberculosis, are caused by the accumulation inside immune cells of harmful substances, such as lipids and bacteria. A multidisciplinary study published in Proceedings B of the Royal Society, by researchers from the Universities of Oxford and Sydney, has shown how cell cannibalism contributes to this process.
Note: unusual time!
Knots and their groups are a traditional topic of geometric topology. In this talk, I will explain how aspects of the subject can be approached as a homotopy theorist, rephrasing old results and leading to new ones. Part of this reports on joint work with Tyler Lawson.
A central task in modeling, which has to be performed each day in banks and financial institutions, is to calibrate models to market and historical data. So far the choice which models should be used was not only driven by their capacity of capturing empirically the observed market features well, but rather by computational tractability considerations. Due to recent work in the context of machine learning, this notion of tractability has changed significantly. In this work, we show how a neural network approach can be applied to the calibration of (multivariate) local stochastic volatility models. We will see how an efficient calibration is possible without the need of interpolation methods for the financial data. Joint work with Christa Cuchiero and Josef Teichmann.
In this talk I will introduce the concept of the path signature and motivate its recent use in analysis of time-ordered data. I will then describe a new feature map for barcodes in persistent homology by first realizing each barcode as a path in a vector space, and then computing its signature which takes values in the tensor algebra over that vector space. The composition of these two operations — barcode to path, path to tensor series — results in a feature map that has several desirable properties for statistical learning, such as universality and characteristicness.
Artificial Intelligence (AI) is a great asset. Artificial Intelligence is a threat to our freedom. Much of the debate around AI seems to focus on these two positions along with a third argument, namely AI could never replicate our creativity or capture what makes us human. We will never go to galleries to look at AI paintings or read AI poetry.
In this paper we define a new object, the momentum amplituhedron, which is the long sought-after positive geometry for tree-level scattering amplitudes in N=4 super Yang-Mills theory in spinor helicity space. Inspired by the construction of the ordinary amplituhedron, we introduce bosonized spinor helicity variables to represent our external kinematical data, and restrict them to a particular positive region. The momentum amplituhedron Mn,k is then the image of the positive Grassmannian via a map determined by such kinematics. The scattering amplitudes are extracted from the canonical form with logarithmic singularities on the boundaries of this geometry.
