Forthcoming Seminars

Please note that the list below only shows forthcoming events, which may not include regular events that have not yet been entered for the forthcoming term. Please see the past events page for a list of all seminar series that the department has on offer.

Past events in this series
Today
14:00
Kirill Serkh
Abstract

It has long been known that many elliptic partial differential equations can be reformulated as Fredholm integral equations of the second kind on the boundaries of their domains. The kernels of the resulting integral equations are weakly singular, which has historically made their numerical solution somewhat onerous, requiring the construction of detailed and typically sub-optimal quadrature formulas. Recently, a numerical algorithm for constructing generalized Gaussian quadratures was discovered which, given 2n essentially arbitrary functions, constructs a unique n-point quadrature that integrates them to machine precision, solving the longstanding problem posed by singular kernels.

When the domains have corners, the solutions themselves are also singular. In fact, they are known to be representable, to order n, by a linear combination (expansion) of n known singular functions. In order to solve the integral equation accurately, it is necessary to construct a discretization such that the mapping (in the L^2-sense) from the values at the discretization points to the corresponding n expansion coefficients is well-conditioned. In this talk, we present exactly such an algorithm, which is optimal in the sense that, given n essentially arbitrary functions, it produces n discretization points, and for which the resulting interpolation formulas have condition numbers extremely close to one.

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A link for this talk will be sent to our mailing list a day or two in advance.  If you are not on the list and wish to be sent a link, please send email to trefethen@maths.ox.ac.uk.

  • Computational Mathematics and Applications Seminar
Today
16:00
Andrea Bertozzi

Further Information: 

We return this term to our usual flagship seminars given by notable scientists on topics that are relevant to Industrial and Applied Mathematics. 

 

Abstract

We revisit the tears of wine problem for thin films in
water-ethanol mixtures and present a new model for the climbing
dynamics. The new formulation includes a Marangoni stress balanced by
both the normal and tangential components of gravity as well as surface
tension which lead to distinctly different behavior. The combined
physics can be modeled mathematically by a scalar conservation law with
a nonconvex flux and a fourth order regularization due to the bulk
surface tension. Without the fourth order term, shock solutions must
satisfy an entropy condition - in which characteristics impinge on the
shock from both sides. However, in the case of a nonconvex flux, the
fourth order term is a singular perturbation that allows for the
possibility of undercompressive shocks in which characteristics travel
through the shock. We present computational and experimental evidence
that such shocks can happen in the tears of wine problem, with a
protocol for how to observe this in a real life setting.

The join button will be published on the right (Above the view all button) 30 minutes before the seminar starts (login required).

  • Industrial and Applied Mathematics Seminar
Tomorrow
12:00
Patrick Kidger
Abstract

Differential equations and neural networks are two of the most widespread modelling paradigms. I will talk about how to combine the best of both worlds through neural differential equations. These treat differential equations as a learnt component of a differentiable computation graph, and as such integrates tightly with current machine learning practice. Applications are widespread. I will begin with an introduction to the theory of neural ordinary differential equations, which may for example be used to model unknown physics. I will then move on to discussing recent work on neural controlled differential equations, which are state-of-the-art models for (arbitrarily irregular) time series. Next will be some discussion of neural stochastic differential equations: we will see that the mathematics of SDEs is precisely aligned with the machine learning of GANs, and thus NSDEs may be used as generative models. If time allows I will then discuss other recent work, such as how the training of neural differential equations may be sped up by ~40% by tweaking standard numerical solvers to respect the particular nature of the differential equations. This is joint work with Ricky T. Q. Chen, Xuechen Li, James Foster, and James Morrill.

The join button will be published on the right (Above the view all button) 30 minutes before the seminar starts (login required).

  • Data Science Seminar
Tomorrow
14:00
Yifan Wang
Abstract

We explore general constraints from unitarity, defect superconformal symmetry and locality of bulk-defect couplings to classify possible superconformal defects in superconformal field theories (SCFT) of spacetime dimensions d>2.  Despite the general absence of locally conserved currents, the defect CFT contains new distinguished operators with protected quantum numbers that account for the broken bulk symmetries.  Consistency with the preserved superconformal symmetry and unitarity requires that such operators arrange into unitarity multiplets of the defect superconformal algebra, which in turn leads to nontrivial constraints on what kinds of defects are admissible in a given SCFT.  We will focus on the case of superconformal lines in this talk and comment on several interesting implications of our analysis, such as symmetry-enforced defect conformal manifolds, defect RG flows and possible nontrivial one-form symmetries in various SCFTs.  

The join button will be published on the right (Above the view all button) 30 minutes before the seminar starts (login required).

  • String Theory Journal Club
Tomorrow
14:00
Abstract

Influenza viruses infect millions of individuals each year and cause a significant amount of morbidity and mortality. Understanding how the virus spreads within the lung, how efficacious host immune control is, and how each influences acute lung injury and disease severity is critical to combat the infection. We used an integrative model-experiment exchange to establish the dynamical connections between viral loads, infected cells, CD8+ T cells, lung injury, and disease severity. Our model predicts that infection resolution is sensitive to CD8+ T cell expansion, that there is a critical T cell magnitude needed for efficient resolution, and that the rate of T cell-mediated clearance is dependent on infected cell density. 
We validated the model through a series of experiments, including CD8 depletion and whole lung histomorphometry. This showed that the infected area of the lung matches the model-predicted infected cell dynamics, and that the resolved area of the lung parallels the relative CD8 dynamics. Additional analysis revealed a nonlinear relation between disease severity, inflammation, and lung injury. These novel links between important host-pathogen kinetics and pathology enhance our ability to forecast disease progression.

The join button will be published on the right (Above the view all button) 30 minutes before the seminar starts (login required).

  • Mathematical Biology and Ecology Seminar
Tomorrow
16:00
Abstract

In this session we discuss techniques to get the most out of your supervision sessions and tips on how to work with different personalities and use your supervisor's skills to your advantage. The session will be run by DPhil students and discussion among students during the session is encouraged.  

The join button will be published on the right (Above the view all button) 30 minutes before the seminar starts (login required).

2 November 2020
14:15
Egor Shelukhin
Abstract

We describe how Smith theory applies in the setting of Hamiltonian Floer homology filtered by the action functional, and provide applications to questions regarding Hamiltonian diffeomorphisms, including the Hofer-Zehnder conjecture on the existence of infinitely many periodic points and a question of McDuff-Salamon on Hamiltonian diffeomorphisms of finite order.

The join button will be published on the right (Above the view all button) 30 minutes before the seminar starts (login required).

  • Geometry and Analysis Seminar

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