Past Forthcoming Seminars

25 May 2018
12:00
Florian Pausinger
Abstract

Persistent homology is an algebraic tool for quantifying topological features of shapes and functions, which has recently found wide applications in data and shape analysis. In the first and introductory part of this talk I recall the underlying ideas and basic concepts of this very active field of research. In the second part, I plan to sketch a concrete application of this concept to digital image processing. 

  • Applied Algebra and Topology
24 May 2018
16:00
Edgar Assing
Abstract

We will briefly revisit Voronoi summation in its classical form and mention some of its many applications in number theory. We will then show how to use the global Whittaker model to create Voronoi type formulae. This new approach allows for a wide range of weights and twists. In the end we give some applications to the subconvexity problem of degree two $L$-functions. 

  • Number Theory Seminar
24 May 2018
16:00
William Petersen
Abstract

The Witten-Reshetikhin-Turaev invariant Z(X,K) of a closed oriented three-manifold X containing a knot K, was originally introduced by Witten in order to extend the Jones polynomial of knots  in terms of Chern-Simons theory. Classically, the Jones polynomial is defined for a knot inside the three-sphere in  a combinatorial manner. In Witten's approach, the Jones polynomial J(K) emerge as the expectation value of a certain observable in Chern-Simons theory, which makes sense when K is embedded in any closed oriented three-manifold X. Moreover; he proposed that these invariants should be extendable to so-called topological quantum field theories (TQFT's). There is a catch; Witten's ideas relied on Feynman path integrals, which made them unrigorous from a mathematical point of view. However; TQFT's extending the Jones polynomial were subsequently constructed mathematically through combinatorial means by Reshetikhin and Turaev. In this talk, I shall expand slightly on the historical motivation of WRT invariants, introduce the formalism of TQFT's, and present some of the open problems concerning WRT invariants. The guiding motif will be the analogy between TQFT and quantum field theory.

  • Junior Geometry and Topology Seminar
24 May 2018
16:00
to
17:30
Frederic Dias
Abstract

Statements in media about record wave heights being measured are more and more common, the latest being about a record wave of almost 24m in the Southern Ocean on 9 May 2018. We will review some of these wave measurements and the various techniques to measure waves. Then we will explain the various mechanisms that can produce extreme waves both in wave tanks and in the ocean. We will conclude by providing the mechanism that, we believe, explains some of the famous extreme waves. Note that extreme waves are not necessarily rogue waves and that rogue waves are not necessarily extreme waves.

  • Industrial and Applied Mathematics Seminar
24 May 2018
16:00
to
17:30
Michael Kupper
Abstract

We present a widely applicable approach to solving (multi-marginal, martingale) optimal transport and related problems via neural networks. The core idea is to penalize the optimization problem in its dual formulation and reduce it to a finite dimensional one which corresponds to optimizing a neural network with smooth objective function. We present numerical examples from optimal transport, and bounds on the distribution of a sum of dependent random variables. As an application we focus on the problem of risk aggregation under model uncertainty. The talk is based on joint work with Stephan Eckstein and Mathias Pohl.

  • Mathematical and Computational Finance Seminar
24 May 2018
14:00
Prof. Michael Ferris
Abstract


In the past few decades, power grids across the world have become dependent on markets that aim to efficiently match supply with demand at all times via a variety of pricing and auction mechanisms. These markets are based on models that capture interactions between producers, transmission and consumers. Energy producers typically maximize profits by optimally allocating and scheduling resources over time. A dynamic equilibrium aims to determine prices and dispatches that can be transmitted over the electricity grid to satisfy evolving consumer requirements for energy at different locations and times. Computation allows large scale practical implementations of socially optimal models to be solved as part of the market operation, and regulations can be imposed that aim to ensure competitive behaviour of market participants.

Questions remain that will be outlined in this presentation.

Firstly, the recent explosion in the use of renewable supply such as wind, solar and hydro has led to increased volatility in this system. We demonstrate how risk can impose significant costs on the system that are not modeled in the context of socially optimal power system markets and highlight the use of contracts to reduce or recover these costs. We also outline how battery storage can be used as an effective hedging instrument.

Secondly, how do we guarantee continued operation in rarely occuring situations and when failures occur and how do we price this robustness?

Thirdly, how do we guarantee appropriate participant behaviour? Specifically, is it possible for participants to develop strategies that move the system to operating points that are not socially optimal?

Fourthly, how do we ensure enough transmission (and generator) capacity in the long term, and how do we recover the costs of this enhanced infrastructure?
 

  • Computational Mathematics and Applications Seminar
24 May 2018
12:00
Abstract

In this talk I will start with a brief overview of the Cauchy problem for the Einstein equations of general relativity, and in particular the nonlinear stability of the trivial Minkowski solution in wave gauge as shown by Lindblad and Rodnianski. I will then discuss the Kaluza Klein spacetime of the form $R^{1+3} \times K$ where $K$ is the $n-$torus with the flat metric.  An interesting question to ask is whether this solution to the Einstein equations, viewed as an initial value problem, is stable to small perturbations of the initial data. Motivated by this problem, I will outline how the proof of stability in a restricted class of perturbations in fact follows from the work of Lindblad and Rodnianski, and discuss the physical justification behind this restriction. 

  • PDE CDT Lunchtime Seminar
23 May 2018
16:00
Abstract

Elements of a finitely generated group have a natural notion of length: namely the length of a shortest word over the generators that represents the element. This allows us to study the growth of such groups by considering the size of spheres with increasing radii. One current area of interest is the rationality or otherwise of the formal power series whose coefficients are the sphere sizes. I will describe a combinatorial way to study this series for the class of virtually abelian groups, introduced by Benson in the 1980s, and then outline its applications to other types of growth series.

  • Junior Topology and Group Theory Seminar

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