Fri, 29 Nov 2019

16:00 - 17:00
L1

Preparing grants and job applications

Jason Lotay, Anna Seigal and Dominic Vella
Abstract

Dominic Vella will talk about writing grants, Anna Seigal will talk about writing research fellow applications and Jason Lotay will talk about his experience and tips for applying for faculty positions. 

 

Tue, 05 Nov 2019

12:00 - 13:00
C1

Population distribution as pattern formation on landscapes

Takaaki Aoki
(Mathematical Institute)
Abstract

Cities and their inter-connected transport networks form part of the fundamental infrastructure developed by human societies. Their organisation reflects a complex interplay between many natural and social factors, including inter alia natural resources, landscape, and climate on the one hand, combined with business, commerce, politics, diplomacy and culture on the other. Nevertheless, despite this complexity, there has been some success in capturing key aspects of city growth and network formation in relatively simple models that include non-linear positive feedback loops. However, these models are typically embedded in an idealised, homogeneous space, leading to regularly-spaced, lattice-like distributions arising from Turing-type pattern formation. Here we argue that the geographical landscape plays a much more dominant, but neglected role in pattern formation. To examine this hypothesis, we evaluate the weighted distance between locations based on a least cost path across the natural terrain, determined from high-resolution digital topographic databases for Italy. These weights are included in a co-evolving, dynamical model of both population aggregation in cities, and movement via an evolving transport network. We compare the results from the stationary state of the system with current population distributions from census data, and show a reasonable fit, both qualitatively and quantitatively, compared with models in homogeneous space. Thus we infer that that addition of weighted topography from the natural landscape to these models is both necessary and almost sufficient to reproduce the majority of the real-world spatial pattern of city sizes and locations in this example.

Tue, 22 Oct 2019

12:00 - 13:00
C1

Learning from signals on graphs with unobserved edges

Micheal Schaub
(Department of Engineering)
Abstract

In many applications we are confronted with the following scenario: we observe snapshots of data describing the state of a system at particular times, and based on these observations we want to infer the (dynamical) interactions between the entities we observe. However, often the number of samples we can obtain from such a process are far too few to identify the network exactly. Can we still reliable infer some aspects of the underlying system?
Motivated by this question we consider the following alternative system identification problem: instead of trying to infer the exact network, we aim to recover a (low-dimensional) statistical model of the network based on the observed signals on the nodes.  More concretely, here we focus on observations that consist of snapshots of a diffusive process that evolves over the unknown network. We model the (unobserved) network as generated from an independent draw from a latent stochastic block model (SBM), and our goal is to infer both the partition of the nodes into blocks, as well as the parameters of this SBM. We present simple spectral algorithms that provably solve the partition and parameter inference problems with high-accuracy.

Tue, 07 Apr 2020

12:00 - 13:00
C1

TBD

Florian Klimm
(Imperial College)
Mon, 18 Nov 2019

18:45 - 19:45
L2

Applied Pure at the Mathematical Institute, Oxford: Music & Light Symbiosis no.3 - An Art Exhibition and a Light & Music Concert

Medea Bindewald & Katharine Beaugié
Further Information

An Art Exhibition and a Light & Music Concert

Katharine Beaugié - Light Sculpture
Medea Bindewald - Harpsichord
Curated by Balázs Szendrői

Concert: 18 November, 6.45pm followed by a reception
Exhibition: 18th November – 6th December 2019, Mon-Fri, 8am-6pm

Applied Pure is a unique collaboration between light sculptor Katharine Beaugié and international concert harpsichordist Medea Bindewald, combining the patterns made by water and light with the sound of harpsichord music in a mathematical environment.

Katharine Beaugié will also be exhibiting a new series of large-scale photograms (photographic shadows), displaying the patterns of the natural phenomena of human relationship with water and light.

The Programme of music for harpsichord and water includes the composers: Domenico Scarlatti (1685-1757), Johann Jakob Froberger (1616-1667), Enno Kastens (b 1967) and Johann Sebastian Bach (1685-1750).

For more information about the concert and exhibition which is FREE please click this link

Image of Drop | God 2018

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Thu, 31 Oct 2019

12:00 - 13:00
L4

The Anderson Hamiltonian and related semi-linear evolution equations

Immanuel Zachhuber
(University of Bonn)
Abstract

The Anderson Hamiltonian is used to model particles moving in
disordered media, it can be thought of as a Schrödiger operator with an
extremely irregular random potential. Using the recently developed theory of
"Paracontrolled Distributions" we are able to define the Anderson
Hamiltonian as a self-adjoint non-positive operator on the 2- and
3-dimensional torus and give an explicit description of its domain.
Then we use these results to solve some semi-linear PDEs whose linear part
is given by the Anderson Hamiltonian, more precisely the multiplicative
stochastic NLS and nonlinear Wave equation.
This is joint work with M. Gubinelli and B. Ugurcan.

Tue, 12 Nov 2019
14:30
L5

Overview of a quotient geometry with simple geodesics for the manifold of fixed-rank positive-semidefinite matrices

Estelle Massart
(UC Louvain)
Abstract

We describe the main geometric tools required to work on the manifold of fixed-rank symmetric positive-semidefinite matrices: we present expressions for the Riemannian logarithm and the injectivity radius, to complement the already known Riemannian exponential. This manifold is particularly relevant when dealing with low-rank approximations of large positive-(semi)definite matrices. The manifold is represented as a quotient of the set of full-rank rectangular matrices (endowed with the Euclidean metric) by the orthogonal group. Our results allow understanding the failure of some curve fitting algorithms, when the rank of the data is overestimated. We illustrate these observations on a dataset made of covariance matrices characterizing a wind field.

Mon, 21 Oct 2019

12:45 - 13:45
L3

The Higgs Mechanism and Hasse diagrams

Antoine Bourget
(Imperial College London)
Abstract

I will explore the geometrical structure of Higgs branches of quantum field theories with 8 supercharges in 3, 4, 5 and 6 dimensions. They are hyperkahler singularities, and as such they can be described by a Hasse diagram built from a family of elementary transitions. This corresponds physically to the partial Higgs mechanism. Using brane systems and recently introduced notions of magnetic quivers and quiver subtraction, we formalise the rules to obtain the Hasse diagrams.

Mon, 25 Nov 2019

15:45 - 16:45
L3

Stochastic impulse control: Recent Progress and Applications

CHRISTOPH BELAK
(TU Berlin University)
Abstract


Stochastic impulse control problems are continuous-time optimization problems in which a stochastic system is controlled through finitely many impulses causing a discontinuous displacement of the state process. The objective is to construct impulses which optimize a given performance functional of the state process. This type of optimization problem arises in many branches of applied probability and economics such as optimal portfolio management under transaction costs, optimal forest harvesting, inventory control, and valuation of real options.

In this talk, I will give an introduction to stochastic impulse control and discuss classical solution techniques. I will then introduce a new method to solve impulse control problems based on superharmonic functions and a stochastic analogue of Perron's method, which allows to construct optimal impulse controls under a very general set of assumptions. Finally, I will show how the general results can be applied to optimal investment problems in the presence of transaction costs.

This talk is based on joint work with Sören Christensen (Christian-Albrechts-University Kiel), Lukas Mich (Trier University), and Frank T. Seifried (Trier University).

References:
C. Belak, S. Christensen, F. T. Seifried: A General Verification Result for Stochastic Impulse Control Problems. SIAM Journal on Control and Optimization, Vol. 55, No. 2, pp. 627--649, 2017.
C. Belak, S. Christensen: Utility Maximisation in a Factor Model with Constant and Proportional Transaction Costs. Finance and Stochastics, Vol. 23, No. 1, pp. 29--96, 2019.
C. Belak, L. Mich, F. T. Seifried: Optimal Investment for Retail Investors with Floored and Capped Costs. Preprint, available at http://ssrn.com/abstract=3447346, 2019.

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