Georg Maierhofer
PhD Student
  • University of Cambridge

  • Department of Applied Mathematics and Theoretical Physics (DAMTP)

  • Member of the
    Waves Research Group

  • Email:
    g.maierhofer[at]
    maths.cam.ac.uk

About Me

I am a PhD student in the Department of Applied Mathematics and Theoretical Physics (DAMTP) and in the Cambridge Centre for Analysis (CCA) at the University of Cambridge, supervised by Professor Nigel Peake and Professor Arieh Iserles. I am also a member of the Waves Research Group within DAMTP as well as of Trinity College.

Before beginning my PhD studies I completed my BA and MMath degree at the University of Cambridge. During my undergraduate studies I interned at the Fields Institute at the University of Toronto, at the Institute for Pure and Applied Mathematics at UCLA and in the Cambridge Image Analysis Group in DAMTP.

My main research interests are located in the intersection of acoustics and numerical analysis. In particular, I am currently interested in hybrid numerical-asymptotic (HNA) methods for computational wave propagation and scattering problems. For more details please see my research page.

Resume

A more extended CV is available upon request.

  • Education

  • University of Cambridge, Trinity College, UK

    2017 - present

    PhD student in the Cambridge Centre for Analysis (CCA)

  • University of Cambridge, Trinity College, UK

    2013 - 2017

    MMath (Part III in Mathematics) & BA (hons) in Mathematics

  • Research Experience

  • Summer research intern, Cambridge Image Analysis Group

    June 2016 - Aug 2016

    University of Cambridge, UK

  • Researcher, Research in Industrial Projects for Students

    June 2015 - Aug 2015

    IPAM, University of California, Los Angeles, US

  • Researcher, Fields Undergraduate Summer Research Program

    June 2015 - Aug 2015

    Fields Institute, University of Toronto, Canada

  • Honors and Awards

  • Smith-Knight & Rayleigh-Knight Prize

    Mar 2019

    Faculty of Mathematics, University of Cambridge, UK

  • Election to Research Scholar

    Oct 2017

    Trinity College, University of Cambridge, UK

  • Election to Senior Scholar

    Oct 2016

    Trinity College, University of Cambridge, UK

  • Undergraduate Research Bursary

    June 2016

    London Mathematical Society, UK

  • Winner TakeAIM competition

    Nov 2015

    Smith Institute, UK

  • Election to Junior Scholar

    Oct 2014

    Trinity College, University of Cambridge, UK

  • High School Student Award

    Sept 2013

    Austrian Mathematical Society, Austria

Research

My main research interests focus on problems in acoustics and numerical analysis. In more detail I am currently working on the following topics:

Computational high-frequency wave propagation

High-frequency wave scattering problems are beyond the reach of most conventional methods for numerical wave propagation due to the infeasible computational cost that large frequencies would require. As a result a significant amount of recent research has focussed on the development of hybrid numerical-asymptotic (HNA) methods, which are robust even for large frequencies and achieve in many cases a near frequency independent solution time. The underlying idea is to incorporate physical knowledge into numerical schemes to enhance quality and efficiency in the high-frequency regime, while preserving the precision and flexibility of a grid based approach. An essential step in boundary HNA methods is the numerical evaluation of highly oscillatory integrals. My current work focusses on the development of (provably) efficient quadrature methods for the specific types of oscillators and singularities encountered in boundary integral methods for computational wave scattering.

Wiener-Hopf method and applications

The Wiener-Hopf method is a very successful technique for solving certain boundary value problems which are relevant in acoustics, electromagnetic theory, hydrodynamics and elasticity. Typically the method exploits analyticity properties of Fourier half-line transforms combined with Liouville’s theorem to arrive at an explicit form of solution. I am currently applying this method to a specific model problem which arises from the need to understand noise development and propagation in turbofan engines.

Publications

Wave scattering by an infinite cascade of non-overlapping blades
Maierhofer, G., Peake, N.
In preparation.

Learning the Sampling Pattern for MRI
Sherry, F., Benning, M., De los Reyes, J. C., Graves, M. J., Maierhofer, G., Williams, G., Schönlieb, C.-B. and Ehrhardt, M.
Submitted.
Download: preprint

Mirror, Mirror, on the Wall, Who’s Got the Clearest Image of Them All? — A Tailored Approach to Single Image Reflection Removal
Heydecker, D., Maierhofer, G., Aviles-Rivero, A. I., Fan, Q., Chen, D., Schönlieb, C.-B. and Süsstrunk, S.
IEEE Transactions on Image Processing (2019)
Download: published version | preprint

Peekaboo - Where are the Objects? Structure Adjusting Superpixels.
Maierhofer, G., Heydecker, D., Aviles-Rivero, A. I., Alsaleh, S. M. and Schönlieb, C.-B.
25th IEEE International Conference on Image Processing (2018)
Download: published version | preprint

An extension of standard Latent Dirichlet Allocation to multiple corpora
Foster, A., Li, H., Maierhofer, G., Shearer, M. (2016)
SIAM Undergraduate Research Online Volume 9
Download: published version

Geometric Measure of Arens Irregularity
Hernandez Palomares, R., Hu, E., Maierhofer, G. A., Rao, P. (2015)
Fields Institute for Research in Mathematical Sciences
Download: published version

Contact Information

  • Address:
    University of Cambridge, DAMTP
    Centre for Mathematical Sciences
    Wilberforce Road
    Cambridge CB3 0WA
    United Kingdom
  • E-mail:
    g.maierhofer[at]maths.cam.ac.uk

  • Direct Office Phone:
    +44 1223 337969

Contact Map