Peter Markowich

  • Department of Applied Mathematics and Theoretical Physics

My research interests

  • nonlinear Schrödinger equations
  • high frequency asymtotics: WKB methods and Wigner functions,
  • Gross-Pitaevskii equation,
  • electron dynamics in crystals and nanostructures,
  • nonlinear wave propagation,
  • dispersion estimates,
  • spectral-time splitting discretisations.
  • classical and quantum kinetic equations
  • entropy dissipation techniques and convex Sobolev inequalities,
  • simulations of Bose-Einstein condensates,
  • quantum scattering in semiconductors: Boltzmann equation,
  • collective behaviour of swimming mirco-organismns and chemotaxis,
  • kinetics and mean field models for human crowding behaviour, Pareto economics and opinion formation in human societies,
  • mean-field limits.
  • reaction-diffusion/convection systems
  • drift and diffusion of charge carries in semiconductors,
  • large-time asymptotics
  • finte element discretisations.

People I collaborate with

I’m currently working on 2 CCIMI projects

Anisotropic Interaction Models for Simulating Fingerprint Patterns

View the project

Formation and Adaption of Biological Transportation Networks

View the project

Key Publications

Deep learning for inverse imaging problems: some recent approaches (Conference Presentation)

Carola-Bibiane Schönlieb
Published 14/03/2019

Enhancing joint reconstruction and segmentation with non-convex Bregman iteration

Veronica Corona Martin Benning Matthias Joachim Ehrhardt Lynn Faith Gladden Richard Mair Andi Reci Andrew J Sederman Stefanie Reichelt Carola-Bibiane Schönlieb
Published 28/02/2019

Anisotropic osmosis filtering for shadow removal in images

Simone Parisotto Luca Calatroni Marco Caliari Carola-Bibiane Schönlieb Joachim Weickert
Published 20/02/2019

Mini-Workshop: Deep Learning and Inverse Problems

Simon R Arridge Maarten V de Hoop Peter Maaß Carola-Bibiane Schönlieb
Published 04/01/2019

Unveiling the invisible: mathematical methods for restoring and interpreting illuminated manuscripts

Luca Calatroni Marie d’Autume Rob Hocking Stella Panayotova Simone Parisotto Paola Ricciardi Carola-Bibiane Schönlieb
Published 01/12/2018

Directional sinogram inpainting for limited angle tomography

Robert Tovey Martin Benning Christoph Brune Marinus Jan Lagerwerf Sean Michael Collins Rowan Leary Paul A Midgley Carola-Bibiane Schönlieb
Published 22/11/2018

Variational image regularization with Euler's elastica using a discrete gradient scheme

Torbjørn Ringholm Jasmina Lazic Carola-Bibiane Schönlieb
Published 15/11/2018

Stochastic primal-dual hybrid gradient algorithm with arbitrary sampling and imaging applications

Antonin Chambolle Matthias J Ehrhardt Peter Richtárik Carola-Bibiane Schönlieb
Published 02/10/2018

Liquid phase blending of metal-organic frameworks

Louis Longley Sean M Collins Chao Zhou Glen J Smales Sarah E Norman Nick J Brownbill Christopher W Ashling Philip A Chater Robert Tovey Carola-Bibiane Schönlieb Thomas F Headen Nicholas J Terrill Yuanzheng Yue Andrew J Smith Frédéric Blanc David A Keen Paul A Midgley Thomas D Bennett
Published 15/06/2018

Presentations from 'Mathematics of Machine Learning'

Published 24/05/2018
Excited to announce that Mark Girolami will give a talk on 'The Statistical Finite Element Method' at the second CC… View on Twitter