## MathsNet: Research Student Directory

Name | Keetch, Blaine |
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Group | Algebra and Analysis |

Room | C17, Math Sci |

Telephone | +44 (0) 115 84 66717 [direct dial] |

Thesis Title | The interplay between partial differential equations and graph based problems |

Thesis Abstract | In recent years the growing importance of image processing and data analysis problems has led to an increased interest in graph based problems among mathematical analysts with a background in the field of partial differential equations (PDEs). The reason for this is that many data analysis problems are naturally formulated on networks. Such problems enjoy a long history in the graph theory, combinatorics, and computer science literature. PDEs have been successfully employed in image processing and in particular variational methods have contributed greatly to the imaging field. As such, the project revolves around these two main questions, which will be considered both theoretically and from an applied point of view: (1) Which questions from graph theory can be (approximately) solved using techniques from PDE and variational methods? (2) Which concepts from the continuum world of PDE can be meaningfully defined on graphs and which role, if any, do they play in the discrete setting? |

School contact information | School of Mathematical Sciences University of Nottingham University Park Nottingham, NG7 2RD UK Tel: +44 (0) 115 951 4949 Fax: +44 (0) 115 951 4951 |