Tim Porter's Home Page
Please note:  This is a picture of a (5,4)-torus knot on a torus,  not a picture of myself: T.P. If you really want to see what I look like see the end of this home page!

Communication

                    Mail:      Emeritus Professor Tim Porter,
                               School of Computer Science, 
                               University of Wales, Bangor,
                               Dean St.,
                               Bangor,
                               Gwynedd LL57 1UT.
                               UK.  

                   Phone:      (01248)-382492  
                     Fax:      (01248)-358811  
                   Email:       t.porter-at-bangor.ac.uk

Whilst the mathematics group still existed as a formal entity at Bangor, I was a member of the Algebraic Topology, Category Theory and their applications research group. Within those areas, my interests include:
• Algebraic Topology, and Homotopical Algebra and their applications, including
• crossed and simplicial algebraic homotopy and non-Abelian cohomology,
• quasi-categories and homotopy coherence,
• strong shape theory and proper homotopy theory,
• global actions, groupoid atlases and their applications,
• fractafolds - fractal analogues of manifolds'
• topological quantum field theory,
and
• abstract homotopy theory.

• Category theory, including:
• enriched and lax category theory,
• n- and infinity categories,
• higher dimensional algebra and its applications,
• applications of category theory in computer science and information technology,

and
• categorical models of spatial phenomena
Extending the applications slightly leads to my other interests:
• AI and Theoretical Computer Science, including Multiagent Systems, Discrete event systems and Scheduling Problems. 
  • I am a member of the AIIA research group, that is Artificial Intelligence and Intelligent Agents, and several papers in the area can be found amongst my preprint and publication lists.
  • With a group based in Paris and Montpellier, I have been involved in a joint research project: Simplicial and cubical sets and Knowledge evolution in Distributed Systems. More details of this can be found here.
  • Mathematical models for multiagent systems The use of modal logics here has also formed a part of my search for good mathematical models for multiagent systems (MAS). Such a project is, of course, doomed to failure as the area of MASs is much to wide and varied, however with the idea of going from locally interacting agents communicating with other similar groups, and exploiting `local-to-global' techniques from various parts of mathematics, some progress looks to be possible. .
  • Geometry of Information:  This grew out of the fractafolds project.  Some indication of what I mean by the title can be gained from the report on that project (see `fractafolds' above) and also the papers on the Dagstuhl website ( http://drops.dagstuhl.de/portals/04351/).
• Topological Data Analysis (TDA) has recently emerged from the general area of Computational Topology. In this project, we will examine not only TDA itself, but will attempt to put it in a historical context by identifying precursor theories both in algebraic topology and, surprisingly, within theoretical physics. The reason for doing this is not just to be scholarly, but is also to, hopefully, suggest some additions to the toolkit of TDA, which might thus widen its applicability. This, in turn, raises new questions both within TDA itself, and also within the related mathematical area of Shape Theory. Here are some slides that I prepared for a talk at Aberystwyth (11 November 2005).<\p>

  This has been augmented recently (2008) by my work in NUI, Galway as SFI-Walton visitor. Working with Graham Ellis and the HAP research team there, we have been attempting to use the packages and ideas from the group of libraries developed for homological algebra and computational algebraic topology, (GAP, HAP,and Kenzo). I am preparing a set of notes outlining possible links bewteen the methods of TDA, those of the computational algebraic topologists and more distant work on statistical shape by Kendall and others.

 

List of publications.
Publication areas
Preprints:
Curriculum Vitae.

Other information

Useful links

• One very  important USEFUL link is to my book with Nick Gilbert on Knots and Surfaces. This was published by Oxford University Press in 1994.
• Another is to Abstract Homotopy and Simple Homotopy Theory  with K.H. Kamps, published by World Scientific in  June 1997. A copy of the Mathematical Review of the book is available here.
• British Topology Homepage
• Geometry and Topology e-mail address list.
• Algebraic Topology Discussion List.
• K-theory archive
• Category Theory Home Page at Mount Allison University, Canada.
• Applied and Computational Category Theory Group at RISC Linz.
• London Mathematical Society
• European Mathematical Society
• Theory and Applications of Categories,  electronic journal of category theory.

University of Wales, Bangor, Links