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Anthony Nixon supervises 3 postgraduate research students. If these students have produced research profiles, these are listed below:

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Dr Anthony Nixon

Senior Lecturer in Pure Mathematics

Fylde College



PhD supervision

I would be interested in discussing PhD opportunities with a student interested in combinatorics, geometry or both. In combinatorics I am interested in graph theory, matroid theory and combinatorial rigidity. In geometry I am interested in discrete and computational geometry, sphere packing and concrete aspects of differential and algebraic geometry. Unifying these topics is the study of geometric graphs and their configuration spaces. As well as the above purely theoretical topics, I am interested in applications of these topics to biophysical materials and control of robotic formations.

Research Interests

  • Combinatorial rigidity
  • Graphs and matroids
  • Discrete and computational geometry
  • Algebraic and geometric techniques in discrete mathematics



Current Research

I am part of Lancaster's Discrete Mathematics and Geometric Rigidity group. Details about our group are available on our webpage. Typical problems in geometric rigidity theory involve determining the nature of the solutions to systems of equations arising from geometric constraint systems. I am particularly interested in the generic behaviour and in understanding this behaviour in purely combinatorial terms.

At a basic level we consider the rigidity or flexibility of structures defined by geometric constraints (fixed length, angle, direction, etc.) on a set of rigid objects (points, lines, etc.). The fundamental example being that of bar-joint frameworks which are geometric realisations of graphs with edges represented by stiff bars and vertices by revolute joints.

To study such frameworks, rigidity uses a range of techniques from analysis, algebra, combinatorics and geometry. In particular the combinatorial side uses ideas from structural graph theory, combinatorial optimization and matroid theory, while the geometric side uses diverse ideas from projective geometry, matrix analysis, real (semi-)algebraic geometry and semi-definite programming, among others. 




Submitted papers:

1. Flexible circuits in the d-dimensonal rigidity matroid, with Georg Grasegger, Hakan Guler and Bill Jackson, 15 pages, https://arxiv.org/abs/2003.06648.

2. Universal rigidity on the line, point order, with Bryan Chen, Robert Connelly and Louis Theran, https://arxiv.org/abs/2104.01892.

3. Rigidity through a projective lens, with Bernd Schulze and Walter Whiteley.

Information on my papers is also available at my google scholar page.



Bryan Chen, Katie Clinch, Robert Connelly (Cornell), James Cruickshank (NUI Galway), Sean Dewar (RICAM, Linz), Yaser Eftekhari (York), Nick Gill (South Wales), Neil Gillespie (Bristol), Georg Grasegger (RICAM, Linz), Hakan Guler (Kastomonu), Bill Jackson (Queen Mary), Viktoria Kaszanitzky (Budapest), Derek Kitson (Mary Immaculate College), Tom McCourt (Queensland), John Owen (Siemens), Stephen Power (Lancaster), Elissa Ross (MESH consultants), Mahdi Sadjadi (Arizona), Bernd Schulze (Lancaster), Jason Semeraro (Leicester), Brigitte Servatius (WPI), Adnan Sljoka (Kyoto), Shin-ichi Tanigawa (Tokyo), Louis Theran (St Andrews), Mike Thorpe (Arizona), Walter Whiteley (York).



Event organisation:



Current Teaching


  • MATH326 Graph Theory


  • MATH326 Graph Theory

 Students on the course should consult the moodle page, https://modules.lancaster.ac.uk/course/view.php?id=31433


  • MATH326 Graph Theory


  • MATH326 Graph Theory
  • MATH491 (pure math) and MATH492 (statistics) Dissertation Coordinator


  • MATH105 Linear Algebra
  • MATH326 Graph Theory



  • MATH105 Linear Algebra



  • MATH103 Matrix Methods



  • MATH103 Matrix Methods
  • MATH143 Differential Equations


Career Details

  • July 2015 - present: Lecturer in Pure Mathematics, Lancaster University.
  • September 2014 - June 2015: Temporary Lecturer in Pure Mathematics, Lancaster University.
  • January 2014 - August 2014: Postdoctoral fellow at York University, Canada.
  • January 2012 - December 2013: Postdoctoral fellow at the University of Bristol.
  • July 2011 - December 2011: Postdoctoral fellow at the Fields Institute, University of Toronto, for the special semester on Discrete Geometry and Applications.
  • Ph.D. Mathematics, Lancaster University, November 2011.

Professional Role

  • Theme lead, Combinatorics, since 2021.
  • Director of Postgraduate Research, since 2021.
  • Member of the British Combinatorial Committee, since 2020.
  • Deputy Director of Natural Science (Part I Director of Studies), since 2018.
  • Year 4 Director of Studies (Mathematics and Statistics), 2018-19.
  • Member of the LMS scientific committee for the British Mathematical Colloquium, 2016-2020.
  • Natural science coordinator (within Mathematics and Statistics), 2014-2019.
  • Department representative for British Combinatorial Bulletin, since 2014.



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