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Anthony Nixon supervises 1 postgraduate research students. If these students have produced research profiles, these are listed below:

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Dr Anthony Nixon

Lecturer in Pure Mathematics

Fylde College

LA1 4YF

Lancaster

Tel: +44 1524 594695

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. Global rigidity of generic frameworks on the cylinder, with Bill Jackson, 31 pages, https://arxiv.org/abs/1610.07755

2. Double-distance frameworks and mixed sparsity graphs, with Stephen Power, 29 pages, https://arxiv.org/abs/1709.06349.

3. Rigidity of symmetric frameworks in normed spaces, with Derek Kitson and Bernd Schulze, 36 pages, https://arxiv.org/abs/1808.04484.

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

 

Collaborators:

Robert Connelly (Cornell), James Cruickshank (NUI Galway), Yaser Eftekhari (York), Nick Gill (South Wales), Neil Gillespie (Bristol), Hakan Guler (Kastomonu), Bill Jackson (Queen Mary), Viktoria Kaszanitzky (Budapest), Derek Kitson (Lancaster), 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

2018/2019

  • MATH326 Graph Theory

 Students on the course should consult the moodle page, https://modules.lancaster.ac.uk/course/view.php?id=23309

  • MATH491 (pure math) and MATH492 (statistics) Dissertation Coordinator

 Students on the course should consult the moodle page, https://modules.lancaster.ac.uk/course/view.php?id=24952 for MATH491 and  https://modules.lancaster.ac.uk/course/view.php?id=249523 for MATH492.

2017/2018

  • MATH105 Linear Algebra
  • MATH326 Graph Theory

 

2016/2017

  • MATH105 Linear Algebra

 

2015/2016

  • MATH103 Matrix Methods

 

2014/2015

  • 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

  • Deputy Director of Natural Science (Part I Director of Studies)
  • Year 4 Director of Studies (Mathematics and Statistics)
  • Department representative for British Combinatorial Bulletin

 

 

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