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Dr Anthony Nixon

Lecturer in Pure Mathematics

Fylde College

LA1 4YF

Lancaster

Tel: +44 1524 594695

PhD supervision

I am interested in supervising research students in combinatorics or geometry. Specific projects I have in mind relate to the local or global uniqueness (rigidity) of geometric graphs. Students with a background in discrete mathematics and with an interest in interactions between graph theory, algebra and geometry are encouraged to contact me for further details.

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. My main interest is in finding combinatorial characterisations of the rigidity, or global rigidity, of generic bar-joint frameworks in a variety of settings.

Rigidity uses techniques from a range of areas to answer questions about the stability of structures. 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 and preprints:

1. Rigidity of frameworks on expanding spheres, with Bernd Schulze, Shin-Ichi Tanigawa and Walter Whiteley, http://arxiv.org/abs/1501.01391

2. Inductive constructions for combinatorial local and global rigidity, with Elissa Ross. Invited chapter for Handbook of Geometric Constraint Systems Principles, edited by Jessica Sidman, Meera Sitharam and Audrey St John.

3. A constructive characterisation of circuits in the simple (2,1)-sparse matroid, with Thomas McCourt, http://arxiv.org/abs/1604.05226

4. Rigid cylindrical frameworks with two coincident points, with Bill Jackson and Viktoria Kaszanitzky, https://arxiv.org/abs/1607.02039

5. Point-hyperplane frameworks, slider joints, and rigidity preserving transformations, with Yaser Eftekhari, Bill Jackson, Bernd Schulze, Shin-Ichi Tanigawa and Walter Whiteley, https://www.arxiv.org/abs/1703.06844

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

7. Tensegrity, with Robert Connelly. Invited chapter for Handbook of Geometric Constraint Systems Principles, edited by Jessica Sidman, Meera Sitharam and Audrey St John.

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

 

Collaborators:

Robert Connelly (Cornell), Yaser Eftekhari (York), Nick Gill (South Wales), Neil Gillespie (Bristol), Bill Jackson (Queen Mary), Viktoria Kaszanitzky (Budapest), 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).

 

 

 

Conference/workshop organisation:

 

 

Current Teaching

2017/2018

  • MATH105 Linear Algebra
  • MATH326 Graph Theory

 

2016/2017

  • MATH105 Linear Algebra

 Students on the course should consult the moodle page, https://modules.lancaster.ac.uk/course/view.php?id=12736

 

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.
  • 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

  • Natural Science Coordinator
  • Department representative for British Combinatorial Bulletin

 

 

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