Dr Anthony Nixon

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 - 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.

Papers under review:

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. Global rigidity of generic frameworks on concentric cylinders, with Bill Jackson, https://arxiv.org/abs/1610.07755

Collaborators:

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 (CWI), Louis Theran (St Andrews), Mike Thorpe (Arizona), Walter Whiteley (York).

Conference/workshop organisation:

• Geometric Rigidity workshop (Lancaster) June 2016, see http://www.lancaster.ac.uk/maths/news-and-events/events/?view=fulltext&month=02&day=25&year=2016&id=d.en.237588&timestamp=1465131600&
• Global Rigidity workshop (BIRS, Canada) July 2015, see http://www.birs.ca/events/2015/2-day-workshops/15w2199
• Geometric and Topological Graph Theory (Bristol) April 2013, see http://www.maths.bris.ac.uk/~maakn/GTGT2013

Current Teaching

2016/2017

• MATH105 Linear Algebra

2015/2016

• MATH103 Matrix Methods

Students on the course should consult the moodle page, https://modules.lancaster.ac.uk/course/view.php?id=7164

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

PhD Supervision Interests

I am interested in supervising research students in combinatorics or geometric rigidity. Specific projects I have in mind relate to the local or global uniqueness (rigidity) of geometric realisations of 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.

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