Newcastle University

Nathan Barker MMath (Dunelm)
Pure Mathematics

• Email: nathan.barker@ncl.ac.uk
• Telephone: 0191 222 7286
• CV: available here
• Research Groups:

  North British Geometric Group Theory

  Quantum Computation

  Group Theory

• My supervisors are Prof. Sarah Rees and Dr Alina Vdovina
• General mathematics fun The Aperiodical

Research Interests

Geometric Group Theory

Decision problems

Thompson's Groups $F$, $T$ and $V$

Publications

• New examples of Beauville surfaces (pdf version), with N. Boston, N. Peyerimhoff, A. Vdovina. To appear in Monatsh. Math. (Online First, 5 February 2011).
  DOI: 10.1007/s00605-011-0284-6
• A note on Beauville $p$-groups, with N. Boston and B. Fairbairn. Accepted for publication, Experimental Mathematics Feb 2012. arXiv:1111.3522v1 [math.GR].
  DOI:10.1080/10586458.2012.669267

Preprints

• An algebraic approach to centralizers and conjugacy problems in the Higman-Thompson group $G_{2,1}$. (A version of this work was submitted May 2011, this is an expanded version edited Feb 2012).
• Regular algebraic surfaces isogenous to a higher product constructed from group representations using projective planes, with N. Boston, N. Peyerimhoff, A. Vdovina (submitted 2011). arXiv:1109.6053v1 [math.GR].
• The power-conjugacy problem in the Higman-Thompson groups $G_{n,r}$ (2011).
• Studying the Automorphism group of the Higman-Thompson group $G_{2,1}$ using Universal Algebra (2011).
• Symbol decompositions for elements of Thompson's group $F$ (2011).

Visits

• Jose Burillo, Departament de Matematica Aplicada IV, Universitat Politecnica de Catalunya, Barcelona, Spain, 2nd-10th April 2011.
• Collin Bleak, School of Mathematics and Statistics, University of St Andrews, Scotland, 13th-15th December 2011.

Talks

• Postgraduate Seminar, Newcastle University 2009 - Galois Theory
• Postgraduate Seminar, Newcastle University 2009 - A Finitely Presented Infinite Simple Group
• Geometry Seminar, Durham University 2010 - Diagrams and Conjugacy in Thompson's Group F
• Pure Mathematics Postgraduate Conference, Newcastle University 2010 - Expander Graphs
• Geometry & Algebra Seminar, Newcastle University 2010 - Finitely Generated torsion free abelian subgroups of the Higman-Thompson group $G_{2,1}$
• Postgraduate Seminar, Newcastle University 2010 - DNA and Knots
• Durham/Newcastle Afternoon of talks, Newcastle University 2011 - Beauville Surfaces
• Seminari de teoria de grups UAB - UPC, Centre de Recerca Matematica, Campus de Bellaterra 2011 - Centralizers in the Higman-Thompson group $G_{2,1}$
• PGTC, Aberdeen University 2011 - A useful group $G=\lt x_{0},...,x_{6} | x_{i}x_{i+1}x_{i+3}=1, i\in \mathbb{Z}/7\mathbb{Z} \gt$.
• Seminar, Open University October 2011 - Decision problems in Richard Thompson's groups $F$, $T$ and $V$.
• Algebra Seminar, University of Glasgow November 2011- Decision problems in Richard Thompson's groups $F$, $T$ and $V$.
• Seminar in Pure and Applicable Mathematics, Birkeck University of London November 2011 - Richard Thompson's groups F, T and V.

Upcoming Talks

Events and Conferences organized

• LMS Northern meeting and workshop, Newcastle University 12th-14th April 2010 (postgraduate coordinator/day-to-day running, main organizer Dr Andrew Duncan, Newcastle University).
• Pure Mathematics Postgraduate Conference 2010, Newcastle University 15th April 2010 (main organizer).
• Durham-Newcastle Postgraduate Afternoon of Talks, Newcastle University 31st March 2011 (co-organizer).
• NBGGT Meeting, 30th November 2011, Newcastle University (co-organizer).
• Beauville surfaces and groups 2012, 7th-9th June 2012, Newcastle University (local organizer).

Grants and Funding

• EPSRC grant for Ph.D. funding for 3.5 years.
• Partial funds for travel to attend Infinite group theory conference (CUNY), New York City, October 2009.
• LMS Grant Ref 8904. Funding for a postgraduate conference in Newcastle April 2010, £ 3050 (application supported by Andrew Duncan).
• Support (from Newcastle University Mathematics School), for Durham-Newcastle Afternoon of talks (at Newcastle University Mathematics School), March 2011.
• Funded postgraduate participant of LMS/EPSRC Durham Symposium on Geometry and Arithmetic of Lattices, Durham University, July 2011.
• Research visit, Departament de Matematica Aplicada IV Universitat Politecnica de Catalunya, Barcelona, Spain, April 2011, (to visit Prof. Jose Burillo).
• Research visit, School of Mathematics and Statistics, University of St Andrews, Scotland, 13th-15th December 2011. (to visit Dr Collin Bleak).

Teaching

• Maths Aid Tutor, Newcastle University, 2008-2012.
• Student Assessment Marker, School of Mathematics and Statistics, Newcastle University, 2008-2012.
• Student Assessment Marker, Department of Mathematical Sciences, University of Durham, 2007-2008.

Service

• Faculty of Science, Agriculture and Engineering postgraduate representative at the Survey for Advancement conference, Nottingham 19th May 2011, run by The Higher Education Academy.
• Staff Student Committee, Newcastle University - Secretary, Semester 1 2011-12.
• Staff Student Committee, Newcastle University - Postgraduate representative, 2010-11.

Conferences, Meetings and Workshops

• Topics in Geometric Group Theory, 1-6th Sept 2008, Heriot-Watt University.
• Quantum Computation, 22nd Sept 2008, Newcastle University.
• NBGGT Meeting, 3rd Dec 2008, University of York.
• Pure mathematics seminar, 8-9th Dec 2008, Durham University.
• MAGIC'09 Conference, 12-14th Jan 2009, Manchester University.
• LMS Northern Meeting, 14th Jan 2009, Manchester University.
• Memorial Lectures - Douglas Munn, 26th Jan 2009, Glasgow University.
• PGTC Manchester, 15-17th April 2009, Manchester University.
• NBGGT Meeting, 30th April 2009, Nottingham University.
• NBGGT Meeting, 13th July 2009, Newcastle University.
• A celebration of the 65th birthday of John Cannon (Sydney) & 60th birthday of Derek Holt (Warwick), 22 July 2009, Warwick University.
• Finitely Presented Groups: Where do we go from here, 1st-2nd Oct 2009, The City College of New York, New York.
• Chriswell Symposium, 9th Nov 2009, Queen Mary's London.
• NBGGT Meeting, 25th Nov 2009, University of Glasgow.
• NBGGT Meeting, 10th March 2010, University of York.
• LMS Northern meeting and workshop, 12-14th April 2010, Newcastle University.
• Pure Mathematics Postgraduate Conference, 15th April 2010, Newcastle University.
• Group Theory Day, 26th April 2010, University of Birmingham.
• Expansion in Groups, 26-27th May 2010, Imperial College London.
• PGTC St. Andrews, 28-30th June 2010, University of St. Andrews.
• NBGGT Meeting, 7th July 2010, Nottingham University.
• Geometry and Analysis on Graphs and Groups, 11-13th November 2010, Exeter College, University of Oxford.
• NBGGT Meeting, 8th December 2010, Edinburgh University.
• Pure Mathematics Colloquium - Terry Tao, 19th January 2011, University of Birmingham.
• EMS meeting - Terry Tao, 11th February 2011, University of Edinburgh.
• Durham-Newcastle Postgraduate Afternoon of Talks, 31st March 2011, Newcastle University.
• PGTC Aberdeen, 23-25th June 2011, Aberdeen University.
• Recent advances in Geometric Group Theory, 29th June - 1st July 2011, University of Southampton.
• LMS Durham Symposium Geometry and Arithmetic of Lattices, 4-14th July 2011, Durham University.
• Geometric presentations of finite and infinite groups, 17-23rd July 2011, University of Birmingham.
• NBGGT Meeting, 28th July 2011, Newcastle University.
• NBGGT Meeting, 30th November 2011, Newcastle University.

Upcoming Events



• Beauville surfaces and groups 2012, 7th-9th June 2012, Newcastle University.
• Cubical complexes and applications, 16th-20th July 2012, ICMS, Edinburgh.