People

Professor Gerald Williams

Professor
Department of Mathematical Sciences
Professor Gerald Williams

Profile

Qualifications

  • Senior Fellow of the Higher Education Academy

  • PGCHE (Postgraduate Certificate in Higher Education), University of Kent 2009.

  • Ph.D. in Mathematics, Heriot Watt University 2000.

  • M.Sc. in Mathematics, University of Warwick 1997.

  • M.Sci. in Mathematics, University of St Andrews 1996.

Research and professional activities

Research interests

Combinatorial, Computational, Geometric, Cohomological aspects of infinite group theory

Open to supervise

Algebraic number theory and connections with Linear Algebra (circulant matrices)

Open to supervise

Current research

Member of Editorial Board for Cogent Mathematics.

Teaching and supervision

Current teaching responsibilities

  • Mathematics Careers and Employability (MA199)

  • Abstract Algebra (MA204)

Previous supervision

Esamaldeen MM Husin Hashem
Esamaldeen MM Husin Hashem
Thesis title: Isomorphisms Amongst Certain Classes of Cyclically Presented Groups
Degree subject: Mathematics
Degree type: Doctor of Philosophy
Awarded date: 1/8/2017

Publications

Journal articles (24)

Williams, G., (2019). Generalized Fibonacci groups H(r,n,s) that are connected labelled oriented graph groups. Journal of Group Theory. 22 (1), 23-39

Mohamed, E. and Williams, G., (2019). Isomorphism theorems for classes of cyclically presented groups. International Journal of Algebra and Computation. 29 (06), 1009-1017

Mohamed, E. and Williams, G., (2019). An Investigation Into the Cyclically Presented Groups with Length Three Positive Relators. Experimental Mathematics, 1-15

Bogley, WA. and Williams, G., (2017). Coherence, subgroup separability, and metacyclic structures for a class of cyclically presented groups. Journal of Algebra. 480, 266-297

Howie, J. and Williams, G., (2017). Fibonacci type presentations and 3-manifolds. Topology and its Applications. 215, 24-34

Bogley, WA. and Williams, G., (2016). Efficient Finite Groups Arising in the Study of Relative Asphericity. Mathematische Zeitschrift. 284 (1), 507-535

Williams, G., (2014). Fibonacci type semigroups. Algebra Colloquium. 21 (4), 647-652

Williams, G., (2014). Smith forms for adjacency matrices of circulant graphs. Linear Algebra and its Applications. 443, 21-33

Williams, G. and Telloni, AI., (2014). Smith forms of circulant polynomial matrices. Linear Algebra and its Applications. 458, 559-572

Williams, G., (2012). Groups of Fibonacci type revisited. International Journal of Algebra and Computation. 22 (8), 1240002-1240002

Williams, G., (2012). Largeness and SQ-universality of cyclically presented groups. International Journal of Algebra and Computation. 22 (4), 1250035-1250035

Howie, J. and Williams, G., (2012). Tadpole Labelled Oriented Graph Groups and Cyclically Presented Groups. Journal of Algebra. 371, 521-535

Williams, G., (2010). Unimodular integer circulants associated with trinomials. International Journal of Number Theory. 06 (04), 869-876

Edjvet, M. and Williams, G., (2010). The cyclically presented groups with relators xi xi+k xi+l. Groups, Geometry, and Dynamics. 4 (4), 759-775

Williams, G., (2009). The aspherical Cavicchioli-Hegenbarth-Repovลก generalized Fibonacci groups. Journal of Group Theory. 12 (1), 139-149

Howie, J. and Williams, G., (2008). The Tits alternative for generalized triangle groups of type (3, 4, 2). Algebra and Discrete Mathematics. 2008 (4), 40-48

Kopteva, N. and Williams, G., (2008). The Tits alternative for non-spherical Pride groups. Bulletin of the London Mathematical Society. 40 (1), 57-64

Williams, G., (2007). Euler Characteristics for One-Relator Products of Groups. Bulletin of the London Mathematical Society. 39 (4), 641-652

Williams, G., (2007). Pseudo-elementary Generalized Triangle Groups. Journal of Group Theory. 10 (1), 101-115

Williams, G. and Howie, J., (2006). Free subgroups in certain generalized triangle groups of type (2,m,2). Geometria Dedicata. 119 (1), 181-197

Williams, G., (2006). The Tits alternative for Groups defined by Periodic Paired Relations. Communications in Algebra. 34 (4), 251-258

Williams, G. and Ellis, G., (2005). On the cohomology of Generalized Triangle Groups. Commentarii Mathematici Helvetici. 80 (3), 571-591

Williams, G., (2003). Arithmeticity of Orbifold Generalised Triangle Groups. Journal of Pure and Applied Algebra. 177 (3), 309-322

Williams, G., (2002). Euler Characteristics for Orbifold Generalised Triangle Groups. Mathematical Proceedings of the Cambridge Philosophical Society. 132 (3), 435-438

Book chapters (2)

Williams, G., Bogley, WA. and Edjvet, M., (2019). Aspherical Relative Presentations All Over Again. In: Groups St Andrews 2017 in Birmingham. Editors: Campbell, CM., Quick, MR., Parker, CW., Robertson, EF. and Roney-Dougal, CM., . Cambridge University Press. 169- 199. 110872874X. 9781108728744

Williams, G., (2000). Generalised Triangle Groups of type (2,m,2). In: Computational and Geometric Aspects of Modern Algebra. Editors: Atkinson, M., Gilbert, N., Howie, J., Linton, S. and Robertson, E., . Cambridge University Press. 266- 279. 9780521788892

Reports and Papers (3)

Cuno, J. and Williams, G., A class of generalized graph groups defined by balanced presentations

Howie, J. and Williams, G., Planar Whitehead graphs with cyclic symmetry arising from the study of Dunwoody manifolds

Noferini, V. and Williams, G., Matrices in companion rings, Smith forms, and the homology of 3-dimensional Brieskorn manifolds

Grants and funding

2019

Visit by Dr Chimere Stanley Anabanti on problems in computational and combinatorial group theory

London Mathematical Society

2017

Visit by Professor W.A. Bogley to give lectures at Essex; Southampton; Nottingham

London Mathematical Society

Searching for gems in the landscape of cyclically presented groups

Leverhulme Trust

2015

Research visit to Oregon State University

London Mathematical Society

2014

Research visit to Professor William Bogley, Oregon State University

London Mathematical Society

Contact

gerald.williams@essex.ac.uk
+44 (0) 1206 873035

Location:

STEM 5.16, Colchester Campus