Publications in peer-reviewed journals

J.Araújo, W. Bentz, and P.J. Cameron, “Orbits of Primitive k-homogenous Groups on (n − k)-partitions with Applications to Semigroups”, to appear in the Transactions of the American Mathematical Society, doi:10.1090/tran/7274.

W. Bentz, P. Gillibert, and L. Sequeira, “Finite Abelian Algebras are Fully Dualizable”, to appear in Communications in Algebra (2017),

J. Araújo, W. Bentz, E. Dobson, J. Konieczny, and J. Morris, “Automorphism Groups of Circulant Digraphs with Applications to Semigroup Theory”, Combinatorica (2017), in press, doi:10.1007/s00493-016-3403-0.

J. Araújo, W. Bentz, P.J. Cameron, G. Royle, and A.Schaefer, “Primitive Groups, Graph Endomorphisms and Synchronization”, Proceedings of the London Mathematical Society 113 (2016), 829–867.

J. Araújo, W. Bentz, and J. Konieczny. Directed Graphs of Inner Translations of Semigroups, Semigroup Forum 94 (2017), 650–673.

J. Araújo, W. Bentz, J.D.Mitchell, and Cs.Schneider. The rank of the semigroup of transformations stabilising a partition of a finite set, Mathematical Proceedings of the Cambridge Philosophical Society 159 (2015), 339–353.

J. Araújo, W. Bentz, and J. Konieczny. The Commuting Graph of the Symmetric Inverse Semigroup, Israel Journal of Mathematics 207 (2015), 103–149.

J. Araújo, W. Bentz, and J. Konieczny. The Largest Subsemilattices of the Endomorphism Monoid of an Independence Algebra, Linear Algebra and Its Applications 458 (2014), 60–79.

W. Bentz, B. A. Davey, J. G. Pitkethly, and R. Willard. Dualizability of Automatic Algebras, Journal of Pure and Applied Algebra 218 (2014), 1324–1345. 

W. Bentz and P. Mayr. Supernilpotence Prevents Dualizability, Journal of the Australian Mathematical Society 96 (2014), 1– 24.

W. Bentz, L. Sequeira. Taylor´s Modularity Conjecture Holds for Linear Idempotent Varieties, Algebra Universalis 71 (2014), 101– 107.

J. Araújo, W. Bentz, and P. J. Cameron. Groups Synchronizing a Transformation of Non-Uniform Kernel, Theoretical Computer Science 498 (2013) 1– 9. 

E. Geangu, P. Hauf, R. Bhardwaj, and W. Bentz. Infant Pupil Diameter Changes in Response to Others' Positive and Negative Emotions. PLoS One 6(11):e27132, 2011.

W. Bentz. Optimal Packings of 13 and 46 Unit Squares in a Square. Electronic Journal of Combinatorics 17 (2): #R126, 2010.

W. Bentz. A Characterization of T3 Separation for a Special Class of Varieties. Algebra Universalis 56 (2007), 399 – 410.

W. Bentz. A Characterization of Hausdorff Separation for a Special Class of Varieties. Algebra Universalis 55 (Special Issue in Honor of Walter Taylor, 2006), 259 – 276.

W. Bentz and S. Bulman-Fleming. On Equalizer-flat Acts. Semigroup Forum 58 (1999), 5 – 16.

W. Bentz. Topological Implications in Varieties. Algebra Universalis, 42 (1999), 9 – 16. 

Outreach Publications

W. Bentz, What’s the point of maths research? It’s the abstract nonsense behind tomorrow’s breakthrough, The Conversation UK, Sep 19, 2016.


On Permutation Groups, Transformation Semigroups, and Graphs, All Kinds of Mathematics Remind me of You, Conference to celebrate the 70th Anniversary of Peter J. Cameron, Lisbon, Portugal, July 2017 [invited speaker]. 

Congruences on the Product of Two Full Transformation Monoids. North British Semigroup and Applications Network, University of York, UK, January 2017 [invited speaker].

Synchronisation for Automata, Semigroups, and Groups. Algorithms and Complexity Seminar, University of Durham, Durham, UK, November 2016 [invited speaker].

The Rank of Partition-Stabilising Monoids of Transformation. Pure Mathematics Seminar, University of East Anglia, Norwich, UK, November 2016 [invited speaker].

The minimal generating sets of the semigroup of transformations stabilising a given partition, University of St Andrews Pure Mathematics Colloquium, September 2016 [invited speaker].

The rank of the semigroup of transformations preserving a partition, University of Leeds Mathematical Seminar, April 2016 [invited speaker].

Synchronizing Groups, University of Hull Mathematics Seminar, December 2015.

The Solution of the Generalized Pei Huisheng Problem, York Semigroup, York, UK, November 2015.

How synchronizing are primitive groups?, London Mathematical Society - EPSRC Durham Symposium, Durham, UK, July 2015.

Supernilpotent algebras are non-dualizable, Seminar of Algebra, Logic and Topology, Centre for Mathematics, University of Coimbra, Portugal, July 2015.

Synchronizing automata, graphs, and transformation monoids, AMS-EMS-SPM 2015 International Meeting, Porto, June 2015.

Squares and the Quest for the Perfect Packing, University of York Mathematics Society, York, UK, January 2015.

New Results on Synchronization, North British Semigroups and Applications Network, York, UK, January 2015.

Three Years out of 34: A Personal Retrospective of the Center of Algebra, Algebra Workshop 2014 - 34 years of CAUL, Lisbon, Portugal, November 2014.

Examining Commutativity in Symmetric Inverse Semigroups, York Semigroup Seminar, University of York, UK, September 2014.

Derivatives as a Tool for Computational Classification, Workshop on Computational Algebra, Lisbon, Portugal, July 2014.

A Tribute to the Center of Algebra, 2014 National Meeting of the Portuguese Mathematical Society, Lisbon, Portugal, July 2014 [Invited Speaker].

Is dualizability of Nilpotent Algebras Decidable?, 86. Arbeitstagung Allgemeine Algebra, Linz, Austria, February 2014.

Square Packings and Optimality Proofs, Colloquium, University of British Columbia, Canada, September 2013 [Invited Speaker].

Duality, the ghost element method, and an application to supernilpotent algebras, Seminar, University of Northern Britsh Columbia, September 2013.

Packing equal squares into squares, PIMS Distinguished Speaker, University of Northern British Columbia, September 2013 [Invited Speaker].

The Commuting Graph of the Symmetric Inverse Semigroup, Discrete Mathematics Seminar, University of British Columbia, September 2013.

The modularity conjecture holds for linear idempotent varieties, Algebra Seminar, La Trobe University, Melbourne, Australia, July 2013.

Supernilpotence as an obstacle to dualizability, General Algebra and its Applications, Melbourne, Australia, July 2013. 

Properties of the Commuting Graph of the Symmetric Inverse Semigroup, Algebra Seminar, JKU Linz, Austria, June 2013.

Dualizability and the ghost element method, Algebra Seminar, JKU Linz, Austria, June 2013.

Quadratpackungen als mathematische Herausforderung, Kepler-Symposium, JKU Linz, Austria, June 2013 [Invited Speaker]

Groups that are almost synchronizing, 4th Novi Sad Algebraic Conference, Novi Sad, Serbia, June 2013.

The effect of nilpotence on the dualizability of an algebra, 86. Arbeitstagung Allgemeine Algebra, Olomouc, Czech Republic, June 2013.

On Synchronizing Automata, 7th Workshop on Statistics, Mathematics and Computation, Tomar, Portugal, May, 2013 [invited Speaker].

The modularity conjecture holds for linear idempotent varieties. 85th Workshop on General Algebra, Luxembourg, February 2013.

Dualizability of Algebras from Congruence Permutable Varieties. Marie Curie Actions Conference, Dublin, Ireland, July 2012.

The Commuting Graph of the Symmetric Inverse Semigroup - Clique Number and Diameter. Workshop on Semigroups (To Remember John M. Howie on the Occasion of his 76th Birthday), Lisbon, Portugal, May 2012.

Packing Equal Squares into Squares. Seminário do Centro de Estruturas Lineares e Combinatórias, Lisbon, Portugal, June 2012.

Milkboxes and their Containers: a Packing Challenge. Seminário para todos, Faculdade de Ciências da Universidade de Lisboa, Portugal, May 2012.

An “easy” problem by McNulty. 83rd Workshop on General Algebra, Novi Sad, Serbia, March 2012.

Automata encoding algebras, and an “easy problem”. Dia de Semigrupos, Vila Real, Portugal, January 2012 [Invited Speaker].

On a problem by McNulty. BLAST 2011, University of Kansas, Lawrence, Kansas, USA, July 2011.

Infant Affect Sharing Reactions to Peer Emotions 
(with E. Geangu and P.Hauf), 40th Annual Meeting of the Jean Piaget Society,
St. Louis, Missouri, USA, June 2010.

Infant Pupil Dilation in Response to Peers' Emotions - A Sign of Affect Sharing (with E. Geangu and P.Hauf), 
International Conference of Infant Studies 2010,
Baltimore, Maryland, USA, March 2010.

Optimal Square Packings. University of Waterloo Pure Mathematics Seminar, 
Waterloo, Ontario, Canada, July 2010.

Construction Techniques in Topological Universal Algebra. BLAST 2010, University of Colorado
Boulder, CO, USA, June 2010.

A result on T3 separation in topological algebras.
 BLAST 2009,
New Mexico State University,
Las Cruces, NM, USA, August 2009.

A Result on Complete Hausdorffness in topological algebras.
 BLAST 2008,
 University of Denver, Denver, CO, USA, August 2008.

A Look on the Interaction between Algebra and other Mathematical Area.
 UNBC Mathematics & Physics Symposium, 
Prince George, BC, Canada, February 2008.

Algebraic characterizations for topological properties.
 AMS-MAA Joint Mathematics Meetings, 
San Antonio, Texas, USA, January 2006.

Algebraic characterizations for topological separation properties.
 Special Section on Universal Algebra and Order, AMS sectional meeting,
 University of Nebraska,
 Lincoln, USA, October 2005.

On the topological implication "T0 implies T2". 
Special Section on Universal Algebra and Lattice Theory, AMS sectional meeting, 
Vanderbilt University, Nashville,
 Tennessee, USA, October 2004.

On the topological implication "T0 implies T2". Algebras, Lattices, Varieties - A Conference in Honor of Walter Taylor,
 University of Colorado at Boulder, USA, August 2004.

Semigroup presentations and deficiency. 
63. Arbeitstagung Allgemeine Algebra,
 Universität Kaiserslautern, Germany, February 2002.

Semigroup presentations and deficiency. University of Waterloo Graduate Student Conference,
 Waterloo, Canada, April 2001.

Semigroup presentations and deficiency. 
The Australian Category Seminar,
 Sydney, Australia, May 2000.

Topological Implications of n-permutable varieties.
 55. Arbeitstagung Allgemeine Algebra, Technische Universität Darmstadt, 
Germany, November 1997.

On Equalizer-flat Acts.
 53. Arbeitstagung Algebra, 
Universität Dresden, Germany, February 1997.