# Publications and Presentations

**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), http://dx.doi.org/10.1080/00927872.2017.1350693.

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.

**Presentations**

*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.