**Department of Mathematical SciencesNorthern Illinois
University**

**Rank: **Professor
Emeritus**Degree: **Ph.D.,
Queen's University, Belfast,
Ireland

Collaborating Member: Cenrto de Álgebra da Universidade de Lisboa, Lisboa, Portugal (CAUL)

Research area:

This program calculates and analyses finite transformation semigroups. It is written in C++ and runs under Windows 95/98/Me/2000/XP. You can download a zip file containing the files needed to install the program by clicking on the link below. Run the exe file to extract the setup files and then run setup. The program will create a directory c: \sgp on your c drive and will install the program and sample files to that directory. (You can change the default directory during the installation process.)

#### (with Filipa Soares) Tiling semigroups of n-dimensional hypercubic tilings,

*Communications in Algebra*39 (2011), 2002-2023.#### (with Paulo J. Medeiros) Compatible total orders on bisimple ω-semigrpoups,

*Semigroup Forum*81 (2010), 200-216.#### (with Filipa Soares) One-dimensional tiling semigroups and factorial languages,

*Communications in Algebra*37 (2009), 276-295.#### (with Ana Paula Garrao) Finite subgroups of v-semilatticed inverse semigroups,

*Semgroup Forum*78 (2009), 187-199.#### Semilattice ordered inverse semigroups,

*Proceedings of International Conference on Semigroups, Lisbon, July 12-15, 2005,*World Scientific (2007), 205-218.

#### Transformation Semigroups: Congruences, Idempotents, and Groups (PDF format)

#### These are the slides of a presentation at the Conference for Young Mathematicians, University of Potsdam, Germany June 23-27, 2011.

#### Coberturas E-unitárias para semigroupos inversos parcialmente ordenados (PDF format)

#### These are the slides of a seminar talk at the University of Minho, Portugal, June 16, 2011.

#### Some things I learned from Douglas Munn and some things I still need to learn (PDF format)

#### These are the slides of a presentationat the workshop in honor of the 80th birthday of Douglas Munn held at the University of Lisbon, April 24, 2009.

#### Generating Finite Transformation Semigroups: SgpWin (PDF format)

#### These are the slides of a presentation at the workshop on computational aspects of semigroup theory at the University of St. Andrews, September 5-9, 2006. Also included is an appendix on the generation of congruences on inverse semigroup.

#### Lattice Ordered Groups and the Structure of Inverse Semigroups (PDF format)

#### Lattice Ordered Groups and the Structure of Inverse Semigroups (DVI format)

#### These are notes of a series of lectures given at the Center of Algebra, University of Lisbon, in May 1998. A hard copy of the notes is available from the Center of Algebra.