ALAN JAMES CAIN - Centre for Interdisciplinary Research in ...
ALAN JAMES CAIN - Centre for Interdisciplinary Research in ...
ALAN JAMES CAIN - Centre for Interdisciplinary Research in ...
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LAN . AIN ..◆ I wrote the course from scratch and produced high-quality pr<strong>in</strong>ted lecturenotes <strong>for</strong> the students, <strong>in</strong>clud<strong>in</strong>g exercises, advanced problems, andsolutions.◆ e notes I wrote were adopted by Attila Egri-Nagy <strong>for</strong> a read<strong>in</strong>g course<strong>for</strong> research and honours students at the University of Western Sydney.Sep. 2008–Jun. 2009 Postdoctoral researcherCentro de Álgebra da Universidade de LisboaAv. Prof. Gama P<strong>in</strong>to 2, 1649–003 Lisboa, Portugal◆ <strong>Research</strong> with<strong>in</strong> the project ‘Semigroups and Languages’, funded by and (//69514/2006).<strong>Research</strong> summary:I studied automatic Clif<strong>for</strong>d semigroups and also studied (with collaborators)how automatic structures and Malcev presentations <strong>in</strong>teracted with the newnotion of Green <strong>in</strong>dex subsemigroups.Teach<strong>in</strong>g:Postgraduate-level short course on automatic groups and semigroups.Sep. 2005–Aug. 2008 <strong>Research</strong> FellowSchool of Mathematics & Statistics, University of St AndrewsSt Andrews, Fife 16 9, United K<strong>in</strong>gdom◆ I was offered this post be<strong>for</strong>e the completion of my Ph.D. based on my achievementsdur<strong>in</strong>g my doctoral studies.◆ Member of Staff Council (March 2007–August 2008).<strong>Research</strong> summary:I worked as part of a large research team on the five-year <strong>in</strong>terdiscipl<strong>in</strong>aryproject ‘Critical Mass <strong>in</strong> Computational Algebra’, funded by the (/523229/1). In particular, I researched decision problems <strong>for</strong> automatic semigroups:given an automatic structure <strong>for</strong> a semigroup, is it possible to decidecerta<strong>in</strong> algebraic properties of the semigroup? In some cases, I proved thatno such algorithm exists (<strong>for</strong> example, cancellativity and le-cancellativity arealgorithmically undecidable). I also worked <strong>in</strong> related areas such as automatonsemigroups (generaliz<strong>in</strong>g automaton groups) and automatic presentations.With collaborators, I classified all f<strong>in</strong>itely generated cancellative semigroupsthat admit automatic presentations.Teach<strong>in</strong>g:3600 ‘Fundamentals of Pure Mathematics’ [with Prof. N. Ruškuc]◆ Completely revised the course to concentrate on establish<strong>in</strong>g the foundationsof mathematics rigorously.◆ Student feedback was enthusiastically supportive, with 85% overall approval.Postgraduate-level short course on comput<strong>in</strong>g with automatic semigroups.2
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