
Courses
Courses
Choosing a course is one of the most important decisions you'll ever make! View our courses and see what our students and lecturers have to say about the courses you are interested in at the links below.

University Life
University Life
Each year more than 4,000 choose NUI Galway as their University of choice. Find out what life at NUI Galway is all about here.

About NUI Galway
About NUI Galway
Since 1845, NUI Galway has been sharing the highest quality teaching and research with Ireland and the world. Find out what makes our University so special – from our distinguished history to the latest news and campus developments.

Colleges & Schools
Colleges & Schools
NUI Galway has earned international recognition as a researchled university with a commitment to top quality teaching across a rang of key areas of expertise.

Research
Research
NUI Galway’s vibrant research community take on some of the most pressing challenges of our times.

Business & Industry
Guiding Breakthrough Research at NUI Galway
We explore and facilitate commercial opportunities for the research community at NUI Galway, as well as facilitating industry partnership.

Alumni, Friends & Supporters
Alumni, Friends & Supporters
There are over 90,000 NUI Galway graduates Worldwide, connect with us and tap into the online community.

Community Engagement
Community Engagement
At NUI Galway, we believe that the best learning takes place when you apply what you learn in a real world context. That's why many of our courses include work placements or community projects.
Mathematics, Statistics & Applied Mathematics
Professor Graham Ellis
MSc, PhD
Contact Details
Established Professor of Mathematics

Room ADB3002
Áras De Brún
School of Mathematics, Statistics and Applied Mathematics
T: Ext. 3011
E: graham.ellis@nuigalway.ie
W: http://hamilton.nuigalway.ie/

Room ADB3002
Áras De Brún
School of Mathematics, Statistics and Applied Mathematics
T: Ext. 3011
E: graham.ellis@nuigalway.ie
W: http://hamilton.nuigalway.ie/
Established Professor of Mathematics
Mathematics
Room C110
Aras de Brun
NUI Galway
T: Ext. 3011
E: graham.ellis@nuigalway.ie
Mathematics
Room C110
Aras de Brun
NUI Galway
T: Ext. 3011
E: graham.ellis@nuigalway.ie
Biography
Peer Reviewed Journals
Year  Publication  

(2016)  'Cohomological periodicities of crystallographic groups'
Ellis, G (2016) 'Cohomological periodicities of crystallographic groups'. Journal Of Algebra, 445 :537544 [DOI] [Details] 

(2015)  'Computing fundamental groups from point clouds'
Brendel, P,Dlotko, P,Ellis, G,Juda, M,Mrozek, M (2015) 'Computing fundamental groups from point clouds'. Applicable Algebra In Engineering Communication And Computing, 26 :2748 [DOI] [Details] 

(2014)  'Homotopy 2Types of Low Order'
Ellis, G,Le, LV (2014) 'Homotopy 2Types of Low Order'. Experimental Mathematics, 23 :383389 [DOI] [Details] 

(1986)  'Free and projective crossed modules and the second homology group of a group'
Ellis, G. J. and Porter, T. (1986) 'Free and projective crossed modules and the second homology group of a group'. J. Pure Appl. Algebra, 40 (1):2731 [DOI] [Details] 

(1987)  'Nonabelian exterior products of Lie algebras and an exact sequence in the homology of Lie algebras'
Ellis, Graham J. (1987) 'Nonabelian exterior products of Lie algebras and an exact sequence in the homology of Lie algebras'. J. Pure Appl. Algebra, 46 (23):111115 [DOI] [Details] 

(1987)  'Nonabelian exterior products of groups and exact sequences in the homology of groups'
Ellis, G. J. (1987) 'Nonabelian exterior products of groups and exact sequences in the homology of groups'. Glasgow Math. J, 29 (1):1319 [DOI] [Details] 

(1987)  'Higherdimensional crossed modules and the homotopy groups of $(n+1)$ads'
Ellis, Graham and Steiner, Richard (1987) 'Higherdimensional crossed modules and the homotopy groups of $(n+1)$ads'. J. Pure Appl. Algebra, 46 (23):117136 [DOI] [Details] 

(1987)  'The nonabelian tensor product of finite groups is finite'
Ellis, Graham J. (1987) 'The nonabelian tensor product of finite groups is finite'. J. Algebra, 111 (1):203205 [DOI] [Details] 

(1988)  'Multirelative algebraic $K$theory: the group $K_2(\Lambda; I_1,\cdots,I_n)$ and related computations'
Ellis, Graham J. (1988) 'Multirelative algebraic $K$theory: the group $K_2(\Lambda; I_1,\cdots,I_n)$ and related computations'. J. Algebra, 112 (2):271289 [DOI] [Details] 

(1988)  'Hopf formulae for the higher homology of a group'
Brown, Ronald and Ellis, Graham J. (1988) 'Hopf formulae for the higher homology of a group'. Bull. London Math. Soc, 20 (2):124128 [DOI] [Details] 

(1988)  'An eight term exact sequence in algebraic $K$theory'
Ellis, Graham J. (1988) 'An eight term exact sequence in algebraic $K$theory'. Bull. London Math. Soc, 20 (3):245247 [DOI] [Details] 

(1988)  'Crossed modules'
Ellis, Graham (1988) 'Crossed modules'. Irish Math. Soc. Bull, (21):2937 [Details] 

(1988)  'Higherdimensional crossed modules of algebras'
Ellis, Graham J. (1988) 'Higherdimensional crossed modules of algebras'. J. Pure Appl. Algebra, 52 (3):277282 [DOI] [Details] 

(1988)  'Homotopy classification the J. H. C. Whitehead way'
Ellis, Graham J. (1988) 'Homotopy classification the J. H. C. Whitehead way'. Exposition. Math, 6 (2):97110 [Details] 

(1989)  'Quelques propri\'et\'es homologiques des modules pr\'ecrois\'es'
Conduch\'e (1989) 'Quelques propri\'et\'es homologiques des modules pr\'ecrois\'es'. J. Algebra, 123 (2):327335 [DOI] [Details] 

(1989)  'An exterior product for the homology of groups with integral coefficients modulo $p$'
Ellis, G. J. and Rodr\'\iguezFern\'andez, C. (1989) 'An exterior product for the homology of groups with integral coefficients modulo $p$'. Cahiers Topologie G\'eom. Diff\'erentielle Cat\'eg, 30 (4):339343 [Details] 

(1989)  'An algebraic derivation of a certain exact sequence'
Ellis, Graham J. (1989) 'An algebraic derivation of a certain exact sequence'. J. Algebra, 127 (1):178181 [DOI] [Details] 

(1989)  'Hopf formulae and an exact sequence for group homology with coefficients in $Z_q$'
Ellis, Graham J. (1989) 'Hopf formulae and an exact sequence for group homology with coefficients in $Z_q$'. Proc. Roy. Irish Acad. Sect. A, 89 (1):6769 [Details] 

(1990)  'Relative derived contravariant functors and the cohomology of groups'
Ellis, Graham J. (1990) 'Relative derived contravariant functors and the cohomology of groups'. J. Pure Appl. Algebra, 64 (1):2133 [DOI] [Details] 

(1990)  'Relative derived functors and the homology of groups'
Ellis, Graham J. (1990) 'Relative derived functors and the homology of groups'. Cahiers Topologie G\'eom. Diff\'erentielle Cat\'eg, 31 (2):121135 [Details] 

(1991)  'A nonabelian tensor product of Lie algebras'
Ellis, Graham J. (1991) 'A nonabelian tensor product of Lie algebras'. Glasgow Math. J, 33 (1):101120 [DOI] [Details] 

(1991)  'On the higher universal quadratic functors and related computations'
Ellis, Graham J. (1991) 'On the higher universal quadratic functors and related computations'. J. Algebra, 140 (2):392398 [DOI] [Details] 

(1992)  'Homology of $2$types'
Ellis, Graham J. (1992) 'Homology of $2$types'. J. London Math. Soc. (2), 46 (1):127 [DOI] [Details] 

(1993)  'On five wellknown commutator identities'
Ellis, Graham J. (1993) 'On five wellknown commutator identities'. J. Austral. Math. Soc. Ser. A, 54 (1):119 [Details] 

(1993)  'Homotopical aspects of Lie algebras'
Ellis, Graham J. (1993) 'Homotopical aspects of Lie algebras'. J. Austral. Math. Soc. Ser. A, 54 (3):393419 [Details] 

(1993)  'On a MayerVietoris sequence in the cohomology of groups'
Ellis, Graham and Hardie, Keith (1993) 'On a MayerVietoris sequence in the cohomology of groups'. Quaestiones Math, 16 (1):7380 [Details] 

(1993)  'Crossed squares and combinatorial homotopy'
Ellis, Graham (1993) 'Crossed squares and combinatorial homotopy'. Math. Z, 214 (1):93110 [DOI] [Details] 

(1995)  'Tensor products and $q$crossed modules'
Ellis, Graham J. (1995) 'Tensor products and $q$crossed modules'. J. London Math. Soc. (2), 51 (2):243258 [DOI] [Details] 

(1995)  'Computing Schur multipliers and tensor products of finite groups'
Ellis, Graham and Leonard, Frank (1995) 'Computing Schur multipliers and tensor products of finite groups'. Proc. Roy. Irish Acad. Sect. A, 95 (2):137147 [Details] 

(1995)  'Corrigendum and addendum: ``Homology of 2types'' [J. London Math.\ Soc.\ (2) \bf 46 (1992), no.\ 1, 127; MR1180879 (93h:55014)]'
Ellis, Graham (1995) 'Corrigendum and addendum: ``Homology of 2types'' [J. London Math.\ Soc.\ (2) \bf 46 (1992), no.\ 1, 127; MR1180879 (93h:55014)]'. J. London Math. Soc. (2), 52 (3):447448 [DOI] [Details] 

(1995)  'A MayerVietoris sequence in group homology and the decomposition of relation modules'
Duncan, A. J. and Ellis, Graham J. and Gilbert, N. D. (1995) 'A MayerVietoris sequence in group homology and the decomposition of relation modules'. Glasgow Math. J, 37 (2):159171 [DOI] [Details] 

(1995)  'A projective homotopy theory of crossed $G$modules'
Ellis, Graham and Hardie, Keith (1995) 'A projective homotopy theory of crossed $G$modules'. Appl. Categ. Structures, 3 (3):201219 [DOI] [Details] 

(1996)  'On the tensor square of a prime power group'
Ellis, Graham (1996) 'On the tensor square of a prime power group'. Arch. Math. (Basel), 66 (6):467469 [DOI] [Details] 

(1996)  'Capability, homology, and central series of a pair of groups'
Ellis, Graham (1996) 'Capability, homology, and central series of a pair of groups'. J. Algebra, 179 (1):3146 [DOI] [Details] 

(1997)  'Spaces with finitely many nontrivial homotopy groups all of which are finite'
Ellis, Graham (1997) 'Spaces with finitely many nontrivial homotopy groups all of which are finite'. Topology, 36 (2):501504 [DOI] [Details] 

(1997)  'On the nilpotent multipliers of a group'
Burns, John and Ellis, Graham (1997) 'On the nilpotent multipliers of a group'. Math. Z, 226 (3):405428 [DOI] [Details] 

(1997)  'Lower central series of groups with small upper central factors'
Burns, J. and Ellis, G. and MacHale, D. and \'O Murch\'u (1997) 'Lower central series of groups with small upper central factors'. Proc. Roy. Irish Acad. Sect. A, 97 (2):113122 [Details] 

(1998)  'On the capability of groups'
Ellis, Graham (1998) 'On the capability of groups'. Proc. Edinburgh Math. Soc. (2), 41 (3):487495 [DOI] [Details] 

(1998)  'A bound for the derived and Frattini subgroups of a primepower group'
Ellis, Graham (1998) 'A bound for the derived and Frattini subgroups of a primepower group'. Proc. Amer. Math. Soc, 126 (9):25132523 [DOI] [Details] 

(1998)  'On the Schur multiplier of a quotient of a direct product of groups'
Ellis, Graham (1998) 'On the Schur multiplier of a quotient of a direct product of groups'. Bull. Austral. Math. Soc, 58 (3):495499 [DOI] [Details] 

(1998)  'Inequalities for Baer invariants of finite groups'
Burns, John and Ellis, Graham (1998) 'Inequalities for Baer invariants of finite groups'. Canad. Math. Bull, 41 (4):385391 [DOI] [Details] 

(1998)  'The Schur multiplier of a pair of groups'
Ellis, Graham (1998) 'The Schur multiplier of a pair of groups'. Appl. Categ. Structures, 6 (3):355371 [DOI] [Details] 

(1998)  'Tensor products of primepower groups'
Ellis, Graham and McDermott, Aidan (1998) 'Tensor products of primepower groups'. J. Pure Appl. Algebra, 132 (2):119128 [DOI] [Details] 

(1998)  'On Peiffer central series'
Ellis, Graham (1998) 'On Peiffer central series'. Glasgow Math. J, 40 (2):177185 [DOI] [Details] 

(1998)  'On groups with a finite nilpotent upper central quotient'
Ellis, Graham (1998) 'On groups with a finite nilpotent upper central quotient'. Arch. Math. (Basel), 70 (2):8996 [DOI] [Details] 

(1999)  'A bound on the Schur multiplier of a primepower group'
Ellis, Graham and Wiegold, James (1999) 'A bound on the Schur multiplier of a primepower group'. Bull. Austral. Math. Soc, 60 (2):191196 [DOI] [Details] 

(1999)  'Enumerating primepower homotopy $k$types'
Ellis, Graham (1999) 'Enumerating primepower homotopy $k$types'. Math. Z, 232 (1):6371 [DOI] [Details] 

(1999)  'On the Schur multiplier of $p$groups'
Ellis, Graham (1999) 'On the Schur multiplier of $p$groups'. Comm. Algebra, 27 (9):41734177 [DOI] [Details] 

(2001)  'Embeddings into $k$efficient groups'
Ellis, Graham (2001) 'Embeddings into $k$efficient groups'. J. Algebra, 243 (2):497503 [DOI] [Details] 

(2002)  'A MagnusWitt type isomorphism for nonfree groups'
Ellis, G. (2002) 'A MagnusWitt type isomorphism for nonfree groups'. Georgian Math. J, 9 (4):703708 [Details] 

(2002)  'Derived functors and the homology of $n$types'
Casas, J. M. and Ellis, G. and Ladra, M. and Pirashvili, T. (2002) 'Derived functors and the homology of $n$types'. J. Algebra, 256 (2):583598 [DOI] [Details] 

(2004)  'Computing group resolutions'
Ellis, Graham (2004) 'Computing group resolutions'. J. Symbolic Comput, 38 (3):10771118 [DOI] [Details] 

(2005)  'On the cohomology of generalized triangle groups'
Ellis, Graham and Williams, Gerald (2005) 'On the cohomology of generalized triangle groups'. Comment. Math. Helv, 80 (3):571591 [DOI] [Details] 

(2006)  'Polytopal resolutions for finite groups'
Ellis, Graham and Harris, James and Sk\"oldberg, Emil (2006) 'Polytopal resolutions for finite groups'. J. Reine Angew. Math, 598 :131137 [DOI] [Details] 

(2009)  'Wythoff polytopes and lowdimensional homology of Mathieu groups'
Dutour Sikiri\'c (2009) 'Wythoff polytopes and lowdimensional homology of Mathieu groups'. J. Algebra, 322 (11):41434150 [DOI] [Details] 

(2010)  'The $K(\pi,1)$ conjecture for a class of Artin groups'
Ellis, Graham and Sk\"oldberg, Emil (2010) 'The $K(\pi,1)$ conjecture for a class of Artin groups'. Comment. Math. Helv, 85 (2):409415 [DOI] [Details] 

(2010)  'A colimit of classifying spaces'
Ellis, Graham and Mikhailov, Roman (2010) 'A colimit of classifying spaces'. Adv. Math, 223 (6):20972113 [DOI] [Details] 

(2010)  'Homology of some Artin and twisted Artin groups'
Clancy, Maura and Ellis, Graham (2010) 'Homology of some Artin and twisted Artin groups'. J. KTheory, 6 (1):171196 [DOI] [Details] 

(2011)  'The mod2 cohomology ring of the third Conway group is CohenMacaulay'
King, Simon A. and Green, David J. and Ellis, Graham (2011) 'The mod2 cohomology ring of the third Conway group is CohenMacaulay'. Algebr. Geom. Topol, 11 (2):719734 [DOI] [Details] 

(2011)  'Computing group cohomology rings from the LyndonHochschildSerre spectral sequence'
Ellis, Graham and Smith, Paul (2011) 'Computing group cohomology rings from the LyndonHochschildSerre spectral sequence'. J. Symbolic Comput, 46 (4):360370 [DOI] [Details] 

(2011)  'Persistent homology of groups'
Ellis, Graham and King, Simon (2011) 'Persistent homology of groups'. J. Group Theory, 14 (4):575587 [DOI] [Details] 

(2011)  'On the integral homology of $\rm PSL_4(\Bbb Z)$ and other arithmetic groups'
Dutour Sikiri\'c (2011) 'On the integral homology of $\rm PSL_4(\Bbb Z)$ and other arithmetic groups'. J. Number Theory, 131 (12):23682375 [DOI] [Details] 

(2012)  'Special issue on computer algebra in algebraic topology and its applications'
Ellis, Graham and S\'aenzdeCabez\'on, Eduardo (2012) 'Special issue on computer algebra in algebraic topology and its applications'. Appl. Algebra Engrg. Comm. Comput, 23 (12):12 [DOI] [Details] 

(2012)  'Computational homology of $n$types'
Ellis, Graham and Luyen, Le Van (2012) 'Computational homology of $n$types'. J. Symbolic Comput, 47 (11):13091317 [DOI] [Details] 

(2014)  'Computational homotopy of finite regular CWspaces'
Ellis, Graham and Hegarty, Fintan (2014) 'Computational homotopy of finite regular CWspaces'. J. Homotopy Relat. Struct, 9 (1):2554 [DOI] [Details] 

(2014)  'The homology of $SL_2(\Bbb Z[1/m])$ for small $m$'
Tuan, Bui Anh and Ellis, Graham (2014) 'The homology of $SL_2(\Bbb Z[1/m])$ for small $m$'. J. Algebra, 408 :102108 [DOI] [Details] 
Book Chapters
Year  Publication  

(2008)  'Homological algebra programming'
Ellis, Graham (2008) 'Homological algebra programming' In: Amer. Math. Soc., Providence, RI. [Details] 

(2009)  'Interoperating between computer algebra systems: computing homology of groups with Kenzo and GAP'
Romero, Ana and Ellis, Graham and Rubio, Julio (2009) 'Interoperating between computer algebra systems: computing homology of groups with Kenzo and GAP' In: ACM, New York. [Details] 

(2010)  'Computing covers of Lie algebras'
Ellis, Graham and Mohammadzadeh, Hamid and Tavallaee, Hamid (2010) 'Computing covers of Lie algebras' In: Amer. Math. Soc., Providence, RI. [Details] 