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Mathematics, Statistics & Applied Mathematics
Professor Graham Ellis
MSc, PhD
Contact Details
Established Professor of Mathematics
Áras De Brún
School of Mathematics, Statistics and Applied Mathematics
T: Ext. 3011
E: graham.ellis@nuigalway.ie
http://hamilton.nuigalway.ie/
Áras De Brún
School of Mathematics, Statistics and Applied Mathematics
T: Ext. 3011
E: graham.ellis@nuigalway.ie
http://hamilton.nuigalway.ie/
Biography
Research Interests
Research Projects
Project  Start Date  End Date  

ESP SEVENTH DE BRUN WORKSHOP  01OCT14  30SEP15  
SEVENTH DE BRUN WORKSHOP ON HOMOLOGICAL PERTUBATION THEORY GRAHAM ELLIS  01SEP14  13AUG15  
SEVENTH DE BRUN WORKSHOP ON HOMOLOGICAL PERTUBATION THEORY GRAHAM ELLIS  01SEP14  13AUG16  
IRC POSTGRADATE AWARD ANH TUI BUAN GRAHAM ELLIS  01OCT13  30SEP15  
IRCSET POSTDOCTORAL FELLOWSHIP FOR ALEXANDER RAHM GRAHAM ELLIS  16NOV11  31AUG14  
GRAHAM ELLIS GENERAL O/H ACCOUNT  01OCT08  31DEC20  
DE BRUN CENTRE FOR COMPUTATIONAL ALGEBRA  01JAN08  29APR14  
EUCOMP. HOMOLOGICAL ALEGBRA ELLIS (M)  01OCT06  30SEP10  
IRCSET EMBARK 05 MARY CLANCY G ELLIS  01OCT05  30SEP08  
MF2003 MF84 03 M G ELLIS  01JAN04  31DEC04  
EI SC 02 64 HOMOTOPICAL SYZYGIES G ELLIS  01OCT02  31OCT06  
EU HPMD CT2001 00079 GROEBNER BASES ELLIS  11DEC01  31JUL08 
Peer Reviewed Journals
Year  Publication  

(2016)  'Computing Bredon homology of groups'
Bui, AT,Ellis, G (2016) 'Computing Bredon homology of groups'. Journal Of Homotopy And Related Structures, 11 :715734 [DOI] [Details] 

(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] 

(2015)  'Editorial [Computational algebraic topology and its applications]'
Ellis, Graham and Murillo, Aniceto and Real, Pedro and S\'aenzdeCabez\'on, Eduardo (2015) 'Editorial [Computational algebraic topology and its applications]'. Appl. Algebra Engrg. Comm. Comput, 26 (12):13 [DOI] [Details] 

(2014)  'Homotopy 2types of low order'
Ellis, Graham and Le, Luyen Van (2014) 'Homotopy 2types of low order'. Exp. Math, 23 (4):383389 [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] 

(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] 

(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] 

(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] 

(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] 

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

(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] 

(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] 

(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] 

(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] 

(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] 

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

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

(2001)  'On the relation between upper central quotients and lower central series of a group'
Ellis, Graham (2001) 'On the relation between upper central quotients and lower central series of a group'. Trans. Amer. Math. Soc, 353 (10):42194234 [DOI] [Details] 

(1999)  'Computing second cohomology of finite groups with trivial coefficients'
Ellis, Graham and Kholodna, Irina (1999) 'Computing second cohomology of finite groups with trivial coefficients'. Homology Homotopy Appl, 1 :163168 [Details] 

(1999)  'Threedimensional presentations for the groups of order at most $30$'
Ellis, Graham and Kholodna, Irina (1999) 'Threedimensional presentations for the groups of order at most $30$'. LMS J. Comput. Math, 2 :93117 [Details] 

(1999)  'Enumerating primepower homotopy $k$types'
Ellis, Graham (1999) 'Enumerating primepower homotopy $k$types'. Math. Z, 232 (1):6371 [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)  'On the Schur multiplier of $p$groups'
Ellis, Graham (1999) 'On the Schur multiplier of $p$groups'. Comm. Algebra, 27 (9):41734177 [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] 

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

(1998)  'On the computation of certain homotopicalfunctors'
Ellis, Graham (1998) 'On the computation of certain homotopicalfunctors'. LMS J. Comput. Math, 1 :2541 [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)  '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)  '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] 

(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] 

(1996)  'Capability, homology, and central series of a pair of groups'
Ellis, G (1996) 'Capability, homology, and central series of a pair of groups'. Journal Of Algebra, 179 :3146 [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)  '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)  '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] 

(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] 

(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] 

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

(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] 

(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] 

(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)  '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] 

(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)  '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] 

(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] 

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

(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)  '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] 

(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] 

(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] 
Books
Year  Publication  

(1992)  Rings and fields.
Ellis, Graham (1992) Rings and fields. : The Clarendon Press, Oxford University Press, New York. [Details] 
Book Chapters
Year  Publication  

(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] 

(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] 

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

(2010)  Computing covers of Lie algebras
Ellis, G,Mohammadzadeh, H,Tavallaee, H,Kappe, LC,Magidin, A,Morse, RF (2010) COMPUTATIONAL GROUP THEORY AND THE THEORY OF GROUPS, II Computing covers of Lie algebras , pp.2531 [Details] 

(2008)  Homological Algebra Programming
Ellis, G,Kappe, LC,Magidin, A,Morse, RF (2008) COMPUTATIONAL GROUP THEORY AND THE THEORY OF GROUPS Homological Algebra Programming , pp.6374 [Details] 
Current Postgraduate Students (Research)
Student  Degree Type  Type  

Nisreen Alokbi  Doctorate  Structured PhD (Science)  Supervisor 