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Academic Staff

Dr John Michael Burns

MSc, PhD

Biography

Research Interests

Differential Geometry, Lie groups and homogeneous spaces. Algebra, Lie algebras and group theory.

Peer Reviewed Journals

	Year	Publication
	(2020)	'PARABOLIC SUBROOT SYSTEMS AND THEIR APPLICATIONS' Burns, JM;Makrooni, MA (2020) 'PARABOLIC SUBROOT SYSTEMS AND THEIR APPLICATIONS'. Glasgow Mathematical Journal, 62 :355-366 [DOI] [Details]
	(2020)	'Coxeter exponents and orthogonal complements of highest roots' Burns, JM;Makrooni, MA (2020) 'Coxeter exponents and orthogonal complements of highest roots'. Communications In Algebra, [DOI] [Details]
	(2020)	'PARABOLIC SUBROOT SYSTEMS AND THEIR APPLICATIONS' Burns, JM,Makrooni, MA (2020) 'PARABOLIC SUBROOT SYSTEMS AND THEIR APPLICATIONS'. Glasgow Mathematical Journal, 62 :355-366 [DOI] [Details]
	(2020)	'Coxeter exponents and orthogonal complements of highest roots' Burns, JM,Makrooni, MA (2020) 'Coxeter exponents and orthogonal complements of highest roots'. Communications In Algebra, [DOI] [Details]
	(1992)	'HOMOTOPY OF COMPACT SYMMETRICAL SPACES' BURNS, JM (1992) 'HOMOTOPY OF COMPACT SYMMETRICAL SPACES'. Glasgow Mathematical Journal, 34 :221-228 [Details]
	(1994)	'POLAR SETS AS NONDEGENERATE CRITICAL SUBMANIFOLDS IN SYMMETRICAL SPACES' BURNS, JM;CLANCY, MJ (1994) 'POLAR SETS AS NONDEGENERATE CRITICAL SUBMANIFOLDS IN SYMMETRICAL SPACES'. Osaka Journal Of Mathematics, 31 :533-559 [Details]
	(1994)	'ON QUASI-PERMUTATION REPRESENTATIONS OF FINITE-GROUPS' BURNS, JM;GOLDSMITH, B;HARTLEY, B;SANDLING, R (1994) 'ON QUASI-PERMUTATION REPRESENTATIONS OF FINITE-GROUPS'. Glasgow Mathematical Journal, 36 :301-308 [Details]
	(2000)	'An elementary proof of the 'strange formula' of Freudenthal and de Vries' Burns, JM (2000) 'An elementary proof of the 'strange formula' of Freudenthal and de Vries'. Quarterly Journal Of Mathematics, 51 :295-297 [Details]
	(2002)	'Weight sum formulae in Lie algebra representations' Burns, JM;Clancy, MJ (2002) 'Weight sum formulae in Lie algebra representations'. Journal Of Algebra, 257 :1-12 [Details]
	(2015)	'COMPACT HOMOGENEOUS SPACES WITH POSITIVE EULER CHARACTERISTIC AND THEIR 'STRANGE FORMULAE'' Burns, JM,Makrooni, MA (2015) 'COMPACT HOMOGENEOUS SPACES WITH POSITIVE EULER CHARACTERISTIC AND THEIR 'STRANGE FORMULAE''. Quarterly Journal Of Mathematics, 66 :507-516 [DOI] [Details]
	(2013)	'On the Jacobi equation and manifolds with multiple conjugate points' Burns, J. M. and Staunton, E. and Wraith, D. J. (2013) 'On the Jacobi equation and manifolds with multiple conjugate points'. Math. Proc. R. Ir. Acad, 113 (1):19-30 [Details]
	(2012)	'Power sums of Coxeter exponents' Burns, JM,Suter, R (2012) 'Power sums of Coxeter exponents'. Advances In Mathematics, 231 :1291-1307 [DOI] [Details]
	(2012)	'Power sums of Coxeter exponents' Burns, John M. and Suter, Ruedi (2012) 'Power sums of Coxeter exponents'. Adv. Math, 231 (3-4):1291-1307 [DOI] [Details]
	(2010)	'Recurrence relations and Dynkin diagrams' Burns, John M. and Clancy, Michael J. (2010) 'Recurrence relations and Dynkin diagrams'. Math. Proc. R. Ir. Acad, 110A (1):13-19 [DOI] [Details]
	(2009)	'Maximal order Abelian subgroups of symmetric groups' BURNS, J.M. et al. (2009) 'Maximal order Abelian subgroups of symmetric groups'. BULLETIN OF THE LONDON MATHEMATICS SOCIETY, [Details]
	(2009)	'EXPONENTS AND HIGHEST ROOT COEFFICIENTS' Burns, JM (2009) 'EXPONENTS AND HIGHEST ROOT COEFFICIENTS'. Communications In Algebra, 37 :3815-3819 [DOI] [Details]
	(2007)	'Recurrence relations, Dynkin diagrams and Plucker formulae' Burns, JM,Clancy, MJ (2007) 'Recurrence relations, Dynkin diagrams and Plucker formulae'. Glasgow Mathematical Journal, 49 :53-59 [DOI] [Details]
	(2006)	'Lattice polygons in the plane and the number 12' Burns, John M. and O'Keeffe, David (2006) 'Lattice polygons in the plane and the number 12'. Irish Math. Soc. Bull, (57):65-68 [Details]
	(2005)	'Smyth surfaces and the drehriss' Burns, JM,Clancy, MJ (2005) 'Smyth surfaces and the drehriss'. Proceedings Of The Edinburgh Mathematical Society, 48 :549-555 [DOI] [Details]
	(2002)	'Weight sum formulae in Lie algebra representations' Burns, JM,Clancy, MJ (2002) 'Weight sum formulae in Lie algebra representations'. Journal Of Algebra, 257 :1-12 [DOI] [Details]
	(2000)	'An elementary proof of the 'strange formula' of Freudenthal and de Vries' Burns, JM (2000) 'An elementary proof of the 'strange formula' of Freudenthal and de Vries'. Quarterly Journal Of Mathematics, 51 :295-297 [Details]
	(1998)	'Inequalities for Baer invariants of finite groups' Burns, J,Graham, E (1998) 'Inequalities for Baer invariants of finite groups'. Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques, 41 :385-391 [Details]
	(1997)	'On the nilpotent multipliers of a group' Burns, J,Ellis, G (1997) 'On the nilpotent multipliers of a group'. Mathematische Zeitschrift, 226 :405-428 [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):113-122 [Details]
	(1995)	'The trace of an abelian group---an application to digraphs' Burns, J. M. and Goldsmith, B. (1995) 'The trace of an abelian group---an application to digraphs'. Proc. Roy. Irish Acad. Sect. A, 95 (suppl):75-79 [Details]
	(1994)	'ON QUASI-PERMUTATION REPRESENTATIONS OF FINITE-GROUPS' BURNS, JM,GOLDSMITH, B,HARTLEY, B,SANDLING, R (1994) 'ON QUASI-PERMUTATION REPRESENTATIONS OF FINITE-GROUPS'. Glasgow Mathematical Journal, 36 :301-308 [Details]
	(1994)	'POLAR SETS AS NONDEGENERATE CRITICAL SUBMANIFOLDS IN SYMMETRICAL SPACES' BURNS, JM,CLANCY, MJ (1994) 'POLAR SETS AS NONDEGENERATE CRITICAL SUBMANIFOLDS IN SYMMETRICAL SPACES'. Osaka Journal Of Mathematics, 31 :533-559 [Details]
	(1993)	'Conjugate loci of totally geodesic submanifolds of symmetric spaces' Burns, J. M. (1993) 'Conjugate loci of totally geodesic submanifolds of symmetric spaces'. Trans. Amer. Math. Soc, 337 (1):411-425 [DOI] [Details]
	(1992)	'Homotopy of compact symmetric spaces' BURNS, JM (1992) 'Homotopy of compact symmetric spaces'. Glasgow Mathematical Journal, 34 :221-228 [Details]
	(1989)	'Maximal order abelian subgroups of symmetric groups' Burns, J. M. and Goldsmith, B. (1989) 'Maximal order abelian subgroups of symmetric groups'. Bull. London Math. Soc, 21 (1):70-72 [DOI] [Details]