Rugare Kwashira

Accomplished educator with extensive experience at the University of the Witwatersrand, specializing in curriculum development and student engagement. Proven track record in academic writing and mentoring, resulting in successful postgraduate dissertations. Recognized for creating dynamic learning environments that foster student success and enthusiasm for mathematics.

• Published author of academic articles in strong research areas (algebra, algebraic topology) in journals of high impact
• Accomplished academic coordinator and administrator for second years
• Successful supervision of postgraduate students resulting in successful dissertations
• Lead promoter of taught topics in algebra at the postgraduate level
• University student evaluation reports are graded at a high level showing that students appreciate my efforts to make the lectures interesting.
• my encouragement to participate and that they gained understanding of concepts with a desire to conduct further study. I also ensure that I communicate effectively, allow students to ask questions, and am available to consult outside lectures if required

• 2023, Central automorphisms in n-abelian groups, Zassenhauss Groups and Friends Conference, Binghamton, USA, virtual
• 2021, Genus of a nilpotent R-group, Zassenhauss Groups and Friends Conference, Virtual
• 2021, School on Graph Theory, virtual
• 2020, On triviality of the non-cancellation set in some classes of groups, Zassenhauss Groups and Friends Conference, Virtual
• 2017, Non cancellation set of a direct product, Groups St Andrews, University of Birmingham, UK
• 2015, Graph Compositions of suspended uniform four combs, BCC, University of Warwick, UK
• 2015, On graph operation and graph composition, SAMS, University of the Witwatersrand, South Africa
• 2013, Samelson products on function spaces, TAAG conference, University of Botswana
• 2012, Sullivan minimal models in rational homotopy theory, School of Mathematics Wits
• 2010, Sullivan minimal models of some homogeneous spaces., Algebra, Geometry and Topology Mini Conference, Gaborone
• 2010, Sullivan minimal model of homogeneous spaces and the Gottlieb group, SAMSA Conference, Gaborone
• 2008, Rational Homotopy Groups of Function Spaces, SAMSA CONFERENCE, Eduardo Mondlane University, Maputo
• 2008, Lie derivations and applications to computations of Homotopy groups, Symposium on African Women in Mathematics, Eduardo Mondlane University, Maputo
• 2007, String Homology of a product of spheres and the Witt algebra, SAMSA CONFERENCE, University of Namibia, Windhoek
• 2009, Rational Homotopy groups of Function Spaces, University of Botswana Departmental Seminars, Algebra, Geometry and Topology Group Seminars
• 2008, Introduction to Homological Algebra, University of Botswana Departmental Seminars, Algebra, Geometry and Topology Group Seminars

• ON GROUPS WHOSE SUBGROUPS ARE EITHER MODULAR OR CONTRANORMAL, Bull. Aust. Math. Soc., 105, 2022, 286-295
• Hochschild cohomology of certain Koszul Sullivan Extensions, Quaestiones Mathematicae
• RATIONAL HOMOTOPY OF MAPPING SPACES BETWEEN COMPLEX GRASSMANNIANS, Quaestiones Mathematicae, 43, 8, 2020, 1109-1120
• Uniqueness of pairings in Hopf-cyclic cohomology
• Upper bounds for the Whitehead-length of mapping spaces
• L infinity models of based mapping spaces
• On the rational cohomology of the total space of the universal fibration with an elliptic fibre

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• 2025, A Modified Prime Number Theorem: A Trigonometric Approach, Ronald Tshelametse, Kago Dikomang, Rugare Kwashira, Abebe Regassa Tufa, Journal of Algebra and its Applications, prime distribution, Sieve of Eratosthenes algorithm, Riemann zeta function, To appear
• 2023, On the Structure of the Mislin Genus of a Pullback, T. Tonisi, R. Kwashira, J.-C. Mba, Mathematics, Mislin genus, pullback, 10.3390/math11122672
• 2023, 'Non-cancellation group of a direct product', R. Kwashira, J.-C. Mba, IJPAM, Vol. 49, 2023, (417425)., localization, non cancellation, restricted genus, groups under a finite group, https://ijpm.uniud.it
• 2022, Central automorphisms in n-abelian groups, R. Kwashira, Mathematics and Statistics, 10(6), 1340-1343, 2022, Central automorphism, n-abelian, pullback, maximal subgroup, 10.13189/ms.2022.100621
• 2019, 'A note on Derivations of a Sullivan models', R. Kwashira, Communications of the Korean Mathematical Society, 34 (2019), No. 1, 279-286., Sullivan model, algebra of derivations, http://dx.doi.org/10.4134/CKMS
• 2016, 'Some properties of Extended Ladder links and Component Numbers', E. MphakoBanda, S. Mdakane, R. Kwashira, British Journal of Math. and Comp. Science, 17(4), 1-9, (2016), http://dx.doi.org/10.9734/bjmcs
• 2016, 'Graph Compositions of Uniform four q-fans', E. MphakoBanda, R. Kwashira, B. Zinsou, British Journal of Math. and Comp. Science, 15(1), 1-15, (2016), Graph compositions, closed set, cycle matroid, fan, http://dx.doi.org/10.9734/BJMCS/2016/24264
• 2015, 'Samelson Products on Function Spaces', R. Kwashira, J. -B. Gatsinzi, Bull. Korean Math. Soc., (2015), 52, 4, 1297 - 1303, Lie model, Lie algebra of derivations, Samelson product, http://dx.doi.org/10.4134/BKMS.2015.52.4.1297
• 2010, 'Cyclotomy over Products of Finite Fields and Combinatorial Applications', G.A. FernandezAlcober, R. Kwashira, L. Martinez, European Journal of Combinatorics, (2010) 31, pp. 1520-1538, cyclotomies, difference sets, Galois domain, https://doi.org/10.1016/j.ejc.2009.08.005
• 2010, 'Rational Homotopy groups of Function Spaces', J.B. Gatsinzi, R. Kwashira, Contemporary Mathematics, (2010), 519, pp 105-114, function space, generalized derivations, Gottlieb group, http://www.ams.org/publications/ebooks/ebooks
• 2008, 'String Homology of a Product of Spheres and the Witt algebra', R. Kwashira, J.-B. Gatsinzi, African Diaspora Journal of Mathematics, (2008), 6(2), pp. 55-61, Hochschild Cohomology, Lie algebras, Algebras of derivations, https://projecteuclid.org/adjm/
• 2003, 'Sobre la dimension global de posets de tipo papalote', R. Kwashira, T. Noriega Sanchez, Ciencias Matematicas, (2003), 21 (1), pp. 115, POSETS, algebras associated to POSETS, projective resolutions, Homological dimension of path algebras

Non-cancellation in groups with abelian automorphism groups, R. Kwashira, J.-C. Mba, Non-cancellation in semi direct products with torsion p-subgroup, R. Kwashira, On triviality of the non-cancellation set in some classes of groups, R. Kwashira, J.-C. Mba, On the structure of a group action as a groupoid (Honors), Asymptotic geometric property of the genus of a nilpotent group (PhD), Genus of a R-nilpotent group (PhD), The description of a nilpotent group as a groupoid (Manuscript), Central automorphisms of groups with contranormal subgroups (Manuscript), On the structure of the Mislin Genus of a pullback (Manuscript)

• 2025, Nilpotent R-powered groups, Carl Ginster, Wits, 1606558
• 2024, Asymptotic geometric property of the genus of a nilpotent group, Thandile Tonisi, Wits, 124739
• 2021, The genus of an R-powered group, Carl Ginster, Wits, 1606558
• 2021, α-nilpotent groups, Paballo Mafaralala, Wits, 1104294
• 2020, Non cancellation set for a semidirect product with torsion subgroup a p-group, Carl Ginster, Wits, 1606558
• 2019, Genus of a pullback, Thandile Tonisi, Wits, 124739
• 2019, Conjugacy classes of the automorphism group of a finite group, Rosina Motsisi, Wits, 867062
• 2018, Non cancellation in the class of FC groups, Rosina Motsisi, Wits, 867062
• 2017, The effect of a group structure G on the non-cancellation set, Elliot Lubisi, Wits, 606539
• 2017, Non cancellation set of a group G, Donald Moyo, Wits, 567121
• 2016, Toeplitz graphs associated with rings, M. Mamba, Wits, 588122
• 2016, Unit graphs associated with Rings, Elliot Lubisi, Wits, 606539
• 2015, The Wiener index and Wiener polynomial of a suspended Y-tree, Nolwazi Dube, Wits, 565597
• 2014, Cohomology of matrix Lie algebras and Nilpotent Lie algebras, Neo Lethulwe, Wits, 455974

• Lecturing Mathematics courses at both undergraduate level and postgraduate level.
• Providing students with detailed, useful feedback on module subjects, results and performance assessments.
• Improving Maths module courses for different program levels which give rise to academic and professional improvements.
• Training/guiding student tutors, associate lectures on teaching (tutorials for student tutors) and marking and filing of results.
• Module administration work e.g. coordination of specific module and leading and guiding lecturers who are involved in group teaching of a specific module.
• Providing scholarly service to profession, for example, peer reviewing of various scholarly articles.