Kenneth Hughes

Senior Lecturer in Mathematics

Degrees: B.Sc.(Hons), Ph.D. (Cape Town); Ph.D. (Warwick)

Email: hughes@maths.uct.ac.za

Teaching and research interests:

Algebraic number theory. Homotopy. Arithmetical algebraic geometry: Diophantine problems.

Commutative Algebra: Krull rings and their generalizations. Forms of higher degree. Number-theoretic applications of Lie algebras; nil-theta functions; invariant theory. Algebraic K-theory. Number-theory in Z[x].

History of Mathematics (and History of Ideas generally, including the history of social thought and historiography). Topics in economic theory such as inflation and unemployment. Topics in South African economic history, such as the economics of racial discrimination. Liberal theories of justice and religion. Jurisprudence.

Teaching: Algebra, Number Theory, Algebraic Geometry, Lie Theory, Harmonic Analysis, Differential Geometry, History of Mathematics. History of Economics (and History of Thought generally). Economic analysis of South African problems. Legal history.

Representative publications:

1. Challenges from the Past, Social Dynamics 3 (1) (1977).

2. A grade-theoretic analogue of the Cousin complex, Quaestiones Mathematicae 9 (1986), 293-300.

3. (with Norman Bromberger) Capitalism and Underdevelopment in South Africa in Butler, Elphick and Welsh (eds), `Democratic Liberalism in South Africa', Wesleyan University Press, 1987, pp203-224.

4. Law, religion and bastardy: comparative and historical perspectives, in Burman and Preston-Whyte (eds) `Questionable Issue: Illegitimacy in South Africa', Oxford University Press, 1991, pp1-20.

5. False antithesis? -- The Debate about the Market and the State, in M. Lipton and C. Simkins, `The Market and the State in Post-Apartheid South Africa', Witwatersrand University Press, 1993.