A biennial conference series in Arithmetic Geometry has been held in Stellenbosch since 1997. The next instalment takes place 14-18 January 2018. Click here
for more information.
See below for some of the recent conferences in this series: 2005 2007 2009 2011 2013 2015 (held at AIMS) 2017
I work in Number Theory. More specifically, my main interst lies in Arithmetic Geometry, where I work on Elliptic curves, Drinfeld modules, Drinfeld modular forms
and related topics. I also sometimes work on more elementary things, such as Ducci sequences.
Publications
Note: for copyright reasons, some of the following PDF files are not the final, published versions.
Discovery and analysis
of gamma doradus type pulsations in the F0 IV star HR 2740 QW pup,
Mon. Not. R. Astron. Soc.292 (1997), 621-630.
(4th author, with E. Poretti, C. Koen, P. Martinez, D. de Alwis and H. Haupt)
[PDF]
Line profile variations in the spectra of the gamma Dor star HR 2740,
In: IAU Symposium 185
"New Eyes to See Inside the Sun and Stars", (F.-L. Deubner, J. Christensen-Dalsgaard, D. Kurtz, eds) Kyoto, Japan, 18-22 August, 1997, p. 387.
(5th author, with E. Poretti, L. Mantegazza, C. Koen, P. Martinez,
D. De Alwis and H. Haupt).
[PDF]
Strategy and complexity of the game of squares.
Bull. London. Math. Soc30 (1998), 274-282.
(With Mike Robson)
[PDF]
A note on a paper by Glaser and Schöffl.
Fibonacci Quart.36.5 (1998), 463-466.
[PDF]
Ducci sequences over abelian groups.
Comm. Algebra27.12 (1999), 5999-6013.
[PDF]
Heights of CM points on complex affine curves.
Ramanujan J.5 (2001), 311-317.
[PDF]
Distinguished liftings and the André-Oort conjecture.
Quaest. Math.25(3) (2002), 363-380.
[PDF]
La conjecture d'André-Oort pour le produit de deux
coubres modulaires de Drinfeld. C. R. Math. Acad. Sci. Paris335 (2002), no. 11, 867--870.
[PDF]
Higher Heegner points on elliptic curves over function
fields. J. Number Theory104 (2004), 315-326.
[PDF]
Images of isogeny classes on modular elliptic curves.
Math. Res. Lett.11 (2004), 649-651.
[PDF]
The André-Oort conjecture for products of Drinfeld modular
curves.
J. reine angew. Math.579 (2005), 115-144.
[PDF]
Monodromy groups associated to non-isotrivial Drinfeld modules
in generic characteristic. In:
"Number Fields and Function Fields - Two Parallel Worlds",
(G. van der Geer, B. Moonen, R. Schoof, eds.),
Progress in Mathematics, 239,
p61-69,
Birkhäuser Verlag, 2005.
(With Richard Pink.)
[PDF]
CM points on products of Drinfeld modular curves.
Trans. Amer. Math. Soc.359 (2007), 1351-1374.
[PDF]
Ducci sequences and cyclotomic polynomials.
Finite Fields Appl.13 (2007), 293-304.
(With Ernest Lötter and Brink van der Merwe.)
[PDF]
Ducci sequences in higher dimensions. Integers: Electronic Journal of Combinatorial
Number Theory7 (2007), #A24.
[PDF]
The André-Oort conjecture for Drinfeld modular varieties.
C. R. Math. Acad. Sci. Paris, Ser. I, 344 (2007), 733-736. [PDF]
Heegner points and the rank of elliptic curves over large extensions of global fields.
Canadian J. Math.60 (2008), no.3, 481-490. (With Bo-Hae Im)
[PDF]
Drinfeld modular polynomials in higher rank.
J. Number Theory129 (2009), 59-83. (With Hans-Georg Rück)
[PDF]
Torsion bounds for elliptic curves and Drinfeld modules.
J. Number Theory130 (2010), 1241-1250.
[PDF]
Ducci sequences and cyclotomic fields.
J. Difference Equ. Appl.16 (2010), no. 7, 847-862.
[PDF]
Special subvarieties of Drinfeld modular varieties.
J. reine angew. Math.668 (2012), 35-57.
[PDF]
Newton identities for Weierstrass products.
Amer. Math. Monthly119, no. 9 (2012), 796-799.
[PDF]
Explicit Drinfeld moduli schemes and Abhyankar's generalized iteration conjecture.
J. Number Theory160 (2016), 432-450.
[PDF]
Drinfeld modular polynomials in higher rank II: Kronecker congruences.
(With Hans-Georg Rück).
J. Number Theory165 (2016), 1-14.
[PDF]
On certain Drinfeld modular forms of higher rank. (with Dirk Basson).
J. Théor. Nombres Bordeaux29 no.3 (2017), 827-843.
[PDF]
Drinfeld modular forms of arbitrary rank, Part I : Analytic theory. (With Dirk Basson and Richard Pink).
ArXiV:1805.12335
Drinfeld modular forms of arbitrary rank, Part II: Relation with algebraic theory. (With Dirk Basson and Richard Pink).
ArXiV:1805.12337
Drinfeld modular forms of arbitrary rank, Part III: Examples. (With Dirk Basson and Richard Pink).
ArXiV:1805.12339
Periods of Ducci sequences and odd solutions to a Pellian equation. [PDF]
Academic qualifications
B.Sc, Hons.B.Sc, University of Stellenbosch, 1997, 1998.
D.E.A., Université Pierre et Marie Curie (Paris 6), 1999.
Ph.D., Université Denis Diderot (Paris 7), 2002.
(Thesis: Sur la conjecture d'André-Oort et courbes
modulaires de Drinfeld (On the André-Oort conjecture
and Drinfeld modular curves)
[PDF]
, Supervisor: Marc Hindry)
Gerard Louw, M.Sc cum laude, 2016, "Elliptic Curve Cryptography"
Taboka Prince Chalebgwa, M.Sc cum laude, 2016, "Geometry of complex polynomials: On Sendov's Conjecture"
(joint supervision with Gareth Boxall);
M.Sc (AIMS), 2014, "Critical points of complex polynomials"
Edwin Phiri, M.Sc (AIMS), 2016, "Arithmetic of polynomials"
Safidy Nandrianina Ratsimbazafy, M.Sc (AIMS), 2015, "The law of quadratic reciprocity"
Tseliso Paul Lekhoaela, M.Sc (AIMS), 2014, "The perfect numbers"
Dirk Basson, Ph.D, 2014, "On the coefficients of Drinfeld modular forms of higher rank".
Yann Ranorovelonalohotsy, M.Sc, 2014, "The Riemann Hypothesis for the zeta function of a function field over a finite field".
AIMS Postgraduate Diploma, 2012, "Meromorphic functions and vector fields".
Darlison Nyirenda, AIMS Postgraduate Diploma, 2011, "Reduction of elliptic curves"
Alex Samuel Bamunoba, M.Sc cum laude, 2011, "Cyclotomic polynomials (in the parallel worlds of number theory)";
AIMS Postgraduate Diploma, 2010, "Cyclotomic Polynomials".
Koos van Zyl, Ph.D 2011. "On the Latimer-MacDuffee Theorem for polynomials over finite fields."
Emma Owusu Kwaakwah, AIMS Postgraduate Diploma, 2010, "Ducci Sequences."
Tahina Rakotoniaina: M.Sc cum laude, 2008, "Explicit class field theory for rational function fields";
AIMS Postgraduate Diploma, 2006, "Function field arithemtic".
Dimbinaina Ralaivaosaona, AIMS Postgraduate Diploma, 2007. "The Prime Number Theorem".
Paul Joubert: M.Sc cum laude, 2006. "Geometric actions of the absolute Galois group".