Rate My Professor Brendan Creutz

Brendan Creutz is an Associate Professor in the School of Mathematics and Statistics in the Faculty of Engineering at the University of Canterbury in Christchurch, New Zealand. He serves as Associate Head of School (Research). His research interests lie in number theory and arithmetic geometry, particularly Brauer-Manin obstructions, explicit descent on elliptic curves and abelian varieties, local-global principles for rational and quadratic points on algebraic varieties, zero-cycles, and étale descent obstructions. Creutz obtained his PhD from Jacobs University Bremen in 2010 with a thesis entitled "Explicit second p-descent on elliptic curves." Before joining the University of Canterbury, he held teaching positions at the University of Sydney (MATH3067 Coding Theory, 2012), Universität Bayreuth (courses including Algebraic Number Theory, Cryptography, and Diophantine Equations, 2008/2009 to 2010/11), and Jacobs University Bremen (Introductory Number Theory, Complex Analysis, 2005 to 2008).

Creutz has authored numerous papers in leading mathematical journals. Select publications include "Quadratic points on intersections of two quadrics" with Bianca Viray (Algebra & Number Theory, 2023), "Brauer-Manin obstructions on hyperelliptic curves" with Duttatrey Nath Srivastava (Advances in Mathematics, 2023), "The Brauer-Manin obstruction for constant curves over global function fields" with Felipe Voloch (Annales de l'Institut Fourier, 2022), "Degrees of points on varieties over Henselian fields" with Bianca Viray (Transactions of the American Mathematical Society, 2025), "Galois invariants of finite abelian descent and Brauer sets" with Jesse Pajwani and Felipe Voloch (Bulletin of the London Mathematical Society, 2024), "Locally trivial torsors that are not Weil-Châtelet divisible" (Bulletin of the London Mathematical Society, 2013), "On the local-global principle for divisibility in the cohomology of elliptic curves" (Mathematics Research Letters, 2016), and "Two torsion in the Brauer group of a hyperelliptic curve" with Bianca Viray (Manuscripta Mathematica, 2015). His research has received over 270 citations on Google Scholar. At the University of Canterbury, he teaches courses such as Engineering Mathematics 1A, Linear Algebra, Topics in Algebra, Cryptography and Coding Theory, and Rings and Fields, often as course coordinator. Creutz organized the Number Theory Workshop in June 2024 and contributes to the COGENT research group.