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Associate Professor

778.782.3794   p

778.782.4947   f

nbruin (AT) cecm.sfu.ca

SCK K10528

Dept of Mathematics CECM Personal Website

Nils Bruin

Research Interests

My research focusses on rational points on varieties. Of special interest are curves and Abelian varieties. For curves, p-adic analytic Chabauty methods in combination with algebraic covering techniques have recently yielded substantial results. The rational points of Abelian varieties, which form finitely generated groups called Mordell-Weil groups, form an important ingredient of those methods.

Mordell-Weil groups, and most importantly their free rank, are most commonly analysed using descent methods to compute Selmer groups. These provide a bound on the free rank but, unfortunately, not always a sharp one. The difference is measured by the Shafarevich-Tate group. Recently visualisation methods have been used to provide lower bounds on Shafarevich-Tate groups.