CECM Home > Members > Permanent Members > Nils Bruin

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.