Nils Bruin

Professor & Director, Centre for Experimental and Constructive Mathematics
Department of Mathematics
Faculty of Science

Areas of interest

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.

Education

  • Ph.D. Mathematics · Leiden University · 1999

Courses

This instructor is currently not teaching any courses.