Diophantine Approximation and Algebraic Curves (17w5045)
Michael Bennett (University of British Columbia)
Aaron Levin (Michigan State University)
Jeff Thunder (Northern Illinois University)
Clearly these topics have intrigued mathematicians for a very long time. The techniques applied have been varied, but machinery originating here has also found use in a wide variety of fields. To mention just one example, it was noted over a century ago that the theories being developed over the rational number field applied equally well to fields of transcendence degree one over a finite field ("function fields"). Now curves defined over finite fields and their corresponding function fields are a cornerstone of modern computer coding theory.
During the proposed conference, experts in the areas of linear forms in logarithms, heights, the subspace theorem, the connections between Diophantine approximation and Nevanlinna theory, and others will come together with those in elliptic curves, abelian varieties and other closely related subjects in algebraic geometry. It is hoped that new light may be shed and insight gained into questions such as the existence of elliptic curves of large rank, the complete solution to certain families of equations, and deeper connections between the approximation of algebraic numbers and algebraic properties of curves and surfaces.