Diophantine and tropical geometry, and uniformity of rational points on curves

We describe recent work connecting combinatorics and tropical/ non-Archimedean geometry to Diophantine geometry, particularly the uniformity conjectures for rational points on curves and for torsion packets of curves. The method of Chabauty–Coleman lies at the heart of this connection, and we emphasize the clarification that tropical geometry affords throughout the theory of p-adic integration, especially to the comparison of analytic continuations of p-adic integrals and to the analysis of zeros of integrals on domains admitting monodromy.

Duke Scholars

Author Joseph D Rabinoff Mathematics