Student Number Theory Seminar

Xingchi Ruan, Department of Pure Mathematics, University of Waterloo

"On the Solubility of Diophantine Systems"

Given a system of r homogeneous polynomial equations with degree d with rational coefficients, we study the number of variables it needs to possess a non-trivial p-adic solution. We improve the earlier work of Leep and Schmidt, and find the most precise estimation of the upper and lower bounds for the number of variables so far. We extend the result to some other fields of interest such as Qp.

This seminar will be held jointly online and in person:

• Room: MC 5417
• Zoom information: https://uwaterloo.zoom.us/j/94550300175?pwd=QnNvZ1Eyc292SmMyeExReWdaQ3dxZz09