Thesiss

Let K be a number field and let C be a curve of genus g > 1 defined over K. In this dissertation we describe techniques for bounding the number of K-rational points on C. In Chapter I we discuss Chabauty techniques. This is a review and synthesis of previously known material, bo…

Real algebraic geometry has a long and beautiful history going back to the 1800s. It is the study of real polynomials using algebraic techniques. Convex optimization plays a key role in applied mathematics and engineering, studying the geometric structure of convex sets that ari…