Carol Rifelj Faculty Lecture Series

Professor of Mathematics, David R. Dorman will give a lecture as part of the Carol Rifelj Faculty Lecture Series.

RIGHT TRIANGLES, ELLIPTIC CURVES, AND THE CONJECTURE OF BIRCH AND SWINNERTON-DYER

Mathematics is often driven by problems with deceptively simple statements that are notoriously difficult to solve or even remain unsolved. The Congruent Number Problem,
found in a 10th century manuscript asks the following innocent looking question: Given a positive integer, n, is there a right triangle, each of whose sides have rational length, that has area n? This problem has stymied mathematicians over the intervening 1100 years. We will trace the history of this problem, demonstrate its interplay with number theory, geometry, algebra and analysis, show its connection with elliptic curves and bring us to the frontier of modern mathematics with the Birch and Swinnerton-Dyer Conjecture. The only mathematics you need to know is from high school!