We will show how ideas from geometry can be used to solve problems in Number Theory. As a warm-up, we will show how the geometry of a circle can be used to find the formula for Pythagorean Triples. Then we will investigate how similar ideas can be used to understand rational solutions to equations of higher degree defining elliptic curves.
Bjorn Poonen received a BA from Harvard, and a Ph.D. degree from the University of California at Berkeley, where he now holds the title of Associate Professor of Mathematics. Other of his affiliations have included the Mathematical Sciences Research Institute, Princeton University, the Isaac Newton Institute, and the Universite de Paris-Sud. His main research is in number theory and algebraic geometry, but he has published also in combinatorics and probability. Recently he published a book, "The William Lowell Putnam Mathematical Competition 1985-2000: Problems, Solutions, and Commentary", with K. Kedlaya and R. Vakil. In addition, Bjorn has been a winner of USAMO, a medallist of the International Mathematical Olympiad, four-time winner of hte Putnam competition, and he is a prominent composer of Olympiad-style math problems.
|101||From US Highway 101, take the De La Cruz Boulevard/Santa Clara exit and follow the signs to El Camino and the main campus entrance.|
|280||From I-280, take I-880 north toward Oakland to the Alameda exit. Turn left onto The Alameda (which becomes El Camino Real) to the main campus entrance.|
|880||From I-880, take the Alameda exit, travel north (The Alameda becomes El Camino Real) to the main campus entrance.|