**Karl Rubin, UC Irvine**

**Abstract: **Which natural numbers occur as the area of a right triangle with three rational sides? This is a very old question and is still unsolved, although partial answers are known (for example, five is the smallest such natural number). In this talk we will discuss this problem and recent progress that has come about through its connections with other important open questions in number theory.

**Biography:** Karl Rubin is the Thorp Professor of Mathematics at the University of California, Irvine. His research deals with elliptic curves and other aspects of number theory. Rubin attended Washington DC public schools, was a Putnam Fellow as an undergraduate at Princeton, and received his Ph.D. from Harvard. He was a professor at Ohio State, Columbia, and Stanford before moving to UC Irvine in 2004. Rubin received the Cole Prize in Number Theory from the American Mathematical Society, a National Science Foundation Presidential Young Investigator award, a Humboldt Research Award, and Guggenheim and Sloan fellowships.

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