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The 22nd Annual Charles R. DePrima Memorial
Bjorn Poonen Undecidability in number theory Abstract: Hilbert's Tenth Problem asked for an algorithm that, given a multivariable polynomial equation with integer coefficients, would decide whether there exists a solution in integers. Around 1970, Matiyasevich, building on earlier work of Davis, Putnam, and Robinson, showed that no such algorithm exists. But the answer to the analogous question with integers replaced by rational numbers is still unknown, and there is not even agreement among experts as to what the answer should be. Bjorn Poonen is the Claude Shannon Professor of Mathematics at MIT. He received his A.B. and Ph.D. degrees from Harvard and Berkeley, respectively, and held positions at MSRI, Princeton, and Berkeley before moving to MIT in 2008. Poonen's research focuses mainly on number theory and algebraic geometry; in particular, he is interested in the rational number solutions to equations. Poonen is the founding managing editor of Algebra & Number Theory and serves on the editorial board of several other journals. He is a fellow of the American Academy of Arts and Sciences and of the American Mathematical Society. He has received the Guggenheim, Packard, Sloan, and Rosenbaum fellowships, as well as a Miller Professorship, and received the Chauvenet Prize in 2011. Earlier, he was a fourtime Putnam Competition winner, and the unique perfect scorer out of 385,000 participants in the 1985 American High School Mathematics Exam. Thirteen mathematicians have completed a Ph.D. thesis under his guidance.
The Charles R. DePrima Memorial Undergraduate Mathematics Lecture was established by a gift from Charles R. DePrima and Margaret Thurmond DePrima. The Institute is privileged to honor the memory of Professor DePrima and his distinguished contribution to mathematics and Caltech, where he served as a faculty member for over forty years, with a lecture each year by an outstanding mathematician. Professor DePrima perceived that there were few or no special talks or seminars designed for undergraduates; he and Margaret DePrima intended that this lecture series would fill that need. 
