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Professor Hamkins undertakes research in pure mathematics, with a focus on mathematical logic and set theory. The theme for much of his work has been the mathematics and philosophy of the infinite. He has been particularly interested in the interaction of two important topics in set theory, namely, the method of forcing, the technique set theorists have used to build alternative mathematical universes, and large cardinals, the strongest known axioms of infinity. He has presented a new class of forcing axioms and undertaken an investigation of the modal logic of forcing, aiming to uncover some of the most general principles of forcing. He has done work in group theory and the connections between set theory and group theory in the context of the automorphism tower problem. In the area of infinitary computability theory, he has introduced infinite time Turing machines, providing a new theoretical model of infinitary computation. Professor Hamkins maintains a very active research program, publishing in the top journals in his field. He has been invited to speak on his research at diverse forums in Austria, Britain, France, Germany, Japan, The Netherlands, Spain, Turkey and all over the United States. He is an energetic organizer of conferences and seminars.

Professor Hamkins earned his Ph.D. at the University of California at Berkeley in 1994 and his B.S. at the California Institute of Technology 1988, with honor. He came to CUNY in 1995, and has held visiting positions at UC Berkeley, at Kobe University in Japan, at Carnegie Mellon University and at the University of Muenster in Germany.

He is currently supervising the dissertations of three Ph.D. students at The CUNY Graduate Center, and teaches all levels of undergraduate mathematics courses at the College of Staten Island.