Karen E. Smith
University of Michigan
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Primary Section: 11, Mathematics Membership Type:
Member
(elected 2019)
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Biosketch
Karen E. Smith is a mathematician recognized for her work in commutative algebra and algebraic geometry. She is known particularly for her innovative applications of algebraic techniques in characteristic p commutative algebra to the study of higher dimensional algebraic geometry. She has made foundational contributions to the theory of tight closure and the use of the Frobenius map to understand complex algebraic varieties. Smith was born Red Bank New Jersey and grew up mostly in Holmdel, NJ. She earned an AB in mathematics from Princeton University in 1987, and a PhD from University of Michigan in 1993, also in mathematics. She was a NSF postdoctoral fellow at Purdue University and Moore Instructor at MIT, and later an Associate Professor at MIT. She is now Keeler Professor of Mathematics at the University of Michigan, where she is Associate Chair for Graduate Studies. Smith is a fellow of the American Mathematical Society. Smith is especially proud of her success training 20 PhD students and about as many post-docs, many of whom are now powerful researchers in their own right.
Research Interests
Karen Smith's research is in commutative algebra and algebraic geometry. She is known for using prime characteristic techniques in commutative algebra to solve problems in algebraic geometry and other subjects. For example, she has been a pioneer in understanding the singularities of varieties over finite fields, characterizing them by considering the action of Frobenius on local cohomology modules. Her paper linking the multiplier ideal with the test ideal has been at the center of an industry connecting the singularities and tools of the minimal model program with singularities and tools in prime characteristic commutative algebra. With Robert Lazarsfeld and Lawrence Ein, Smith discovered a surprisingly tight relationship between symbolic and ordinary powers of ideal sheaves in smooth complex varieties, founding a major field of investigation. She developed a theory of differential operators in prime characteristic for strongly F-regular rings (jointly with Michel Van den Bergh) which spawned new singularity invariants such as the F-signature.
