Melvin Hochster

Melvin Hochster ( born August 2, 1943 in Brooklyn, New York) is an American mathematician who has made in the field of commutative algebra outstanding contributions. He is currently the Jack E. McLaughlin Distinguished University Professor of Mathematics at the University of Michigan in Ann Arbor.

Hochster attended Stuyvesant High School, received his BA in 1964 from Harvard University in 1967 and his Ph.D. from Princeton University under Goro Shimura for a work that characterizes the spectrum of a Noetherian ring. He served from 1967 to 1973 positions at the University of Minnesota and then to 1977 a professorship at Purdue University. In 1976 he came first as a visiting professor at the University of Michigan. Hochster 1980 he received the Cole Price ( alongside Michael Aschbacher ), 1982, a Guggenheim Fellowship and is a member of the National Academy of Sciences and the American Academy of Arts and Sciences since 1992.

Hochster works mainly in the field of commutative algebra, in particular on modules over local rings. He proved key phrases about Cohen- Macaulay rings, invariant theory and homological algebra. The set of Hochster - Roberts says that the invariant ring of a reductive linear group Cohen- Macaulay is. Much of his work relates to homological conjectures, many of which he could in the case that the rings contain a body, confirm, by proving the existence of so-called big Cohen- Macaulay modules. Another focus is the proof technique of reduction to positive characteristic. In this direction, the theory of tight closure (such as ' tighter financial statements '), the Hochster 1986 is introduced along with Craig Huneke and has a variety of applications in homological algebra, commutative algebra and algebraic geometry.

Hochster supervised more than thirty doctoral students, in his spare time he enjoys playing bridge.

In 1978 he was invited speaker at the International Congress of Mathematicians in Helsinki ( Cohen- Macaulay rings and modules).

His doctoral Karen Smith belongs.