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Melvin Hochster -LRB- born August 2 , 1943 -RRB- is an eminent American mathematician , regarded as one of the leading commutative algebraists active today .. American. United States. mathematician. mathematician. He is currently the Jack E. McLaughlin Distinguished University Professor of Mathematics at the University of Michigan .. Mathematics. Mathematics. University of Michigan. University of Michigan. Hochster attended Stuyvesant High School , where he was captain of the Math Team , and received a B.A. from Harvard University .. Harvard University. Harvard University. Stuyvesant High School. Stuyvesant High School. While at Harvard , he was a Putnam Fellow in 1960 .. Putnam Fellow. William Lowell Putnam Mathematical Competition. He earned his Ph.D. in 1967 from Princeton University , where he wrote a dissertation under Goro Shimura characterizing the prime spectra of commutative rings .. Princeton University. Princeton University. Goro Shimura. Goro Shimura. prime spectra. spectrum of a ring. He held positions at the University of Minnesota and Purdue University before joining the faculty at Michigan in 1977 .. University of Minnesota. University of Minnesota. Purdue University. Purdue University. Hochster shared the 1980 Cole Prize with Michael Aschbacher , received a Guggenheim Fellowship in 1981 , and has been a member of both the National Academy of Sciences and the American Academy of Arts and Sciences since 1992 .. Cole Prize. Cole Prize. Guggenheim Fellowship. Guggenheim Fellowship. American. United States. Michael Aschbacher. Michael Aschbacher. National Academy of Sciences. United States National Academy of Sciences. American Academy of Arts and Sciences. American Academy of Arts and Sciences. In 2008 , on the occasion of his 65th birthday , he was honored with a conference in Ann Arbor and with a special volume of the Michigan Mathematical Journal .. Michigan Mathematical Journal. Michigan Mathematical Journal. Hochster 's work is primarily in commutative algebra , especially the study of modules over local rings .. commutative algebra. commutative algebra. He has established classic theorems concerning Cohen-Macaulay rings , invariant theory and homological algebra .. invariant theory. invariant theory. homological algebra. homological algebra. invariant. invariant polynomial. For example , the Hochster-Roberts theorem states that the invariant ring of a linearly reductive group acting on a regular ring is Cohen-Macaulay .. invariant. invariant polynomial. ring. ring ( algebra ). reductive group. reductive group. regular ring. regular ring. His best-known work is on the homological conjectures , many of which he established for local rings containing a field , thanks to his proof of the existence of big Cohen-Macaulay modules and his technique of reduction to prime characteristic .. homological conjectures. homological conjectures. big Cohen-Macaulay modules. big Cohen-Macaulay modules. reduction to prime characteristic. reduction to prime characteristic. His most recent work on tight closure , introduced in 1986 with Craig Huneke , has found unexpected applications throughout commutative algebra and algebraic geometry .. commutative algebra. commutative algebra. tight closure. tight closure. Craig Huneke. Craig Huneke. algebraic geometry. algebraic geometry. Hochster has been recognized for his efforts in mentoring and popularizing mathematics through lectures and articles .. He has had more than 40 doctoral students , and the Association for Women in Mathematics has pointed out his outstanding role in mentoring women students pursuing a career in mathematics .. Mathematics. Mathematics. Association for Women in Mathematics. Association for Women in Mathematics. He is currently -LRB- since 2009 -RRB- serving as the chair of the department of Mathematics at the University of Michigan .. Mathematics. Mathematics. University of Michigan. University of Michigan. Hochster 's hobbies are cryptic crosswords and contract bridge .. cryptic crosswords. cryptic crosswords. contract bridge. contract bridge