Mathematical Sciences: Free Resolutions in Commutative Algebra

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This award supports research on free resolutions in commutative algebra. The principal investigator will study a conjecture of Vasconcelos, the Poincare series and asymptotic behavior of betti numbers of modules over rings with small linking number, higher order multiplication in Tor-algebras, and the cokernel of generic exterior multiplication. This research is concerned with a number of questions in commutative algebra and algebraic geometry. Algebraic geometry studies solutions of families of polynomial equations. One can either study the geometry of the solution set or approach problems algebraically by investigating certain functions on the solution set that form what is called a commutative ring. This dual perspective creates a close connection between commutative algebra and algebraic geometry.