Irena Peeva

Associate Professor of Mathematics

Web Site www.math.cornell.edu/~irena/ Contact Information Office:  547 Malott Hall Phone:  (607) 255-4365 Fax:  (607) 255-7149 Email:  irena@math.cornell.edu Courses & Office Hours

Education

Ph.D. (1995) Brandeis University

Research Area: Commutative algebra and algebraic geometry

My research is broad and at the interface between the fields of Commutative Algebra, Algebraic Geometry, and Combinatorics. I have worked on problems involving free resolutions, toric varieties, Hilbert schemes, complete intersections, subspace arrangements, monomial resolutions, Gröbner basis, Koszul algebras, shellings, and Castelnuovo-Mumford regularity.

Some of my research interests are focused on the structure of free resolutions and their applications. I study resolutions over polynomial rings and their quotients. In essence constructing a resolution over a ring R consists of repeatedly solving systems of R-linear equations. From another point of view, resolutions provide a homological method for describing the structure of modules (the idea to associate a resolution to a module was introduced in Hilbert's famous 1890,1893-papers).

Selected Publications

Complete intersection dimension (with L. Avramov and V. Gasharov), Publications Mathematiques IHES 86 (1997), 67–114.

Generic lattice ideals (with B. Sturmfels), J. American Mathematical Society 11 (1998), 363–373.

Deformations of codimension 2 toric varieties (with V. Gasharov), Compositio Mathematica 123 (2000), 225–241.

Finite regularity and Koszul algebras (with L. Avramov), American J. Math. 123 (2001), 275–281.

Toric Hilbert schemes (with M. Stillman), Duke Math. J. 111 (2002), 419–449.

Last modified: July 7, 2004