Irena Peeva

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 interests are in commutative algebra and its connections to 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 is focused on the structure of free resolutions and their applications. I study resolutions over polynomial rings and their quotients. The idea to associate a free resolution to a module was introduced in Hilbert's famous 1890,1893-papers. 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.

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.

Connectedness of Hilbert schemes (with M. Stillman), J. Alg. Geometry 14 (2005), 193–211.

Flips and Hilbert schemes over exterior algebras (with M. Stillman), Math. Ann. 339 (2007), 545–557.

Last modified: July 23, 2009