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# Irena Peeva

Professor

### Departments/Programs

- Mathematics

### Graduate Fields

- Mathematics

## Research

Commutative Algebra

My primary work is in Commutative Algebra, and my primary research is focused on Free Resolutions and Hilbert Functions. I have also done work on the many connections

of Commutative Algebra with Algebraic Geometry, Combinatorics, Computational Algebra, Noncommutative Algebra, and Subspace Arrangements, and I remain very interested in these fields as well.

The study of free resolutions and Hilbert functions is a beautiful and core area in Commutative Algebra. It contains a number of challenging conjectures and open problems. The idea to associate a free resolution to a module was introduced by Hilbert in his famous paper "Über the Theorie von algebraischen Formen." Resolutions provide a method for describing the structure of modules.

## Courses

## Publications

*Counterexamples to the Eisenbud-Goto regularity conjecture*, (with J. McCullough), Journal of the AMS**31**(2018), 473–496.*Tor as a module over an exterior algebra*, (with D. Eisenbud and F.-O. Schreyer), Journal of the EMS, to appear.*Minimal free resolutions over complete intersections*, (with D. Eisenbud), research monograph, Lecture Notes in Mathematics**2152**, Springer, 2016.*Hilbert schemes and Betti numbers over Clements-Lindström rings*, (with S. Murai), Compositio Mathematica**148**(2012), 1337–1364.*Graded Syzygies*,*Flips and Hilbert schemes over exterior algebras*, (with M. Stillman), Mathematische Annalen**339**(2007), 545-557.*Connectedness of Hilbert schemes*, (with M. Stillman), Journal of Algebraic Geometry**14**(2005), 193–211.*Finite regularity and Koszul algebras*, (with L. Avramov), American Journal of Mathematics**123**(2001), 275–281.*The lcm-lattice in monomial resolutions*, (with V. Gasharov and V. Welker), Mathematical Research Letters**6**(1999), 521–532.*Generic lattice ideals*, (with B. Sturmfels), Journal of the AMS**11**(1998), 363–373.*Complete intersection dimension*, (with L. Avramov and V. Gasharov), Publications Mathématiques IHÉS**86**(1997), 67–114.