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# Irena Peeva

Professor and Director of Graduate Studies

### 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.

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

### Fall 2020

- MATH 4315 : Linear Algebra with Supplements
- MATH 4900 : Supervised Research
- MATH 4901 : Supervised Reading
- MATH 6340 : Commutative Algebra with Applications in Algebraic Geometry

## 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,**21**(2019), 873–896.*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.