About

Irena Peeva is a Distinguished Professor of Arts & Sciences in the Department of Mathematics at Cornell University. Her primary research area is Commutative Algebra, with a focus on Free Resolutions and Hilbert Functions. She has also worked on the connections of Commutative Algebra with Algebraic Geometry, Combinatorics, Computational Algebra, Noncommutative Algebra, and Subspace Arrangements. Her work on free resolutions and Hilbert functions involves a core area in Commutative Algebra that contains numerous challenging conjectures and open problems. Peeva's research includes associating free resolutions to modules, a concept introduced by Hilbert, which provides a method for describing the structure of modules. She has contributed to the field through various publications, including research monographs and articles in reputable journals.

Research topics

• Mathematics
• Pure mathematics
• Combinatorics
• Arithmetic
• Mathematical analysis
• Statistics
• Discrete mathematics

Selected publications

• Koszul binomial edge ideals

  Forum of Mathematics Sigma · 2026-01-01

  articleOpen accessSenior author

  Abstract The study of Koszul binomial edge ideals was initiated by V. Ene, J. Herzog, and T. Hibi in 2014, who found necessary conditions for Koszulness. The binomial edge ideal $J_G$ associated to a finite simple graph G is always generated by quadrics. It has a quadratic Gröbner basis if and only if the graph G is closed. However, there are many known nonclosed graphs G where $J_G$ is Koszul. We characterize the Koszul binomial edge ideals by a simple combinatorial property of the graph G .

  PublisherOA PDFDOI

• Koszul Binomial Edge Ideals

  arXiv (Cornell University) · 2026-01-21

  preprintOpen accessSenior author

  As the binomial edge ideal of a graph is always generated by homogeneous quadratic polynomials corresponding to the edges of the graph, the question of when a binomial edge ideal defines a Koszul algebra has been studied by many authors ever since the class of ideals was first defined. Several partial results are known, including a characterization of those binomial edge ideals that possess a quadratic Gröbner basis. However, a complete characterization of the graphs determining Koszul binomial edge ideals has remained elusive. Inspired by our recent work characterizing when the graded Möbius algebras of graphic matroids are Koszul, we answer the question once and for all by proving that a graph defines a Koszul binomial edge ideal if and only if it is strongly chordal and claw-free.

  PublisherDOI

• Koszul graded Möbius algebras and strongly chordal graphs

  Selecta Mathematica · 2025-03-05

  articleSenior author
  PublisherDOI

• Koszul Graded Möbius Algebras and Strongly Chordal Graphs

  arXiv (Cornell University) · 2024-12-24

  preprintOpen accessSenior author

  The graded Möbius algebra of a matroid is a commutative graded algebra which encodes the combinatorics of the lattice of flats of the matroid. As a special subalgebra of the augmented Chow ring of the matroid, it plays an important role in the recent proof of the Dowling-Wilson Top Heavy Conjecture. Recently, Mastroeni and McCullough proved that the Chow ring and the augmented Chow ring of a matroid are Koszul. We study when graded Möbius algebras are Koszul. We characterize the Koszul graded Möbius algebras of cycle matroids of graphs in terms of properties of the graphs. Our results yield a new characterization of strongly chordal graphs via edge orderings.

  PublisherOA PDFDOI

• Syzygies over a polynomial ring

  EMS Press eBooks · 2023-12-15

  book-chapterOpen access1st authorCorresponding
  PublisherOA PDFDOI

• Closed binomial edge ideals

  Journal für die reine und angewandte Mathematik (Crelles Journal) · 2023-08-30

  article1st authorCorresponding

  Abstract We prove a conjecture by Ene, Herzog, and Hibi (2011) that the Betti numbers of the binomial edge ideal <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msub> <m:mi>J</m:mi> <m:mi>G</m:mi> </m:msub> </m:math> {J_{G}} of a closed graph G coincide with the Betti numbers of its lex initial ideal <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msub> <m:mi>M</m:mi> <m:mi>G</m:mi> </m:msub> </m:math> {M_{G}} . We describe the Betti numbers of the ideal <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msub> <m:mi>M</m:mi> <m:mi>G</m:mi> </m:msub> </m:math> {M_{G}} .

  PublisherDOI

• Binomial edge ideals over an exterior algebra

  MATHEMATICA SCANDINAVICA · 2023 · 1 citations

  1st authorCorresponding
  • Mathematics
  • Pure mathematics
  • Statistics

  We introduce the study of binomial edge ideals over an exterior algebra.

  PublisherDOI

• The Regularity Conjecture for prime ideals in polynomial rings

  EMS Surveys in Mathematical Sciences · 2021 · 3 citations

  Senior authorCorresponding
  • Mathematics
  • Combinatorics
  • Pure mathematics

  This paper presents a survey on recent developments on regularity of prime ideals in polynomial rings.

  PublisherDOI

• Layered resolutions of Cohen–Macaulay modules

  Journal of the European Mathematical Society · 2020 · 6 citations

  Senior authorCorresponding
  • Mathematics
  • Pure mathematics
  • Arithmetic

  Let S be a Gorenstein local ring and suppose that M is a finitely generated Cohen–Macaulay S -module of codimension c . Given a regular sequence f_1, \ldots, f_c in the annihilator of M we set R = S/(f_1, \ldots, f_c) and construct layered S -free and R -free resolutions of M . The construction inductively reduces the problem to the case of a Cohen–Macaulay module of codimension c-1 and leads to the inductive construction of a higher matrix factorization for M . In the case where M is a sufficiently high R -syzygy of some module of finite projective dimension over S , the layered resolutions are minimal and coincide with the resolutions defined from higher matrix factorizations we described in [EP]. Our results provide a characterization of all MCM modules over a complete intersection in terms of higher matrix factorizations.

  PublisherDOI

• Quadratic complete intersections

  Journal of Algebra · 2019-12-03 · 2 citations

  articleCorresponding
  PublisherDOI

Recent grants

• CAREER: Free Resolutions

  NSF · $401k · 2004–2009

• Free Resolutions in Commutative Algebra

  NSF · $192k · 2017–2021

• Free Resolutions

  NSF · $177k · 2014–2017

• Minimal Free Resolutions and Syzygies

  NSF · $272k · 2020–2024

• Free Resolutions

  NSF · $108k · 2009–2011

Frequent coauthors

• David Eisenbud

  29 shared

• Vesselin Gasharov

  Philips (Germany)

  25 shared

• Volkmar Welker

  Philipps University of Marburg

  11 shared

• Marc Chardin

  7 shared

• Bernd Sturmfels

  7 shared

• Mike Stillman

  7 shared

• Jason McCullough

  6 shared

• Frank–Olaf Schreyer

  5 shared

Awards & honors

• A&S honors 10 faculty with endowed professorships
• Two mathematics professors honored with 2019 Simons Fellowsh…