Claudiu Raicu

Department of Mathematics
University of Notre Dame
255 Hurley
Notre Dame, IN 46556

I am a Professor in the math department at University of Notre Dame. Previously I was an Instructor in the math department at Princeton University. During the Spring 2013 semester I was a post-doctoral fellow at MSRI. I received my Ph.D. in May 2011 from the math department at UC Berkeley. My advisor was David Eisenbud. My thesis was titled Secant Varieties of Segre-Veronese Varieties. I am interested in algebraic geometry, commutative algebra and related fields. Here is my CV.

Notre Dame Algebraic Geometry/Commutative Algebra Seminar

MEGA 2024 — Call for Papers

Commutative Algebra Semester, MSRI 2024

Macaulay2: expanded functionality and improved efficiency

Pragmatic 2023

MSRI/SLMath CMND Summer School on “Commutative Algebra and its Interaction with Algebraic Geometry”

D-modules, Group Actions, and Frobenius, 2021

ALGECOM-XXI, 2021

Thematic Program in Commutative Algebra and its Interactions with Algebraic Geometry, 2019 — in honor of Bernd Ulrich

A View Toward Algebraic Geometry, 2017 — a conference in honor of David Eisenbud's 70th birthday

Preprints

• Cohomology on the incidence correspondence and related questions
  (with Annet Kyomuhangi, Emanuela Marangone, Ethan Reed)
  arXiv
• Stable sheaf cohomology on flag varieties
  (with Keller VandeBogert)
  arXiv

Books

• Determinants, Gröbner bases and cohomology
  (with Winfried Bruns, Aldo Conca, Matteo Varbaro)
  Springer Monogr. Math. Springer, Cham, 2022, xiii+507 pp.
  SpringerLink
• Recent developments in commutative algebra. Levico Terme, Trento, July 1–5, 2019.
  (with Claudia Polini, Matteo Varbaro, Mark E. Walker)
  Lecture Notes in Math., 2283 C.I.M.E. Summer Sch. Springer, Cham, 2021, xi+116 pp.
  Edited by Aldo Conca, Srikanth B. Iyengar and Anurag K. Singh.
  SpringerLink

Articles

• Reduced resonance schemes and Chen ranks
  (with Marian Aprodu, Gavril Farkas, Alexander I. Suciu)
  J. Reine Angew. Math. 814 (2024), 205–240.
  arXiv | Journal
• Higher resonance schemes and Koszul modules of simplicial complexes
  (with Marian Aprodu, Gavril Farkas, Alessio Sammartano, Alexander I. Suciu)
  J. Algebraic Combin. 59 (2024), no. 4, 787–805.
  arXiv | Journal
• Some questions arising from the study of cohomology on flag varieties
  (with Zhao Gao, Keller VandeBogert)
  Proc. Sympos. Pure Math., vol. 110, 333–348.
  Open Problems in Algebraic Combinatorics, American Mathematical Society, Providence, Rhode Island, 2024.
  arXiv | Book
• Koszul modules with vanishing resonance in algebraic geometry
  (with Marian Aprodu, Gavril Farkas, Jerzy Weyman)
  Selecta Math. (N.S.) 30 (2024), no.2, Paper No. 24, 33 pp.
  arXiv | Journal
• Cohomology of line bundles on the incidence correspondence
  (with Zhao Gao)
  Trans. Amer. Math. Soc. Ser. B 11 (2024), 64–97.
  arXiv | Journal
• Borel-Moore homology of determinantal varieties
  (with András C. Lőrincz)
  Algebr. Geom. 10 (2023), no. 5, 576–606.
  arXiv | Journal
• Topological invariants of groups and Koszul modules
  (with Marian Aprodu, Gavril Farkas, Ştefan Papadima and Jerzy Weyman)
  Duke Math. J. 171 (2022), no. 10, 2013–2046.
  arXiv | Journal
• Euler obstructions for the Lagrangian Grassmannian
  (with Paul LeVan)
  Algebr. Comb. 5 (2022), no. 2, 299–318.
  arXiv | Journal
• Local Euler obstructions for determinantal varieties
  (with András C. Lőrincz)
  Topology Appl. 313 (2022), Paper No. 107984, 21 pp. Special issue: Proceedings of the conference Hyperplane Arrangements and Singularities, 2019.
  arXiv | Journal
• On some modules supported in the Chow variety
  (with Steven V Sam, Jerzy Weyman)
  Vietnam J. Math. 50 (2022), no. 2, 501–521. Special issue celebrating the 60th birthday of Bernd Sturmfels.
  arXiv | Journal
• An equivariant Hochster’s formula for S_n-invariant monomial ideals
  (with Satoshi Murai)
  J. Lond. Math. Soc. (2) 105 (2022), no. 3, 1974–2010.
  arXiv | Journal
• Bi-graded Koszul modules, K3 carpets, and Green's conjecture
  (with Steven V Sam)
  Compos. Math. 158 (2022), no. 1, 33–56.
  arXiv | Journal
• Feasibility criteria for high-multiplicity partitioning problems
  J. Pure Appl. Algebra 226 (2022), no. 6, Paper No. 106937, 22 pp.
  arXiv | Journal
• Hermite reciprocity and Schwarzenberger bundles
  (with Steven V Sam)
  Commutative Algebra, Springer, Cham, 2021, 689–721. Expository papers dedicated to David Eisenbud on the occasion of his 75th birthday, edited by Irena Peeva.
  arXiv | Book chapter
• Relations between the 2x2 minors of a generic matrix
  (with Hang Huang, Michael Perlman, Claudia Polini, Alessio Sammartano)
  Adv. Math. 386 (2021), Paper No. 107807, 29 pp.
  arXiv | Journal
• Hodge ideals for the determinant hypersurface
  (with Michael Perlman)
  Selecta Math. (N.S.) 27 (2021), no. 1, Paper No. 1, 22 pp.
  arXiv | Journal
• Regularity of S_n-invariant monomial ideals
  J. Combin. Theory Ser. A 177 (2021), Paper No. 105307, 34 pp.
  arXiv | Journal
• Iterated local cohomology groups and Lyubeznik numbers for determinantal rings
  (with András C. Lőrincz)
  Algebra Number Theory 14 (2020), no. 9, 2533–2569.
  arXiv | Journal
• Koszul modules and Green’s conjecture
  (with Marian Aprodu, Gavril Farkas, Ştefan Papadima, Jerzy Weyman)
  Invent. Math. 218 (2019), no. 3, 657–720.
  arXiv | Journal
• On the (non-)vanishing of syzygies of Segre embeddings
  (with Luke Oeding, Steven V Sam)
  Algebr. Geom. 6 (2019), no. 5, 571–591.
  arXiv | Journal
• Equivariant D-modules on binary cubic forms
  (with András C. Lőrincz, Jerzy Weyman)
  Comm. Algebra 47 (2019), no. 6, 2457–2487. Special issue in honor of Gennady Lyubeznik.
  arXiv | Journal
• Syzygies of determinantal thickenings and representations of the general linear Lie superalgebra
  (with Jerzy Weyman)
  Acta Math. Vietnam. 44 (2019), no. 1, 269–284. Special issue: Proceedings of the conference The Prospects for Commutative Algebra, 2017.
  arXiv | Journal
• Homological invariants of determinantal thickenings
  Bull. Math. Soc. Sci. Math. Roumanie (N.S.) 60(108) (2017), no. 4, 425–446. Honorary volume dedicated to Prof. Dorin Popescu.
  arXiv | Journal
• Regularity and cohomology of determinantal thickenings
  Proc. Lond. Math. Soc. (3) 116 (2018), no. 2, 248–280.
  arXiv | Journal
• Computing Schur complexes
  (with Michael K. Brown, Hang Huang, Robert P. Laudone, Michael Perlman, Steven V Sam, João Pedro Santos)
  J. Softw. Algebra Geom. 9 (2019), no. 2, 111–119.
  arXiv | Journal
• Bernstein—Sato polynomials for maximal minors and sub-maximal Pfaffians
  (with András C. Lőrincz, Uli Walther, Jerzy Weyman)
  Adv. Math. 307 (2017), 224–252.
  arXiv | Journal
• Characters of equivariant D-modules on Veronese cones
  Trans. Amer. Math. Soc. 369 (2017), no. 3, 2087–2108.
  arXiv | Journal
• The syzygies of some thickenings of determinantal varieties
  (with Jerzy Weyman)
  Proc. Amer. Math. Soc. 145 (2017), no. 1, 49–59.
  arXiv | Journal
• Local cohomology with support in ideals of symmetric minors and Pfaffians
  (with Jerzy Weyman)
  J. Lond. Math. Soc. (2) 94 (2016), no. 3, 709–725.
  arXiv | Journal
• Characters of equivariant D-modules on spaces of matrices
  Compos. Math. 152 (2016), no. 9, 1935–1965.
  arXiv | Journal
• Representation stability for syzygies of line bundles on Segre-Veronese varieties
  J. Eur. Math. Soc. (JEMS) 18 (2016), no. 6, 1201–1231.
  arXiv | Journal
• Introduction to uniformity in commutative algebra
  (with Craig Huneke)
  Commutative Algebra and Noncommutative Algebraic Geometry, I, 163–190.
  Math. Sci. Res. Inst. Publ., 67 Cambridge University Press, New York, 2015.
  arXiv | Book chapter
• Non-simplicial decompositions of Betti diagrams of complete intersections
  (with Courtney Gibbons, Jack Jeffries, Sarah Mayes, Branden Stone, and Bryan White)
  J. Commut. Algebra 7 (2015), no. 2, 189–206.
  arXiv | Journal
• Local cohomology with support in generic determinantal ideals
  (with Jerzy Weyman)
  Algebra Number Theory 8 (2014), no. 5, 1231–1257.
  arXiv | Journal
• Tangential Varieties of Segre-Veronese Varieties
  (with Luke Oeding)
  Collect. Math. 65 (2014), no. 3, 303–330.
  arXiv | Journal
• Products of Young symmetrizers and ideals in the generic tensor algebra
  J. Algebraic Combin. 39 (2014), no. 2, 247–270.
  arXiv | Journal
• Local cohomology with support in generic determinantal ideals
  (with Jerzy Weyman, Emily Witt)
  Adv. Math. 250 (2014), 596–610.
  arXiv | Journal
• 3x3 Minors of Catalecticants
  Math. Res. Lett. 20 (2013), no. 4, 745–756.
  arXiv | Journal
• Secant Varieties of Segre-Veronese Varieties
  Algebra Number Theory 6 (2012), no. 8, 1817–1868.
  arXiv | Journal
• Affine Toric Equivalence Relations are Effective
  Proc. Amer. Math. Soc. 138 (2010), no. 11, 3835–3847.
  arXiv | Journal
• Appendix to Quotients by Finite Equivalence Relations, by János Kollár
  Current developments in algebraic geometry, 227–256.
  Math. Sci. Res. Inst. Publ., 59, Cambridge University Press, Cambridge, 2012
  arXiv | Book chapter
  Macaulay2 code that verifies the assertions made in this appendix.

Reading Seminars

• Graduate reading seminar on Algebraic Curves, Fall 2018.
• Graduate reading seminar on Intersection Theory, Fall 2017.
• Undergraduate reading seminar on Coxeter groups, Fall 2013.

Macaulay2

With Michael K. Brown, Hang Huang, Robert P. Laudone, Michael Perlman, Steven V Sam, João Pedro Santos, we wrote the package SchurComplexes for computing Schur complexes. A short presentation of the package is available here.

With Michael Perlman, we wrote the package GLmnReps for computing with representations of the Lie superalgebra gl(m|n).

Here is the most up to date version (with documentation) of the Macaulay2 SchurRings package, developed jointly with Mike Stillman. A short presentation of the package is available here.

I also wrote a package implementing the push forward functor for finite ring maps.

Posters and Slides

• Slides on local cohomology with support in determinantal ideals, from the SIAM Conference on Applied Algebraic Geometry, August 1-4, 2013 at Colorado State University, Fort Collins.
• Slides on tangential varieties of Segre-Veronese varieties, from the SIAM Conference on Applied Algebraic Geometry, August 1-4, 2013 at Colorado State University, Fort Collins.
• Slides on local cohomology modules with support in ideals of maximal minors and sub-maximal Pfaffians, from the Joint International Meeting of the American Mathematical Society and the Romanian Mathematical Society, June 27 - 30, 2013, Alba Iulia, Romania.
• Slides on secant varieties of Segre-Veronese varieties, from the SIAM Conference on Applied Algebraic Geometry, October 6-9, 2011 at North Carolina State University, Raleigh.
• Poster on the GSS conjecture, from WAGS, Nov 6-7, 2010 at University of Arizona, Tucson.
• Slides on finite equivalence relations, from the Eighth AMS-SMM International Meeting, June 4, 2010 at UC Berkeley.
• Poster on finite equivalence relations, from WAGS, May 1-2, 2010 at UBC, Vancouver.

Other writings

Notes compiled together with Enric Nart during the ``Computing Integral Closure'' Workshop at MSRI, July 2010.

Mathematics Research Communities report on Boij-Söderberg Theory in the nonstandard graded case, with B. Barwick, J. Biermann, D. Cook II, W. F. Moore and D. Stamate, Snowbird, June 2010.

Teaching

Spring 2024 :

Math 80210 - Topics in Algebra

Fall 2023 :

Math 20580 - Introduction to Linear Algebra and Differential Equations

Spring 2023 :

Math 20580 - Introduction to Linear Algebra and Differential Equations

Fall 2022 :

Math 60210 - Basic Algebra I

Spring 2022 :

Math 60710 - Introduction to Algebraic Geometry

Fall 2021 :

Math 20580 - Introduction to Linear Algebra and Differential Equations

Spring 2021 :

Math 60220 - Basic Algebra II

Spring 2020 :

Math 20580 - Introduction to Linear Algebra and Differential Equations
Math 60220 - Basic Algebra II

Spring 2019 :

Math 40510 - Introduction to Algebraic Geometry
Math 80210 - Homological Commutative Algebra and Symmetry

Fall 2018 :

Math 20550 - Multivariable Calculus

Spring 2018 :

Math 30820 - Honors Algebra IV

Fall 2017 :

Math 20580 - Introduction to Linear Algebra and Differential Equations
Math 30810 - Honors Algebra III

Spring 2017 :

Math 80620 - Algebraic Geometry II

Fall 2016 :

Math 60710 - Algebraic Geometry I

Spring 2016 :

Math 80220 - Introduction to Toric Varieties

Fall 2015 :

Math 10560 - Calculus II

Spring 2015 :

Math 20580 - Introduction to Linear Algebra and Differential Equations

Spring 2014 :

Math 346 - Algebra II

Fall 2013 :

Math 345 - Algebra I
Math 984 - Junior seminar on Coxeter groups

Fall 2012 :

Math 345 - Algebra I

Spring 2012 :

Math 202 - Linear Algebra

Fall 2011 :

Math 201 - Multivariable Calculus

Spring 2011 :

Math 16B - Analytic Geometry and Calculus

Fall 2010 :

Math 54 - Linear Algebra

Spring 2010 :

Math 1B - Calculus

Fall 2009 :

Math 1B - Calculus