Northeastern University, Department of Mathematics

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Anthony Iarrobino


Office Number:

526B NI

Phone Number:


Fax Number:


E-Mail Address:

Mailing Address:

Northeastern University
Department of Mathematics
360 Huntington Avenue,
Boston, MA 02115, USA

I grew up in Marblehead, Massachusetts, a seacoast town, in a family of artists (members of Folly Cove Designers, painting, pottery, design), went to high school there and at Phillips Academy, to M.I.T. as an undergraduate 1961-1964, and as a graduate student, Ph.D. 1970. I then moved to Austin, Texas, a city of country and folk music, teaching at University of Texas for eight years, before coming to Northeastern in 1978. I have spent several years in France, one at University of Nice as a Senior Fulbright Fellow, another in Paris, as an NSF-CNRS exchange fellow; and have made other research visits to Europe, both West and East, as well as to Japan and Vietnam.


PhD received from MIT

Areas of Interest

Algebraic geometry, commutative rings and their deformations, singularities of maps, families of points on a variety (Hilbert scheme of points), Gorenstein algebras, Waring problem for forms, hook differences of partitions, catalecticant matrices, commuting nilpotent matrices, Jordan type

Papers and Publications

Publications (list)
Annotated publication list
(Includes brief descriptions, and some context)
CV (pdf)

Overheads from talks

"Artinian Gorenstein Algebras and symmetric decomposition of the Associated Graded Algebra.''
KIAS-Research Station on Commutative Algebra, Yangpyeong, June 2016 (pdf).

"Jordan type of Multiplication Maps" at KIAS-Research Station on Commutative Algebra, Yangpyeong, June 2016, revised November, 2016 (pdf).

"Equations for loci of commuting nilpotent matrices" at CAAC: Combinatorial Algebra and Algebraic Combinatorics,at Western University, London, Ontario January 2016 (pdf).

``Types de Jordan de deux matrices nilpotentes qui commutent'' Seminar of Algebra, Topology and Geometry, University of Nice-Sofia-Antipolis, June, 2015.

"Commuting nilpotent matrices and generic Jordan type" Commutative Algebra and Algebraic Geometry Seminar, University of Southern California, April 2015.

"When do two nilpotent matrices commute?" Seminar di Algebra Geometria, Universit`a degli Studi di Genova, June 25, 2014.

"When do two nilpotent matrices commute?" Commutative Algebra and Algebraic Geometry Seminar, CUNY April 2014.

"Combinatorics of two commuting matrices" MIT Combinatorics Seminar, November, 2013.

Article (with R. Basili and L. Khatami) "Commuting nilpotent matrices and Artinian algbebras", J. Commutative Algebra (2) (Fall 2010), p. 295-325 (Froberg volume).


    Power Sums, Gorenstein Algebras, and Determinantal Varieties

    by A. Iarrobino and V. Kanev, SLNM #1721, 346+xxix p., December, 1999.

Book Homepage

drawing by Dad, for frontispiece of book


Undergraduate Research Our undergraduate research UR page is Undergraduate Research
Undergrad research has become standard requirement for graduate study, and can give insight into doing projects in industry. It also allows students to get to know professors better, and vice-versa.  The UR page mostly presents courses. There are links to summer REU opportunities.  We have been fortunate to be able to support travel of several students to Univ. of Nebraska for NCUWM (undergrad conference for women) in February, 2016 (,   and for another at Smith College in September .  

Research related capstones: Here is a syllabus for Math 4020, which I will teach in fall 2017 and have taught for several years (the 2017 syllabus will be similar to 2016)
Math4020 Syllabus- Fall 2016

There are 2 other math capstones: Math 5131 with Fourier series- modeling focus taught by Prof Jekel in fall, and Math 4025 - Applied Math capstone - data focus- taught by Prof. McOwen in the Spring.

MATH 4020 Undergraduate Research: Math 4020 has more focus on an individual or several person project: the main work of the course is to develop a substantial project. Once having chosen a project topic (with support from the instructor), students make presentations to the class that help other students understand the mathematics behind the project. A project in math 4020 can be either pure or applied and it requires writing a paper and doing research ``new to the student’’ with consultant a Mathematics Department professor or grad student (the instructor helps find this person, and that is a key aspect of choosing a project). Or, it could be an instructor the student already knows and has contacted.  The student normally meets the consultant about once a week (this is not yet at the level of a directed study or thesis project with an advisor). The class meets 3X/week, and consists almost entirely of student presentations and discussions.       Students should have had linear algebra Math 2331 and, preferably group theory Math 3175 and real Analysis (Math 3150) before taking Math 4020 (they are prereqs, can be waived by instructor). Past students have suggested that if you are planning to take Math 4020, a good idea is to choose a topic say in summer before starting the class, and preparing by reading in the area of the topic. However, most students have chosen a topic soon after beginning the class in September. Key is to choose a topic that does not require to much technical learning for the student, but which also has some room for creative thought. Students write proposal for a paper, and submit partial write ups regularly, which I comment in detail. Students also present to the class. Coming out of the course, you will have had substantial practice at writing up a technical report, and presenting to a class of non-experts.
I’D WELCOME MORE potential students in this  Fall Math 4020!  We have had about 7 in each of 2014,2015, 2016, this has been a good number for class discussion, presentations.
  There are a number of professors willing to be consultants for (math 4020) or to supervise directed study or a Junior-Senior honors thesis research project – some are listed on line and some prefer not to be listed. Students may speak with  Profs. McOwen, Jekel, Don King, Stan Eigen, or me for further information on the undergrad research opportunities.

  HONORS In Mathematics: a 2 course thesis is needed for graduating with honors in Mathematics. 


Courses: I have often in the past taught Math 1242, Calculus II for majors in Health Sciences, or Geology, Economics, Psychology. These sections are oriented toward applications of calculus to motion and problems involving the connection between rate of flow of liquids and the amount; they require use of a graphing calculator. In Math 1242 we also discuss probability density functions, as an example of the connection between rate and amount, multivariable calculus, and differential equations.
  I have often taught, Math 3175 Group Theory.
  Math 3175 Group Theory concerns symmetry, which is one of the most useful tools in mathematics and in applications of math. Math 3175 involves learning how to understand and write proofs related to group theory. It also includes in my sections a reflective component, a chance to review one's development as a mathematician/math student. There is an optional project concerning an application of group theory, that some students take. The course itself concerns the basics of group theory, but we offer optional readings in applications to physics, computer science, chemistry. Our text is Beachy and Blair, ``Abstract Algebra'', chapters 1,2, 4.
  Math 3533 Combinatorics can be a good sequel to Math 1365 for math majors, but is often taken by non-math majors, as it has relevance   Math 3175 Group Theory concerns symmetry, which is one of the most useful tools in mathematics and applications of math. Math 3175 involves learning how to understand and write proofs related to group theory. It also includes in my sections a reflective component, a chance to review one's development as a mathematician/math student.
  I have also taught Math 1365 Mathematical Reasoning course intended for incoming math majors, but often taken by other science/engineering students. This introduces the kind of careful analysis of questions and problems continued in later courses, and also a gentle introduction to proofs.

More on my undergraduate teaching philosophy, and advising.

Past undergraduate courses


Graduate Courses
I have taught Algebra III (Galois Theory), Commutative Algebra, Algebraic Geometry, as well as more specialized reading courses.

Ph.D. Students
I have been dissertation advisor to 4 Ph.D. students,: David Berman, Abderrahim Miri, Susan Diesel,
and Masoumeh (Sepideh) Shafiei.
I was informal advisor to Art Weiss who completed his Ph.D. in 2006 at Tufts, on work begun with me. His advisor was George McNinch. Art's Ph.D. dissertation is posted to ArXiv: Some non-unimodal level algebras

Masoumeh Sepideh Shafiei studied apolar varieties to determinants and permanents of generic matrices ArXiv 1212.0515 and generic symmetric matrices ArXiv 1303.1860 , and defended her dissertation in March 2013.

Postdoctoral student: Leila Khatami (2008-2011 at NU, now Assistant Professor at Union College) is coauthor of
"Commuting nilpotent matrices and Artinian algbebras", J. Commutative Algebra (2) (Fall 2010), p. 295-325 (Froberg volume, see link above), and of
``Bound on the Jordan type of a generic nilpotent matrix commuting with a given matrix'', J. of Algebraic Combinatorics, 3-2013 DOI: 10.1007/s10801-013-0433-1. See also ArXiv 1204.4635.
Dr. Khatami has written several related papers:
``The poset of the nilpotent commutator of a nilpotent matrix'' ArXiv 1202.6089, and
``The smallest part of the generic partition of the nilpotent commutator of a given matrix''ArXiv 1302.5741.

I have had a number of postdoctoral visitors, including Joachim Yameogo and Clare D'Cruz, and was senior mentor to two NSF Postdoctoral Fellows at Northeastern, Carol Chang, in algebraic combinatorics, and Hal Schenck in commutative algebra. [These are a nationally competitive fellowship, and only about 100 are awarded through all the US, each year].

Visiting Scholars
Pedro Marques (U. Edora), Spring 2012-2016
Roberta Basili, summer 2003,2006, 2008 (working with J. Weyman and I).
Mats Boij: various 2006-2015
Hema Srinivasan. January-June 2000.
Ruth Michler, Associate Professor, Univ. North Texas: NSF POWRE VISITOR for 2000-2001.


Tragic accident

Dr. Ruth Michler died Nov. 1, 2000 in an pedestrian-construction truck accident a block from the Mathematics Department. She was returning to the Department on her bike, to get printout, to apply for a Radcliffe Bunting Fellowship for 2001-2002. She had just given talks at BU's Algebra Seminar on Mon. Oct 30, and to NU's GASC Seminar on Mon. Oct 16.

Volume of Contemporary Mathematics in memory of Ruth I. Michler

  The volume, of Contemporary Mathematics ``Topics in algebraic and noncommutative geometry (Luminy/Annapolis, MD, 2001)'', is dedicated to the memory of Ruth Michler and comprises Proceedings of the Conference "Resolution of Singularities and Noncommutative Geometry'' held in Luminy, July 20Đ22, 2001 and the Algebraic Geometry Conference held in Annapolis, MD, October 25-28, 2001.
Edited by Caroline Grant Melles, Jean-Paul Brasselet, Gary Kennedy, Kristin Lauter and Lee McEwan. Contemp. Math., 324, Amer. Math. Soc., Providence, RI, 2003, xvi+233 pp. ISBN: 0-8218-3209-3.

  An article ``Dr. Ruth I. Michler's Research'' that I wrote with the help of many is p. 1-7 of the volume,

Commemorative Web Page for Dr. Ruth Michler

AWM Memorial Web Page for Dr. Ruth Michler
Ruth I. Michler Memorial Prize of AWM

Other Academic Activities:

Co-Organizer of GASC Seminar, Co-Organized "Syzygy" Conference at NU, Mentoring, Issues in Academic Tenure Process, Referee, Reviews by A. Iarrobino (requires access to MathSciNet).

Sabbatical 2007: Projects with R. Basili, M. Boij, Participant in Moduli Year at Mittag-Leffler Institute.

Other Interests:

Hiking, Swimming, Sea Kayaking, International Exchange/Visits, Art and Design, Psychology/Counseling, Dance

Some other math links:

Visual Calculus (U. Tenn)

AWM site (Association for Women in Mathematics): this site is of interest not only to women. It also has links to many resources at many levels, including programs and information for parents, teachers, and students in K-12 math.

AMS (American Mathematical Society): a main resource for mathematicians, and students or others interested in math.

Commutative Algebra Center This has many links to commutative algebra sites, conferences in Commutative Algebra, commutative algebraists.

Optimal packing problems: sphere packing

An Overview of the Kepler Conjecture, by T. Hales (1998)/A> (15 p. includes very nice historial discussion of the problem and 3p. references)

T. Hales' proof of The Kepler Sphere packing conjecture Annals of Mathematics, 2005. This is the actual proof. Pages 1065-1185 from Volume 162 (2005), Issue 3.

The thirteenth problem: Tomaso Aste and Tiziana Di Matteo Brief, readable, discussion of Kepler packing problem, finite version,2000)

Kepler problem- by Keith Devlin Short 1 page summary of the Kepler problem

T. C. Hales, A proof of the Kepler conjecture, Ann. of Math. (2) The Kepler Sphere packing conjecture solved Stacking oranges in crates as usual is the best way! (this is a link from T. Hale's homepage, with details)

Fermat's Last Theorem (from Wolfram's MathWorld). Proven by A. Wiles, with an assist by R. Taylor, 1995 Annals Paper.

Dense packings in 8 dimensions (Maryna Viazovska), and 24 dimensions (Vlazovska,H. Cohn, A. Kumar, S.D Miller, D. Radchenko).
Article by Henry Cohn A Conceptual Breakthrough in Sphere PackingAmer Math. Society Notices, February, 2017.

Mark Haiman's proof of the n! conjecture,using the ``Isospectral'' punctual Hilbert scheme, see "Hilbert schemes, polygraphs, and the Macdonald positivity conjecture".

   My review for AMS of Mark's related earlier article, "$q,t$-Catalan numbers and the Hilbert scheme" (need Math-Sci-Net access)

7 Millennium Problems (Clay Mathematics Institute)Prize problems for the next century. The site contains brief descriptions of each problem for the curious lay person, as well as links to downloadable technical accounts by experts (pdf files).

Math for K-12 students, or recreation

Geometry CenterThe Center is no longer in existence, but the site is maintained.
Science U.Fun site, maintained by a commercial spin-off of the Geometry Center.
Sonia Kovalevsky High School Mathematics Days
Ask Dr. Math(Swarthmore College Project)
Education resources (AWM)

A few other links:

2014 conference on the history of Science for the People at U. Massachusetts, Amherst,

Current revitalization of Science for the People

Some organizations involved with peacework:

American Friend's Service Committee
Physicians for Social Responsibility
Medicins Sans Frontieres

Mathematics Department Home Directory Faculty List Faculty Reserach Areas Faculty in Algebra Officers & Committees

Last modified May 15, 2013.