Mathematics Department Home Directory Faculty List Faculty Reserach Areas Faculty in Algebra Officers & Committees
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
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.
by A. Iarrobino and V. Kanev, SLNM #1721, 346+xxix p., December, 1999.
Table of Contents
TeachingUndergraduate 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 (https://www.math.unl.edu/~ncuwm/19thAnnual/), and for another at Smith College in September http://www.math.smith.edu/center/events.php .
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.
UNDERGRADUATE TEACHING, ADVISING
J. Yameogo (Families of graded ideals):
Joachim Yameogo's Home page at University of Nice. Clare D'Cruz (Multivariate Hilbert functions),Clare D'Cruz's Home page at Chennai Mathematical Institute,
Clare D'Cruz (Multivariate Hilbert functions),Clare D'Cruz's Home page at Chennai Mathematical Institute, Madras, India.
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. MichlerThe 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 20Ð22, 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-Organized "Syzygy" Conference at NU, Mentoring, Issues in Academic Tenure Process, Referee,
Reviews by A. Iarrobino
(requires access to MathSciNet).
Hiking, Swimming, Sea Kayaking, International Exchange/Visits,
Art and Design, Psychology/Counseling, Dance
Some other math links:
Visual Calculus (U. Tenn)
Optimal packing problems: sphere packingAn 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.
A few other links:
2014 conference on the history of Science for the People at U. Massachusetts, Amherst,
Last modified May 15, 2013.URL: http://www.math.neu.edu/~iarrobino/mathindex.html