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, level algebras, commuting nilpotent matrices.
Papers and Publications
Annotated publication list
(Includes brief descriptions, and some context)
Overheads from talk "Irreducible components of families of level algebras.''
at Fields Insitute, Toronto, August 2006 (pdf). See related article, ArXiv posting just below.
Article (with M. Boij) ``Reducible family of height three level algebras'', J. Algebra 321 (2009), pp. 86-104.
ArXiv AC 0707.2148 (ArXiv version).
Article (with R. Basili): ``Pairs of commuting nilpotent matrices, and Hilbert function,'' J. Algebra Vol 320/3 (2008), pp 1235-1254.
See: ``Pairs of commuting nilpotent matrices, and Hilbert function''
ArXiv AC: 0709.2304 17p.
Overheads from a talk "An algebra of commuting nilpotent matrices" at
IMAR, Bucharest, July 3, 2008. Work joint with R. Basili.
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.
drawing by Dad, for frontispiece of book
UNDERGRADUATE TEACHING, ADVISING
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 recently taught the upperclass elective Math 3533 Combinatorics, and the required course for Math majors, Math 3175 Group Theory.
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
to fields from computer science to engineering as well. It involves careful analysis of questions and problems to understand
what is being counted, so develops combinatorial skill. The course includes an opportunity for students to work together in class to develop solutions to counting problems involving
partially ordered sets, Catalan numbers, partitions, and there is opportunity to do a project.
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 recently 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.
On occasion I have taught Math 3175 Linear Algebra, a basic course
taken often in the sophomore year, that is a useful prerequisite for usually later courses such as Group Theory. I have also taught Rings and Fields, a sequel to
Math 3175 Group Theory, and individual Directed Study intended for undergrad research.
More on my undergraduate teaching philosophy, and advising.
Spring 2013 teaching
In Spring 2013 I taught Math 3533 (Combinatorial Mathematics) and Math 3175 (Group Theory)
A student from Math 3175 Spring 2011 began a combinatorics undergrad research project
related to pairs of commuting nilpotent matrices. This led to several presentations and an excellent result, this student is currently n a graduate
If you are a NU mathematics major who has taken group theory and combinatorics, and wish to discuss doing undergraduate
research in a topic related to algebra and combinatorics, please feel free to contact me. For First or Second year students, you might consider the PRISM
The Mathematics Department will soon have a web page with information about undergraduate research, including a proposed capstone course with a research focus.
In Fall 2012: Math 1365 (Introduction to Mathematical Reasoning), and Math 3175 Group Theory.
In Spring 2012: Math 3533 (Combinatorial Mathematics), and Math 3175 (Group Theory)
In Fall 2011 Section of Math 1242 Calculus 2 (coordinator)
Math 1242 Fall 2011 General Syllabus Text, list of HW problems.
Math 1242 Fall 2011 Information/policies Expectations, grading, other policies.
Math 1365 Introduction to Mathematical Reasoning (one section, MWTH at 1:35 PM).
Math 1365 Fall 2011 General syllabus. Text, grading, other policies.
In Spring 2011 I taught Combinatorial Mathematics, which emphasizes problem solving
Math 3533 Spring 2011 Syllabus Text,
list of HW problems
I provided work sheets for in class problems and we explored some topics
(partially ordered sets) using both text and supplementary notes. Students found the course understandable,
even fun (instructor rating 3.9).
This could be a good foundation for some undergraduate research.
Math 3175 Spring 2011 Syllabus
Modified from previous times I taught it. We began with much more emphasis on the basic material from chapter 0, involving number theory (Greatest common divisor, least common multiple), and learning to
understand and write proofs. This helped students prepare for later sections. A small class
allowed for individual work on problems from the text and some worksheets.
A few students who got behind due to unusual events/illness/senior tasks spent extra time, used office hours, and finished doing quite well.
As usual there was a reflection component, beginning with Thurston's
article "What is a proof"; many students liked this aspect (Instructor rating 3.7).
Past undergraduate courses
GRADUATE TEACHING, GRADUATE ADVISING, MENTORING and VISITING SCHOLARS
I have taught Algebra III (Galois Theory), Commutative Algebra, Algebraic Geometry, as well
as more specialized reading courses.
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'', online J. of Algebraic Combinatorics, 3-2013 DOI: 10.1007/s10801-013-0433-1, print version to appear, see also
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
Carol Chang, in algebraic combinatorics, and
in commutative algebra. [These are a nationally competitive
fellowship, and only about 100 are awarded through all the US, each year].
Pedro Marques (U. Edora), Spring 2012, 2013.
Roberta Basili, summer 2003,2006, 2008 (working with J. Weyman and I).
Mats Boij: various 2006-2013
Hema Srinivasan. January-June 2000.
Ruth Michler, Associate Professor, Univ. North Texas: NSF POWRE VISITOR for 2000-2001.
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 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).
Sabbatical 2007: Projects with R. Basili, M. Boij, Participant in Moduli Year at Mittag-Leffler Institute.
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,
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.
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"
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:
Some organizations involved with peacework:
American Friend's Service Committee
Physicians for Social Responsibility
Medicins Sans Frontieres