Math 689, fall 2005:
Computational complexity and geometry Homepage.
Meeting MWF 9-9:50 in Milner 216

Instructor: Joseph (JM) Landsberg

Office: Milner 329

Phone: (979)-458- 0625
E-mail: jml@math.tamu.edu
office hours: Tues 3-4pm, Wed. 4-5 pm or by appointment.

Syllabus: We will cover material from chapters 15,17,19 and 20 of
Algebraic complexity theory by Burgisser et. al rephrased in geometric
language, as well as basics regarding geometry of subvarieties of projective
space and the representation theory of the general linear group, with almost
exclusive emphasis on aspects relevant to the study of matrix multiplication,
that is, the study of secant varieties of  triple Segre products.

Prerequisite: A good backround in linear algebra.

Texts:
The most important will be the class notes, which will be posted from
this webpage. All the supplementary texts will be on
reserve at Evans library. Supplementary texts include:

1.
Bürgisser, Peter; Clausen, Michael; Shokrollahi, M. Amin Algebraic complexity theory. With the collaboration of Thomas Lickteig. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 315. Springer-Verlag, Berlin, 1997. xxiv+618 pp. ISBN: 3-540-60582-7

This is the main computer science  text on the subject. One goal of this class will be to reformulate the relevant
chapters of this book in geometric language.

2.
Prasolov, V. V. Problems and theorems in linear algebra. Translated from the Russian manuscript by D. A. Le\u\i tes. Translations of Mathematical Monographs, 134. American Mathematical Society, Providence, RI, 1994. xviii+225 pp. ISBN: 0-8218-0236-4

This is mostly for students who need help with linear algebra and tensors.


3.
Fulton, William; Harris, Joe Representation theory. A first course. Graduate Texts in Mathematics, 129. Readings in Mathematics. Springer-Verlag, New York, 1991. xvi+551 pp. ISBN: 0-387-97527-6; 0-387-97495-4

We will follow chapters 4 and 6 of this book when covering the representation theory
of the general linear group.

4.
Harris, Joe Algebraic geometry. A first course. Corrected reprint of the 1992 original. Graduate Texts in Mathematics, 133. Springer-Verlag, New York, 1995. xx+328 pp. ISBN: 0-387-97716-3

This is for backround in algebraic geometry

5.
Ivey, Thomas A.; Landsberg, J. M. Cartan for beginners: differential geometry via moving frames and exterior differential systems. Graduate Studies in Mathematics, 61. American Mathematical Society, Providence, RI, 2003. xiv+378 pp. ISBN: 0-8218-3375-8

Also for backround in algebraic geometry and projective differential geometry


Homework:  There will be a weekly homework assignment, due
on Monday of each week (with the exception of the first assignment
which is due Friday Sept. 2). I will spend each Monday going over
assigned homework problems.  Assignments will be posted at least one
week in advance in the class notes (although the full set of notes may not
be available in advance).

Final project: Everyone will need to do a final project that may either
be handed in or presented to the class at the end of the semester (or both).
Students will be pretty much free to choose their own project, but must
decide upon it by October 24. Many good final projects can come from
taking a topic in chapter 16 of "Algebraic complexity theory" and
geometrizing it as we will do for matrix multiplication.

Rough plan for the course (subject to change!)

Homework Assignments and class notes:

Notes set 1.
Notes set 2. 
Notes set 3.
Notes set 4.
Notes set 5.
Notes set 6.
Notes set 7. (rough draft)
Notes set 8.
Notes set 9. (rough draft)

If you would like a copy of Lickteig's paper on secant
varieties of segre varieties, click here.
 

For more advanced students, I recommend attending the
working seminar.
Try to go at least the first week to get an idea of what its all about.

For students interested in going further in geometry, I recommend
attending the geometry seminar
at least occasionally.
 
 

Grading policy: homework 75%, Final project 25%.  Each homework assignment will only
be partially graded. You will get two grades, one noting the number of problems you attempted and one
on the graded problems.

Americans with Disabilities Act (ADA) Policy Statement

The following ADA Policy Statement (part of the Policy on Individual Disabling Conditions) was submitted to the University Curriculum Committee by the Department of Student Life. The policy statement was forwarded to the Faculty Senate for information.

The Americans with Disabilities Act (ADA) is a federal anti-discrimination statute that provides comprehensive civil rights protection for persons with disabilities. Among other things, this legislation requires that all students with disabilities be guaranteed a learning environment that provides for reasonable accommodation of their disabilities. If you believe you have a disability requiring an accommodation, please contact the Department of Student Life, Disability Services Office, in Room B116 of Cain Hall or call 862-4570.

Academic Integrity Statement

“An Aggie does not lie, cheat, or steal or tolerate those who do.” All syllabi shall contain a section that states the Aggie Honor Code and refers the student to the Honor Council Rules and Procedures on the web http://www.tamu.edu/aggiehonor


typo/correction/suggestion score sheet (1 point per correction, useful suggestion, 2 if it was
a good one):

  0  KIMBALL, JAMES LEE      
  0  KO, YOUNGDEUG           
  1  MCDONALD, TERRY LYNN   
  11  OEDING, LUKE AARON      
  2  RUFFO, JAMES VINCENT    
  16  SEO, MINJUNG 
  9  Bernardi, Alessandra