Joseph (JM) Landsberg, professor of mathematics

Office: Milner 329
Phone: (979)-458- 0625
E-mail: jml@math.tamu.edu

Office hours: , Tues 1-2pm  or by appointment.

Math 666: Algebraic complexity theory
 MWF 10:20-11:10     ENPH 212     

Texts: I will hand out  von Zur Gathen's article "Feasible Arithmetic computations: Valiant's hypothesis"
as well as class notes on the first day of class.

Outline:

Part I: Introduction and backround
 A. What is complexity theory?
 B. Multi-linear algebra  
 C. Cook's hypothesis,
 D. Valiant's hypothesis
 E. Projective algebraic geometry

Part II: Permanent v.s. Determinant:
geometry of the associated hypersurfaces, groups preserving them, singularities, dual
varieties, Reyser's formula for the permanent, explicit projections of  det onto perm,
 lower bounds for projections of  det  onto  perm  via local differential
geometry.

Part III: Holographic algorithms: 
Holographic algorithms,  the FKT algorithm,
relation to spinors, state of the art.


Part IV: The Mulmuley-Sohoni program for VP v.s. VNP:
  orbits and orbit closures in general - invariant theory, stability,
nomality, representations of the general linear group and
the symmetric group, state of the art.