Rough plan of lectures for computational complexity and geometry, fall 2005


8/29: Introduction and overview, Strassen's algorithm
8/31  Tensors I
Sept.
1. Hmwk 1 discussion (HW1)
5. Tensors 2
7. lower bounds on rank, seperation lemma, extension lemma
9. lower bounds cont.
12  HW2
14 projective space, projective varieties, Zariski topology
16 examples of projective varieties, secant varieties
19 HW3
21 border rank and secant varieties of Segre varieties
23 the general linear group and its homogeneous spaces I
26 HW4
28 the general linear group and its homogeneous spaces II
30 Terracini's lemma and typical rank I
Oct.
3 HW 5
5 Terracini's lemma and typical rank II
7 Lower bounds on the border rank I
10 HW6
12 Lower bounds on the border rank II.
14 Equations for secant varieties of Segre varieties I: flattenings, set theoretic GSS conj
17 HW7
19 Equations for secant varieties of Segre varieties II: Strassen's eqns and generalizations.
21 representation theory of general linear group I
24 HW8 and hand in outline of proposed project
26 representation theory of general linear group II
28 representation theory of general linear group III
31 HW9
Nov.
2 representation theory of general linear group IV
4 more on equations, subspace varieties.
7 HW10
9 TBA
11 TBA
14 HW11
16 TBA
17 TBA
21 HW12
23 no class
28 project presentations
30 project presentations
December
2 project presentations
5 project presentations