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Date | Who | What | Minutes |
W-M 1/30 - 2/4 | T.Z. | Overview of matroids: sources, axioms, examples, drawings, etc. | - |
W 2/6 | Jackie | Prove 1.3.10. | 30 |
W 2/6 | Eric | Prove 1.4.10. | 10 |
H 2/7 | Yash | Prove 1.4.11. | 5 |
H 2/7 | Garry | Prove 1.6.2. | 30 |
F 2/8 | Eric | Describe L(M) for a paving matroid. | 15 |
F 2/8 | Simon | Prove L(M) is a geometric lattice. | 30 |
M 2/11 | Jackie | Prove a geometric lattice L gives a matroid (whose lattice is L). | 30 |
M-W 2/11-13 | T.Z. | Duality for matrices. | - |
F 2/15 | Eric | Prove 2.1.1, (2.1.3). Order dual need not be geometric. | 25 |
F 2/15 | Garry | 2.1.11, 16, 17. | 20 |
F 2/15 | Yash | Exer. 2.1.10. | 20 |
M 2/18 | Simon | Prove Prop. 2.1.20. | 20 |
M 2/18 | Jackie | Prove Prop. 2.2.22 & lemmas. | 25 |
W 2/20 | Eric | Prove Prop. 2.3.3. | 10 |
W 2/20 | Garry | Prove Lemma 2.4.3. | 25 |
W 2/20 | T.Z. | Over- and underview of minors. | - |
F 2/22 | T.Z. | Points, lines, planes, and all that. | - |
F 2/22 | Yash | Prove Lemma 2.3.7. | 20 |
F 2/22 | Simon | Prove Theorem 2.4.4. | 15 |
M 2/25 | Eric | Prove 3.1.8-9. | 20 |
M 2/25 | Jackie | Prove Prop. 3.1.11. | 10 |
M 2/25 | T.Z. | Over- and underview of minors (cont'd). | - |
W 2/27 | Simon | Prove Prop. 3.2.1. | 15 |
W 2/27 | Yash | Prove Prop. 3.2.4-5. | 10 |
F 2/29 | Garry | Prove Prop. 3.2.6. | 15 |
F 2/29 | Jackie | Prove (3.2.8), present 3.2.9, prove Prop. 3.2.10, show 3.2.11. | 30 |
F 2/29 | T.Z. | Preview of connectedness. | - |
M-W 3/3-5 | Simon | Prove Prop./Cor. 3.3.1-4. | 20 |
M-W 3/3-5 | Garry | Prove the Scum Theorem, 3.3.5-7. | 25 |
W 3/5 | Yash | Prove Prop. 4.1.6, 8. | 25 |
F 3/7 | Eric | Prove Prop. 4.1.2. | 15 |
F 3/7 | Jackie | Prove Prop. 4.2.1. | 15 |
F-M 3/7-10 | Simon | Prove Prop. 4.3.6. | 25 |
M 3/10 | Eric | Prove Prop. 4.3.5. | 20 |
M 3/10 | Jackie | Prove Prop. 5.1.3, 2, 4. | 25 |
M 3/10 | T.Z. | Half and loose edges in graphs. | - |
W 3/12 | Garry | Construction on top of page 141; 5.1.5. | 20 |
W 3/12 | Yash | Prove Theorem 5.2.2 and lemmas. | 30 |
W 3/12 | T.Z. | Projective and affine geometry (quick course): Projective and affine planes/spaces over a field; Homogeneous coordinates; Constructions from AG(F,d) and from Fd+1. | - |
- | - | In 5.3.1-6 and 5.4.11, try for a proof that is not very technical but uses pictures to be intuitive, fast, and reasonably rigorous. | - |
Th 3/13 | Jackie | Lemma 5.3.4: fast proof by picture. | 15 |
Th 3/13 | Eric | Lemmas 5.3.5-6: fast proof by picture. | 30 |
F 3/14 | Simon | Theorem 5.3.1: fast proof by picture (assuming all lemmas). | 25 |
F 3/14 | T.Z. | Projective and affine geometry (quick course): Affine and projective flats, The three (four, for R or C) approaches to projective spaces. | - |
M 3/17 | Yash | Lemma 5.4.11: fast proof by picture. | 10 |
M 3/17 | Garry | Theorem 5.4.10. | 15 |
M 3/17 | T.Z. | Projective and affine geometry (quick course): Analytic vs. synthetic, Synthetic axiomatic definitions, Desargues' Theorem and coordinatizability; the special case of planes. | - |
W 3/19 | Garry | Prove Prop. 6.1.13. | 10 |
W 3/19 | Simon | Prop. 6.2.5. | 25 |
W 3/19 | T.Z. | Equivalent representations: the real story. | - |
M 3/31 | Yash | Prop. 6.2.3(i). | 10 |
M 3/31 | T.Z. | q-Factorials, q-analogs; Problems with exact definition of PG(r-1,q); Modular matroids and projective geometries; Preview of the rest of Ch. 6. | - |
W 4/2 | Garry | Example 6.3.12. | 10 |
W 4/2 | T.Z. | Matroid automorphisms, semilinear transformations, and equivalent representations. Constructing linear representations. | - |
Th 4/3 | Everyone | Exer. 5.3.4: Try to figure it out! | |
F 4/4 | Jackie | Lemma 6.4.4 (all details!). | 25 |
F 4/4 | Eric | Prop. 6.4.5. | 10 |
F 4/4 | Simon | Theorem 6.4.7. | 25 |
M 4/7 | Jackie | Prop. 6.4.8 with Lemma 6.4.9. | 15 |
M 4/7 | Eric | Lemma 6.4.13. | 15 |
M 4/7 | Simon | Prop. 6.5.5. | 10 |
W 4/9 | Garry | Lemma 6.6.2 as corrected. | 25 |
W 4/9 | Simon | Prop. 6.9.2 (iii)->(ii). | 20 |
W 4/9 | Yash | Cor. 6.9.6. | 10 |
F 4/11 | Jackie | Prop. 6.9.7. | 30 |
F 4/11 | Garry | Theorem 6.9.9 (i)->(ii). | 15 |
F 4/11 | T.Z. | Single-element extensions and coextensions; modular cuts and linear classes; elementary lifts. | - |
M 4/14 | Eric | Prop. 6.9.11. | 15 |
M 4/14 | Yash | Prop. 7.1.4 CP . | 25 |
M 4/14 | T.Z. | Continuing single-element extensions, etc. | - |
W 4/16 | Garry | Theorem 7.1.16(i). | 30 |
W 4/16 | Simon | Prop. 7.1.21: explain how the construction works (Fig. 7.6). | 10 |
W 4/16 | T.Z. | Biased graphs and their matroids. | - |
Th 4/17 | T.Z. | More on biased graphic matroids. | - |
Th 4/17 | Jackie | Lemma 7.2.1. | 15 |
Th 4/17 | Simon | Theorem 7.2.2 (R3). | 30 |
F 4/18 | Eric | Example 7.2.3 (be thorough). | 15 |
F 4/18 | Yash | Example 8.1.16. | 15 |
F 4/18 | Jackie | Theorem 8.2.6. | 15 |
F 4/18 | T.Z. | Characteristic polynomial. | - |
W 4/23 | Garry | Prop. 8.1.10. | 15 |
W 4/23 | Yash | Lemma 8.3.2. | 10 |
W 4/23 | T.Z. | Signed and gain graphs, characteristic polynomial, and hyperplane arrangements. Readings on the polynomial in Chapter 7 of Combinatorial Geometries. | - |
Th 4/24 | Eric | Lemma 8.3.3. | 20 |
Th 4/24 | Simon | Theorem 8.3.1. | 20 |
Th 4/24 | T.Z. | Tutte polynomial. Readings in Chapter 7 of Combinatorial Geometries. | - |
F 4/25 | Jackie | Example 8.4.2 | 20 |
F 4/25 | Yash | Theorem 9.1.2 (iii)⇒(ii) | 20 |
F 4/25 | Garry | Theorem 9.1.2 (vi)⇒(vii) | 10 |
M 4/28 | Simon | Theorem 9.1.2 (viii)⇒(i) | 25 |
M 4/28 | Eric | Prop. 9.2.4. (Be efficient!) | 20 |
M 4/28 | Jackie | Prop. 11.1.1. (Be efficient!) | 15 |
W 4/30 | Yash (cancelled) | Lemma 11.1.6. | 15 |
W 4/30 | Garry | Lemma 11.1.8. | 30 |
W 4/30 | T.Z. | Wheels and whirls as biased graphs. | - |
Th 5/1 | Simon | Derive Cors. 11.2.5-6 from Cor. 11.2.7. | 10 |
Th 5/1 | Jackie | Cors. 11.2.1-2. | 25 |
Th 5/1 | Eric | Lemma 13.1.6 (explaining how this proof uses signed graphs). | 25 |
Th 5/1 | Garry | Prop. 13.2.1: state and explain; no proof. | 10 |