Matroid Theory Presentation Schedule

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Daily assigned presentations

DateWhoWhatMinutes
W-M 1/30 - 2/4T.Z.Overview of matroids: sources, axioms, examples, drawings, etc.-

W 2/6JackieProve 1.3.10.30
W 2/6EricProve 1.4.10.10
H 2/7YashProve 1.4.11.5
H 2/7GarryProve 1.6.2.30
F 2/8EricDescribe L(M) for a paving matroid.15
F 2/8SimonProve L(M) is a geometric lattice.30

M 2/11JackieProve a geometric lattice L gives a matroid (whose lattice is L).30
M-W 2/11-13T.Z.Duality for matrices.-
F 2/15EricProve 2.1.1, (2.1.3).
Order dual need not be geometric.
25
F 2/15Garry2.1.11, 16, 17.20
F 2/15YashExer. 2.1.10.20

M 2/18SimonProve Prop. 2.1.20.20
M 2/18JackieProve Prop. 2.2.22 & lemmas.25
W 2/20EricProve Prop. 2.3.3.10
W 2/20GarryProve Lemma 2.4.3.25
W 2/20T.Z.Over- and underview of minors.-
F 2/22T.Z.Points, lines, planes, and all that.-
F 2/22YashProve Lemma 2.3.7.20
F 2/22SimonProve Theorem 2.4.4.15

M 2/25EricProve 3.1.8-9.20
M 2/25JackieProve Prop. 3.1.11.10
M 2/25T.Z.Over- and underview of minors (cont'd).-
W 2/27SimonProve Prop. 3.2.1.15
W 2/27YashProve Prop. 3.2.4-5.10
F 2/29GarryProve Prop. 3.2.6.15
F 2/29JackieProve (3.2.8), present 3.2.9, prove Prop. 3.2.10, show 3.2.11.30
F 2/29T.Z.Preview of connectedness.-

M-W 3/3-5SimonProve Prop./Cor. 3.3.1-4.20
M-W 3/3-5GarryProve the Scum Theorem, 3.3.5-7.25
W 3/5YashProve Prop. 4.1.6, 8.25
F 3/7EricProve Prop. 4.1.2.15
F 3/7JackieProve Prop. 4.2.1.15
F-M 3/7-10SimonProve Prop. 4.3.6.25

M 3/10EricProve Prop. 4.3.5.20
M 3/10JackieProve Prop. 5.1.3, 2, 4.25
M 3/10T.Z.Half and loose edges in graphs.-
W 3/12GarryConstruction on top of page 141; 5.1.5.20
W 3/12YashProve Theorem 5.2.2 and lemmas.30
W 3/12T.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 3/13JackieLemma 5.3.4: fast proof by picture.15
Th 3/13EricLemmas 5.3.5-6: fast proof by picture.30
F 3/14SimonTheorem 5.3.1: fast proof by picture (assuming all lemmas).25
F 3/14T.Z.Projective and affine geometry (quick course):
  Affine and projective flats,
  The three (four, for R or C) approaches to projective spaces.
-

M 3/17YashLemma 5.4.11: fast proof by picture.10
M 3/17GarryTheorem 5.4.10.15
M 3/17T.Z.Projective and affine geometry (quick course):
  Analytic vs. synthetic,
  Synthetic axiomatic definitions,
  Desargues' Theorem and coordinatizability; the special case of planes.
-
W 3/19GarryProve Prop. 6.1.13.10
W 3/19SimonProp. 6.2.5.25
W 3/19T.Z.Equivalent representations: the real story.-

M 3/31YashProp. 6.2.3(i).10
M 3/31T.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 4/2GarryExample 6.3.12.10
W 4/2T.Z.Matroid automorphisms, semilinear transformations, and equivalent representations.
Constructing linear representations.
-
Th 4/3EveryoneExer. 5.3.4: Try to figure it out!
F 4/4JackieLemma 6.4.4 (all details!).25
F 4/4EricProp. 6.4.5.10
F 4/4SimonTheorem 6.4.7.25

M 4/7JackieProp. 6.4.8 with Lemma 6.4.9.15
M 4/7EricLemma 6.4.13.15
M 4/7SimonProp. 6.5.5.10
W 4/9GarryLemma 6.6.2 as corrected.25
W 4/9SimonProp. 6.9.2 (iii)->(ii).20
W 4/9YashCor. 6.9.6.10
F 4/11JackieProp. 6.9.7.30
F 4/11GarryTheorem 6.9.9 (i)->(ii).15
F 4/11T.Z.Single-element extensions and coextensions; modular cuts and linear classes; elementary lifts.-

M 4/14EricProp. 6.9.11.15
M 4/14YashProp. 7.1.4 CP .25
M 4/14T.Z.Continuing single-element extensions, etc.-
W 4/16GarryTheorem 7.1.16(i).30
W 4/16SimonProp. 7.1.21: explain how the construction works (Fig. 7.6).10
W 4/16T.Z.Biased graphs and their matroids.-
Th 4/17T.Z.More on biased graphic matroids.-
Th 4/17JackieLemma 7.2.1.15
Th 4/17SimonTheorem 7.2.2 (R3).30
F 4/18EricExample 7.2.3 (be thorough).15
F 4/18YashExample 8.1.16.15
F 4/18JackieTheorem 8.2.6.15
F 4/18T.Z.Characteristic polynomial.-

W 4/23GarryProp. 8.1.10.15
W 4/23YashLemma 8.3.2.10
W 4/23T.Z.Signed and gain graphs, characteristic polynomial, and hyperplane arrangements.
Readings on the polynomial in Chapter 7 of Combinatorial Geometries.
-
Th 4/24EricLemma 8.3.3.20
Th 4/24SimonTheorem 8.3.1.20
Th 4/24T.Z.Tutte polynomial.
Readings in Chapter 7 of Combinatorial Geometries.
-
F 4/25JackieExample 8.4.220
F 4/25YashTheorem 9.1.2 (iii)⇒(ii)20
F 4/25GarryTheorem 9.1.2 (vi)⇒(vii)10

M 4/28SimonTheorem 9.1.2 (viii)⇒(i)25
M 4/28EricProp. 9.2.4. (Be efficient!)20
M 4/28JackieProp. 11.1.1. (Be efficient!)15
W 4/30Yash (cancelled)Lemma 11.1.6.15
W 4/30GarryLemma 11.1.8.30
W 4/30T.Z.Wheels and whirls as biased graphs.-
Th 5/1SimonDerive Cors. 11.2.5-6 from Cor. 11.2.7.10
Th 5/1JackieCors. 11.2.1-2.25
Th 5/1EricLemma 13.1.6 (explaining how this proof uses signed graphs).25
Th 5/1GarryProp. 13.2.1: state and explain; no proof.10


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