Kevin Milans : Teaching : Spring 2017 Math773: Extremal Combinatorics

Kevin Milans (milans@math.wvu.edu)
Office: Armstrong Hall 408H
Office Hours: TuWTh 11:00am-12:00pm, and by appointment
Class Meetings: TuTh 2:30pm-3:45pm in Armstrong Hall 203
Home | Course Syllabus (PDF) | Homework

Sources

Course Schedule

No. Date Class Summary Source(s) Comments
1 Jan 10 Introduction; Mantel's Theorem; Turán's Theorem C1 -
2 Jan 12 Turán's Theorem; Ore's condition C1,C2 HW1 assigned.
3 Jan 17 Erdős--Sós; Erdős--Stone--Simonovits I C2,C3 -
4 Jan 19 Erdős--Stone--Simonovits II C3 -
5 Jan 24 Mean square density; Szemerédi's regularity lemma I C4 -
6 Jan 26 Szemerédi's regularity lemma II C4,C5 HW1 due; HW2 assigned.
7 Jan 31 Triangle Counting Lemma; Triangle removal lemma C5,C6 -
8 Feb 2 Corners; Roth's Theorem; Behrend's Construction C6 -
9 Feb 7 Embedding Lemma; Erdős--Stone--Simonovits via regularity C7 -
10 Feb 9 Ruzsa--Szemerédi; (6,3)-theorem L3 -
11 Feb 14 Ramsey Theory W 10.2 -
12 Feb 16 Graph Ramsey Theory W 10.2 HW2 due; HW3 assigned.
13 Feb 21 Linear Ramsey Numbers for Bounded Degree Graphs W 10.2 -
14 Feb 23 Stability; exact Turan result for odd cycles L4 -
15 Feb 28 Bipartite Turan Theory C8 -
16 Mar 2 Prob. Method Tutorial; Bipartite Turan number lower bound C8 -
17 Mar 14 Dependent Random Choice; Turan Theory for bounded max degree C9 -
18 Mar 16 Poset Turan Theory - HW3 due; HW4 assigned.
19 Mar 21 Bondy--Simonovits: cycle + chord coloring lemma C 10 -
20 Mar 23 Bondy--Simonovits: proof C 11 -
21 Mar 28 Hypergraph Turan Theory: de Caen's bounds C 14 -
22 Mar 30 Hypergraph Turan Theory: upper bound C 14 -
23 Apr 4 Hypergraph Turan Theory: construction C 15 -
24 Apr 6 Hales--Jewett: background, applications J Ch. 26 HW4 due.
25 Apr 11 Hales--Jewett: proof J Ch. 26 HW5 assigned.
26 Apr 13 Absorption I: introduction, nearly spanning subgraphs - -
27 Apr 18 Absorption II: approximate Corradi-Hajnal - -
28 Apr 20 Absorption III: approximate to exact (sketch) - -
29 Apr 25 Hajnal-Szemeredi - -
30 Apr 27 Kierstead-Kostochka proof of Hajnal-Szemeredi - -
milans@math.wvu.edu