Petar Maymounkov's
18.317 Probability and Combinatorics on Groups with Prof. Igor Pak,
Spring 2006
Related links:
Project:
Scripted Notes:
- Script (2/8): Overview
- Script (2/10): Basic Cycle Structure of Sn
- Script (2/15): Erdös-Turan Theorem (Original proof was wrong for many years. Pak fixed it!)
- Script (2/17): Dixon's Theorem (Part I)
- Script (2/21): Dixon's Theorem (Part II)
- Script (2/22): The Random Group Process
- Script (2/24): Lubotsky and Hall Theorems
- Script (2/27): Abelian and Solvability Tests (Part I)
- Script (3/1): Abelian and Solvability Tests (Part II),
Test for G=Sn and Goldbach's Conjecture
- Script (3/3): Counting Groups
- Script (3/6): Erdös-Renyi Lemma for group isomorphisms, Group Membership Test
- Script (3/8): Product Replacement Graphs
- Script (3/10): 312-avoiding Permutations, Catalan Number on Graphs
- Script (3/13): Product Replacement Graphs
- Script (3/15): Dunwoody's Theorem, Generating Sets for Solvable Groups
- Script (3/17): Cayley Graph of An with 3 Generators, Product Replacement Algorithm
- Script (3/20): Lower-bounds on Generating Set Sizes
- Script (4/3): Random Walks (on Cayley Graphs) and Mixing Times
- Script (4/5): Mixing Time and Eigenvalues
- Script (4/7): Conductance, Strook-D.? Bound on Mixing Time
- Script (4/10): Dirichlet Forms (Part I)
- Script (4/12): Dirichlet Forms (Part II), Minimax Principle in Linear Algebra
- Script (4/19): Erdös-Renyi Machine, Self-avoiding Paths
- Script (4/21): Long Paths in Cayley Graphs
- Script (4/24): Cayley Graphs with Small Diameter over O(1) Generating Sets, Kassabov's Results, Conjecture
- Script (4/26): History of Expanders (Part I): Margulius, Kazhdan
- Script (4/28): History of Expanders (Part II): Alon, Bopana, Ramanujan Graphs
- Script (5/1): Bounded Generation, and S¥
- Script (5/3): Growth of Groups
- Script (5/5): Definition of Grigorchuk's Group
- Script (5/8): Grigorchuk's Group has Super-polynomial Growth (The Lower Bound)
- Script (5/10): Grigorchuk's Group has Sub-exponential Growth (The Upper Bound)
- Script (5/12): Group of Upper-Trianglular Matrices and its Growth, Conjecture
- Script (5/15): Continued: Viennot Representation
- Script (5/17): Percolation of Finite and Infinite Cayley Graphs
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