Lecture  Topic  Notes  Bonus Materials 
Lecture 1 (03/30/15)  Background, Matrix Tree Theorem  tex, pdf 

Lecture 2 (04/01/15)  Negative Correlation and Burton and Pemantle Theorem 
Lecture 3 (04/06/15)  Characteristic Polynomials and proof of Burton,Pemantle Theorem  tex, pdf

Lecture 4 (04/08/15)  Electrical Flows and Effective Resistance 
tex, pdf 

Lecture 5 (04/13/15)  Effective Resistance and Random Walks 
Lecture 6 (04/15/15)  An O(logn/loglogn) Approximation Algorithm for Asymmetric TSP  tex, pdf 

Lecture 7 (04/20/15) 
Lecture 8 (04/22/15) 
Lecture 9 (04/27/15)  The Pipage Rounding Method 
tex, pdf 

Lecture 10 (04/29/15)  Hyperbolic and Real Stable Polynomials 
tex, pdf 

Lecture 11 (05/04/15)  Interlacing and Strongly Rayleigh distributions 

Lecture 12 (05/06/15)  A Randomized Rounding Algorithm for STSP 
tex, pdf 

Lecture 13 (05/11/15)  A Construction of Linear size Thin Forests  tex, pdf 

Lecture 14 (05/13/15)  Spectrally Thin Subsets using Interlacing Polynomials  tex, pdf  
Lecture 15 (05/18/15)  KadisonSinger Conjecture and its Extensions 
tex, pdf 

Lecture 16 (05/20/15)  Proof of the Kadison Singer Conjecture 
Lecture 17 (06/01/15)  Cheeger's Inequality and the Sparsest Cut Problem 
tex, pdf  
Lecture 18 (06/03/15)  Existence of Spectrally Thin Trees 
tex, pdf  
Lecture 19 (05/08/15)  The Dual of Effective Resistance CP 