8680 Spring 2017
MF 12:05PM-1:20PM CivE 214
Papers for presentations:
1 - Sunita, May 5
2 - Carolynn, May 1
3 - Esther, May 1
4 - Eric, April 28
5 - Biesel, April 24
6 - Owen, April 24
8 - Theo, April 21
11 - Galen, May 5
12 - Tara, April 28
The topic of the course is algebraic combinatorics of electrical networks. Things to be covered if time permits:
- Rayleigh monotonicity, Polya theorem, relation to Markov chains
Random Walks and Electric Networks
- Matrix-tree theorem, loop-erased walks, Wilson's algorithm
Loop erased walks and total positivity
- Electrical networks and abelian sandpile
The Engel algorithm for absorbing Markov chains
- Inverse problem
Circular planar graphs and resistor networks
The Laplacian on planar graphs and graphs on surfaces
- Kenyon-Wilson groves
Boundary partitions in trees and dimers
Combinatorics of tripartite boundary connections for trees and dimers
- Positivity phenomena
Circular planar electrical networks II: positivity phenomena
The space of circular planar electrical networks
Proof of conjecture of Kenyon and Wilson on semicontiguous minors
- Alternating current
Tiling by rectangles and alternating current
- Half-plane property
Homogeneous multivariate polynomials with the half-plane property
Polynomials with the half-plane property and matroid theory
- Electroid varieties and cellular structure
Electroid varieties and a compactification of the space of electrical networks
The uncrossing partial order on matchings is Eulerian
Circular Planar Electrical Networks I: The Electrical Poset EP_{n}
- Cylindrical electrical networks
Inverse problem in cylindrical electrical networks