Course Archives Theoretical Statistics and Mathematics Unit

Course: Games, Graphs and Algebra Level: Undergraduate Time: Currently not offered

Syllabus Past Exams Syllabus: Divisors - Dollar Game, Picard and Jacobian groups. Discrete Laplacian, Matrixtree theorem and Structure of Picard group. Dhar’s algorithm and Abel-Jacobi map. Acylic orientations. Rank function, Riemann-Roch theorem on graphs and applications. Sandpiles, Sandpile group and Recurrent sandpiles. Existence, Uniqueness and Dhar’s burning algorithm. Harmonic morphisms. Riemann Hurwitz formula. ADDITIONAL TOPICS FROM: Parking functions and divisors on complete graphs; Matroids and Tutte Polynomials, Merino’s theorem for superstable configurations; Introduction to Abelian networks. Reference Texts: (a) S. Corry and D. Perkinson. Divisors and Sandpiles: An Introduction to ChipFiring (b) B. Bond and L. Levine. Abelian Networks: Foundations and Examples, arXiv:1309.3445v1. (c) D. Perkinson, J. Perelman and John Wilmes. Primer for the Algebraic Geometry of Sandpiles, arXiv:1112.6163 Top of the page Past Exams

Midterm 25.pdf Semestral 25.pdf Supplementary and Back Paper 25.pdf Top of the page

[ Semester Schedule ][ Statmath Unit ] [Indian Statistical Institute]