UNIVERSITY OF MINNESOTA 
SCHOOL OF MATHEMATICS

Math 8680: Topics in Combinatorics
Graphs on surfaces

Fall 2014


Location, time: Monday-Wednesday-Friday 9:05 - 9:55pm in Vincent Hall 2 
Instructor: Victor Reiner (You can call me "Vic"). 
Office: Vincent Hall 256
Telephone (with voice mail): 625-6682
E-mail: reiner@math.umn.edu 
Office hours: Tuesdays 9:05-9:55am. 
Study group(!): Tuesday 1:25-2:15 in Vincent Hall 203a.
Check out their schedule.
Prerequisites:
We will assume knowledge of basic abstract algebra, and complex analysis (e.g. analytic functions, Cauchy integral formula). Although we will review them, it would be help to have also seen a little topology of covering spaces and fundamental groups, along with some basic representation theory of finite groups,
Course content:
We plan to cover as much as we can of the beautifully written book:
S.K. Lando and A.V. Zvonkin, Graphs on Surfaces and Their Applications.
People with our library subscription can get a PDF or $25 softcover edition.
Some of the topics we should discuss are
  • Riemann surfaces as ramified coverings of the sphere
  • Hurwitz numbers, permutation factorizations
  • Maps, hypermaps, Goulden and Jackson's formula counting cacti
  • Belyi functions and dessins d'enfants
  • Harer and Zagier's formula counting 1-face planar maps on surfaces by genus, and various proofs, including
    • Wick's formula and integrals over the space of Hermitian matrices
    • Lass's proof via the BEST theorem.
Here are a few survey articles that give some overview on these topics:
Grading: Grad students who are registered for the class and want to get an A should attend regularly, and give a talk once during the semester on a paper listed below, or some other paper that you can convince the instructor is related:
Papers for student talks:
Back to Reiner's Homepage.