Location, time: 
MondayWednesdayFriday 9:05  9:55pm in Vincent Hall 2 
Instructor: 
Victor Reiner (You can call me "Vic"). 

Office: Vincent Hall 256
Telephone (with voice mail): 6256682
Email: reiner@math.umn.edu 
Office hours: 
Tuesdays 9:059:55am.

Study group(!): 
Tuesday 1:252:15 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 1face 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: 
 Abedessalam, Anderson and Miller,
A tridiagonal approach to matrix integrals
 Ambjorn and Chekhov,
The matrix model for dessins d'enfants
 Armstrong, Mingo, Speicher, and Wilson,
The noncommutative cycle lemma
 Bernardi and Fusy,
Unified bijections for planar hypermaps with general cyclelength constraints
 Arizmendi et al,
Relations between cumulants in noncommutative probability
 Bernardi,
An analogue of the HarerZagier formula for unicellular maps on general surfaces
 Biane and Dehornoy,
Dual Garside structure of braids and free cumulants of products
 Bini, Goulden and Jackson,
Transitive factorizations in the hyperoctahedral Group
 Bollobas and Riordan,
A polynomial invariant of graphs on orientable surfaces
 Bose, Gundry and He,
Gauge theories and dessins d' enfants: beyond the torus
 Carrell and Chapuy,
Simple recurrence formulas to count maps on orientable surfaces
 Chapuy and Stump,
Counting factorizations of Coxeter elements into products of reflections
 Chmutov and VignesTourneret,
Partial duality of hypermaps
 Ekedahl, Lando, Shapiro, and Vainshtein,
Hurwitz numbers and intersections on moduli spaces of curves
 Forrester and Warnaar,
The importance of the Selberg integral
 Goulden and Jackson,
The combinatorial relationship between trees, cacti
and certain connection coefficients for the symmetric group
 Goulden and Jackson,
Transitive factorizations into transpositions and holomorphic mappings on the sphere
 Goulden and Jackson,
A proof of the conjecture for the number of ramified coverings of the sphere by the torus
 Goulden and Jackson,
Symmetric functions and Macdonald's result for top connexion coefficients in the symmetric group
 Goulden and Nica,
A direct bijection for the HarerZagier formula
 Goulden and Yong,
Treelike Properties of Cycle Factorizations
 Goulden et al,
Monotone Hurwitz numbers in genus zero
 Goupil,
Reflection decompositions in the classical Weyl groups
 GuayPaquet and Harnad,
2D Toda taufunctions as combinatorial generating functions
 GuayPaquet and Harnad,
Generating functions for weighted Hurwitz numbers
 Harnad and Orlov,
Hypergeometric taufunctions, Hurwitz numbers and enumeration of paths
 Harer and Zagier,
The Euler characteristic of the moduli space of curves
 Krattenthaler and Mueller,
Decomposition numbers for finite Coxeter groups and generalized noncrossing partitions
 Lass,
Demonstration combinatoire de la formule de HarerZagier
 McMullen,
Moduli spaces in genus zero and inversion of power series
 Michel,
"Casefree" derivation for Weyl groups of the number of reflection factorizations of a Coxeter element
 Mingo and Speicher,
Second order freeness and fluctuations of random matrices: I. Gaussian and Wishart matrices and cyclic Fock spaces
 Novak,
Complete symmetric polynomials in JucysMurphy elements and the Weingarten function
 Speicher,
Free probability theory and random matrices
 Turner,
Riemann, Hurwitz, and branched covering spaces
 Zoladek,
The topological proof of the AbelRuffini Theorem
 Zvonkin,
Enumeration of weighted plane trees
