Math 7590: Graphs on Surfaces (a.k.a. Dessins D'enfant

Additional Course Information

Basic Course Structure

Math 7590:      Seminar in Topology: Graphs on Surfaces

Time/Place:     1:30 p.m. - 3:00 pm TTh --- 119 Lockett Hall.

Instructor:     Neal Stoltzfus

Email:          stoltz@math.lsu.edu

Office:         Lockett 258:   578.1656

Office Hours:   TTh 10:30am or by appointment

Web Page:	URL: http://www.math.lsu.edu/~stoltz/Courses/F09/7590/

                This site will contain this document on course information, 
                and links to additional web resources.

Prerequisite:   Point-set topology, fundamental groups and modules over rings, basic Galois theory.

Textbook:   Lando-Zvonkin, Graphs on Surfaces and Their Application

Textbook Website: Lando-Zvonkin Textbook

Author Abstract: Graphs drawn on two-dimensional surfaces have always attracted researchers by their beauty and by the variety of difficult questions to which they give rise. The theory of such embedded graphs, which long seemed rather isolated, has witnessed the appearance of entirely unexpected new applications in recent decades, ranging from Galois theory to quantum gravity models, and has become a kind of a focus of a vast field of research. The book provides an accessible introduction to this new domain, including such topics as coverings of Riemann surfaces, the Galois group action on embedded graphs (Grothendieck's theory of "dessins d'enfants"), the matrix integral method, moduli spaces of curves, the topology of meromorphic functions, and combinatorial aspects of Vassiliev's knot invariants and, in an appendix by Don Zagier, the use of finite group representation theory. The presentation is concrete throughout, with numerous figures, examples (including computer calculations) and exercises, and should appeal to both graduate students and researchers.

Instructor Choice: The study of fixed embeddings of graphs in surfaces is known by many names: dessin d'enfant, rotation systems, combinatorial maps, ribbon graphs, inter alia. The course will develop the equivalences between the following objects:

	We will cover Chapters:  1,2,3(parts),4 and 6, if time permits

Portfolio & Project:  The portfolio for the course primarily consists of a project which develops a
	topic related to graphs embedded on surfaces. An oral presentation of your 
	project will be made during the last weeks of class. A written report will be submitted
	by the Final Exam date.  More portfolio Information .

Grades:  Grading will be weighted as follows:

	Project:  		 50%
	Research Paper Reviews:  20%
	Other "portfolio" items: 30%