Department of Mathematics

MA 792B-001 – Vertex Algebras

Spring 2008, TH 10:15-11:30 am, HA 377

Project presentations: May 5, 12-4 pm, HA 274

Instructor: Dr. Bojko Bakalov, office HA 138, phone 513-7442, email bojko_bakalov at ncsu dot edu

Office Hours: TH 1:00-2:00 pm or by appointment, in HA 138.

Prerequisite: Linear Algebra (MA 520). Knowledge of Lie algebras (MA 720) is useful but not required.

Course Objectives: This is an introduction to vertex algebras starting from scratch. Several important examples of vertex algebras will be studied in detail. If time permits, we will also discuss topics of current research interest, including representation theory and Zhu theory.

Texts: Vertex Algebras for Beginners, by Victor G. Kac, AMS Univ. Lecture Series vol. 10, 2nd corrected ed., 2001, ISBN: 082181396X;

Introduction to Vertex Operator Algebras and Their Representations, by J. Lepowsky and H. Li, Birkhäuser Boston, 2004, ISBN: 0817634088.

I will mostly follow the first book. Both books are recommended but not required. Suggestion: Buy the first one directly from AMS if you are an AMS member; buy the second one from Amazon.

Web Resources: WolfWare (Grade Book and Feedback), calendars and exam schedules, math courses, history of mathematics.

Syllabus can be found here, and a tentative plan of the lectures here.

Homework will be assigned regularly and will be collected every Thursday at 10:15 am. Collaboration on the homework is allowed but everyone should write their own solutions. Selected problems will be discussed in class. Click here for Homework Assignments.

Presentation: At the end of the course every student will have to give a presentation on a topic related to but not covered in the lectures. The topics will be chosen about a month in advance with the help of the instructor. The project presentations are scheduled for Monday, May 5, 2008 from 12-4 pm in HA 274.

Grade will be based on the presentation (60%), homework (30%), and attendance and class participation (10%).

Attendance: Students are expected to arrive on time, to contribute to group work and class discussions, and to stay until the class ends. Attendance at all meetings of the class is expected. Occasional absences will be approved if they meet University policies.

Adverse Weather: Announcements regarding scheduled delays or the closing of the University due to adverse weather conditions will be broadcast on local radio and television stations and posted on the University homepage.

Cell Phones: Pagers, cellular phones and other types of telecommunication equipment are prohibited from use during class. Make sure that any pagers, phones or other equipment are turned OFF during the class period. If you have a special need to have your pager or phone on during class, please let me know.

Academic Integrity Statement: Students are required to follow the NCSU policy.  “Academic dishonesty is the giving, taking, or presenting of information or material by a student that unethically or fraudulently aids oneself or another on any work which is to be considered in the determination of a grade or the completion of academic requirements or the enhancement of that student's record or academic career.’’ (NCSU Code of Student Conduct). The Student Affairs website has more information.

Students with Disabilities: Reasonable accommodations will be made for students with verifiable disabilities. In order to take advantage of available accommodations, students must register with Disabilities Services for Students. Click here for more information on the NCSU policy on working with students with disabilities.

Class Evaluations: Online class evaluations will be available for students to complete during the last two weeks of class. Students will receive an email message directing them to a website where they can login using their Unity ID and complete evaluations. All evaluations are confidential; instructors will never know how any one student responded to any question, and students will never know the ratings for any particular instructors.