Översikt

  • Allmänt


    The course has ended.

    Lecture notes and exercise sheets will be cleaned up and available here.


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    All lectures and exercise sessions have been completed for Period II.  The first lecture in Period III will be on 13.1.2023.


    This course introduces the theory of vertex operator algebras (VOA), both their structure and representation theory. VOA is a mathematical framework that gives an algebraic formulation of two-dimensional conformal field theory. VOAs also have application to a lot of fields of mathematics from geometry to number theory. One of the most prominent example is the moonshine phenomenon; a mysterious relationship between finite groups and modular forms. One or two of those applications will be discussed.

    Here is important course information:

    Credits: 5

    The lecturer is Shinji Koshida (shinji.koshida@aalto.fi).

    The lectures are held on Fridays in periods II and III. The first lecture will be on 28.10.

    • Time: 12-14
    • Place: M3 (Undergraduate center)

    The exercise sessions are held every two weeks on Fridays. The first session will be on 4.11.

    • Time: 14-16
    • Place: M3 (Undergraduate center) during period II, M2 (Undergraduate center) during period III

    The grading is NOT numerical, but only pass/fail. There is no exam for this course. The evaluation will be based on performance in the exercise sessions.

    Prerequisites: MS-C1081 Abstract algebra, MS-C1342 Linear algebra (MS-E1200 Lie groups and Lie algebras and MS-C1300 Complex Analysis can be helpful)


    References

    • James Lepowsky and Haisheng Li, Introduction to Vertex Operator Algebras and Their Representations, https://doi.org/10.1007/978-0-8176-8186-9.
    • Victor G. Kac, Vertex Algebras for Beginners, American Mathematical Soc., 1998.
    • Edward Frenkel and David Ben-Zvi, Vertex Algebras and Algebraic Curves, American Mathematical Soc., 2004.