國家理論科學研究中心(南區)數學組

Coordinator:

Ching Hung Lam (NCKU)

Vertex Algebras, Lie Algebras, Finite Group Theory

chlam@math.ncku.edu.tw

Tel: +886-6-2757575 Ext. 65142

 

Participants:

  1. Wen-Fong Ke(NCKU)
  2. Ngau Lam(NCKU)
  3. Ching Hung Lam(NCKU)
  4. Shu-Yen Pan(NCKU)
  5. Yung Yu(NCKU)

 

Topics:

In this project, we shall study certain algebraic structures with its original from mathematical physics. Our main aim is to obtain various applications of such structures to mathematical physics and other areas such as finite group theory, number theory and operator algebras. We shall concentrate on the following three themes.

  1. Vertex operator algebras and their applications to finite groups
    The main focus will be on the study of the famous Moonshine VOA and the application to the Monster simple group and the Moonshine phenomenon.
  2. Representations of groups and Lie algebras
    Topics include theta correspondence and local Langlands parameters of a classical group over a local field and Howe duality and dual pairs of Lie (super)algebras and vertex operator algebras.
  3. Quantum Algebraic Codes and Quantum Algorithms
    The main focus is on constructing algebraic quantum error correcting codes and explicitly finding efficient coding and decoding schemes. We will also try to develop quantum algorithms for solving difficult problems in algebras.