(2021.12.10 9:00-10:00)Ziqing Xiang :Designs and codes

Time:2021-12-07  Source:

  Title: Designs and codes

  Speaker:Ziqing Xiang (Institute of Mathematics, Academia Sinica)

  Time: 2021.12.10 9:00-10:00

  Venue: 617-589-031 Passport:314159

  Abstract: Given a space, designs are finite subsets that approximate the whole space, and codes are finite subsets has good separation properties in the space. These two concepts are closely related to each other, and both have many applications. On spheres, typical examples of designs and codes come from shells of lattices and orbits of finite groups. A central problem in the study of designs and codes is to find small designs and find large codes. I will first give an overview of the theory on general spaces, and then discuss various constructions, bounds, and existence and nonexistence results on both general spaces and specific interesting spaces. Such interesting spaces include geometric spaces such as spheres, and combinatorial spaces such as Johnson association schemes. At the end, I will discuss their connections with other branches of mathematics.