Academy of Mathematics and Systems Science, CAS Colloquia & Seminars | Speaker: | 向子卿,Institute of Mathematics, Academia Sinica | Inviter: | | Title: | Designs and codes | Time & Venue: | 2021.12.10 09:00-10:00 腾讯会议:617-589-031 会议密码: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. | | | |