From the mapping class group via codes to generalized Kummer manifolds | |
Student No.： | 50 |
Time： | 16:30-17:30, 2016-9-30 (Fri.) |
Instructor： | Matthias Kreck [Bonn University] |
Place： | Lecture hall, Floor 3, Jin Chun Yuan West Building |
Starting Date： | 2016-9-30 |
Ending Date： | 2016-9-30 |
Abstract:
Codes are in this lecture binary linear codes. Codes seem to be completely boring mathematical objects but surprisingly there are special codes, self dual codes, which are related to some very interesting mathematical areas including number theory. This will be shortly explained. The construction of interesting codes is a difficult question. The fact that they occur from other areas of mathematics like algebraic geometry or topology might help. I will explain a construction which associates to a diffeomorphism on a Riemannian surface a self dual code. This leads to the question, which self dual codes occur this way. This is an open question. Examples show that many interesting codes occur this way. Fundamental properties of the corresponding codes can be seen from a construction of some 4-manifolds which widely generalize the construction of the famous Kummer surface. This itself leads to interesting open questions about 4-manifolds.