Наредни састанак Семинара биће одржан у петак, 13. децембра 2024. године, у сали 301ф Математичког института САНУ са почетком у 14.15.
Предавач: Stephan Klaus, Mathematisches Forschungsinstitut Oberwolfach
Наслов предавања: CONFIGURATION SPACES IN PROBABILITY THEORY, TOPOLOGY AND MATHEMATICAL PHYSICS
Апстракт: Consider a subset M of the n-dimensional Euclidean space, for example an embedded smooth manifold. A k-sample from M is given by (randomly) choosing k points on M, where the order can be part of the data or not. Moreover, repetitions can be allowed or not. This defines 4 types of spaces of all possible k-samples from M. These spaces have an induced topology and are playing prominent roles also in other branches of mathematics, such as topology and mathematical physics. We give a report on the basic facts for the topology of these space. In particular, the limit space RM is very interesting in topology (if k tends to infinity, repetitions allowed, no order). Here R is a commutative ring which can be interpreted as a „particle charge“ on the sample points.