W dniach 19-23.11.2012 gościem Instytutu Matematycznego będzie Ton Dieker (Georgia Institute of Technology, USA). Wygłosi on cykl wykładów pod tytułem Stochastic processes and algorithms. Streszczenie: In these lectures, we discuss algorithms for sampling from high-dimensional objects. Our focus lies on Markov Chain Monte Carlo algorithms, for which one needs to analyze certain Markov chains. This requires tools for bounding mixing times for these Markov chains, and leads to excursions into topics such as isoperimetric inequalities. We also discuss an application to "ranking and selection", where the aim is to identify a \'best\' system based on noisy performance measurements. Rozkład godzin: 19.11.2012, 16.15-18.15, sala WS, IM 20.11.2012, 16.15-18.15, sala WS, IM 21.11.2012, 14.15-16.15, sala 602, IM 22.11.2012, 12.15-14.15, sala 602, IM 23.11.2012, 10.15-12.15, sala 602, IM Serdecznie zapraszamy
Ondřej Kalenda (Uniwersytet Karola w Pradze) Topological methods in Banach spaces. Harmonogram wykładów: wt, 23.10: 12:15-15:00 (WS) śr, 24.10: 14:15-16:00 (602) czw, 25.10: 14:15-16:00 (711) Opis Banach spaces are an important tool in several areas of mathematics. This theory allows us to consider complicated objects (functions, sequences, operators) as points in a space with certain structure. There are several structures on Banach spaces - metric, geometrical, topological etc. In the present minicourse we will focus on the topological point of view. We will study various topologies on Banach spaces (norm, weak, weak* and general weak topologies) and the relationship of topological properties with other type of properties. In particular, we will discuss certain duality between Banach spaces and compact spaces, properties of weakly compact sets and related classes of Banach spaces.