Economic phenomena occur on networks formed by agents, such as firms and financial institutions. In order to understand the dynamic nature of economy, we need to understand structures of those networks and interactions between economic agents on it. In this talk, I will review several important research results on this theme, most of which uses Japanese rich, actual (not simulated) network data, including trade (production) network of about one million firms. Community structures, simulation of effect of natural disasters, new methodology required for such inquiry are some of the topics to be covered.

The aim of this workshop is to gather researchers of high-energy and condensed-matter physics working on chiral Matter and Topology, to exchange ideas and establish collaborations to tackle unsolved issues and carry out future extensions. The workshop expects to welcome 40-60 participants who are interested in the aforementioned topics.

Organizers:
Tomoki Ozawa, Tetsuo Hatsuda (RIKEN iTHEMS)
Di-Lun Yang (RIKEN Nishina Center; YITP, Kyoto)
Chang-Tse Hsieh (Kavli IPMU / ISSP, the Univ. of Tokyo)
Jiunn-Wei Chen, Guang-Yu Guo (National Taiwan Univ.)
Hsiang-Nan Li (Academia Sinica)

Title: An introduction to operator algebras

Abstract: Operators are linear maps from a (usually an infinite dimensional) linear space (most frequently the Hilbert space) to itself, which is like matrices of infinite degree. Operators form an algebra by obvious addition and multiplication. Operators appear in most of the fields in mathematics, in algebra, in geometry, in analysis, ... Some of the key words at the beginning of these lectures are "spectral theory" "operator algebras" "Tomita-Takesaki theory". These lectures are for non-professional people.