# Upcoming Events

## Lecture

### Introduction to Random Matrix Theory 1

September 25 at 10:00 - 16:30, 2018

Dr. Taro Kimura

Venue: #435-437, Main Research Building, RIKEN

Event Official Language: Japanese

## Lecture

### Introduction to Random Matrix Theory 2

September 26 at 10:00 - 16:30, 2018

Dr. Taro Kimura

Venue: #435-437, Main Research Building, RIKEN

Event Official Language: Japanese

## Colloquium

### Economic Networks: a Physicist's View

October 3 at 15:00 - 16:30, 2018

Prof. Hideaki Aoyama (Senior Visiting Scientist, iTHEMS)

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.

Venue: Large Meeting Room, 2F Welfare and Conference Building (Cafeteria), RIKEN

Broadcast: R511, Computational Science Research Building, R-CCS, Kobe Campus, RIKEN / SUURI-COOL (Kyoto), #204-205, 2F Maskawa Building for Education and Research, North Campus, Kyoto University / SUURI-COOL (Sendai), #303, 3F AIMR Main Building, Advanced Institute for Materials Research (AIMR), Tohoku University

Event Official Language: English

## Math Lecture

### Theory of Operator Algebras (4th)

October 18 at 15:30 - 17:00, 2018

Dr. Yosuke Kubota (Research Scientist, iTHEMS)

Venue: Seminar Room #160, 1F Main Research Building, RIKEN

Event Official Language: Japanese

## Math Lecture

### Theory of Operator Algebras (5th)

November 8 at 13:30 - 15:00, 2018

Dr. Yosuke Kubota (Research Scientist, iTHEMS)

Venue: Seminar Room #160, 1F Main Research Building, RIKEN

Event Official Language: Japanese

## Workshop

### Workshop on Recent Developments of Chiral Matter and Topology

December 6 - 9, 2018

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)

Venue: National Taiwan University, Taipei, Taiwan

Event Official Language: English

## Math Lecture

### Theory of Operator Algebras (6th)

December 20 at 15:30 - 17:00, 2018

Dr. Yosuke Kubota (Research Scientist, iTHEMS)

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.

Venue: Seminar Room #160, 1F Main Research Building, RIKEN

Event Official Language: Japanese

# Paper of the Week

## The relative Mishchenko--Fomenko higher index and almost flat bundles

2018-09-19

Existence of a positive scalar curvature (PSC) metric has been one of the central topics in differential topology of higher dimensional manifolds. Index theory provides a topological invariant whose vanishing is an effective necessary condition of the existence of a PSC metric. Recently, Chang-Weinberger-Yu introduce a new index theoretic invariant called the relative higher index detecting the non-existence of a PSC metric on spin manifolds with boundary. The aim of this paper is to understand this invariant from Riemannian gemetric point of view. Firstly, we introduce a new definition of the relative higher index and prove that it is equivalent to the existing definitions. Secondly, by using our new definition, we relate the relative higher index with a Riemannian geometry of vector bundles; the index pairing with almost flat vector bundles. This is a relative analogue of the theory of Gromov-Lawson for closed spin manifolds.

Reference:

Yosuke Kubota

"The relative Mishchenko--Fomenko higher index and almost flat bundles I:
The relative Mishchenko--Fomenko index"

arXiv: 1807.03181

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