# Seminar Report

## Math seminar by Hiroki Kodama

2019-07-04

Hiroki Kodama had a seminar talk in the iTHEMS math seminar on 20 June. The topic was the foundation of metric space and its generalizations. Metric space is one of the most primitive setting of geometry. This notion is defined in an abstract way by metric function satisfying 3 axioms. Not only the Euclidean metric, which is familiar for all of us, many ideas arising all over the science (e.g. the distance of two DNAs) are formulated as a kind of metric. A main interest of this seminar was a generalization of metric space, which is less popular even for mathematicians. A function satisfying the axioms of metric space except for the symmetry axiom d(x,y)=d(y,x) is called an asymmetric metric (a typical example is the cost for a ship on a river to move from one point to another). In the first half of the talk, Kodama introduced the basic notion of (asymmetric) metric spaces with various examples. In the second half, he introduced an interest of asymmetric metric space by showing rich information it includes.

# Upcoming Events

## Workshop

### RIKEN-OIST mini Workshop 2019 "Mathematical Condensed Matter Physics"

July 5 - 6, 2019

Topics: Boson-Fermion duality, Operator product expansion, Random matrix

Lecturers:

Takuya Furusawa (TIT/RIKEN)

Yuta Sekino (RIKEN)

Shinobu Hikami (OIST)

Organizers:

Masahiro Nozaki (RIKEN) Chair person

Masaru Hongo (Keio Univ./RIKEN)

Kanato Goto (RIKEN)

Hidehiko Shimada (OIST)

Venue: Okinawa Institute of Science and Technology Graduate University (OIST)

Event Official Language: English

## Workshop

### SOKENDAI-iTHEMS Joint Workshop "Genetics meets Mathematics"

July 7 - 8, 2019

Dr. Jeffrey Fawcett (Senior Research Scientist, iTHEMS)

Venue: LecTore Hayama

Event Official Language: Japanese

## Workshop

### Workshop on Sine-square deformation and related topics 2019

July 11 at 10:00 - 18:00, 2019

Sine-Square Deformation (SSD) is a newly found boundary condition that involves the spatial modulation of the coupling constant of quantum systems.

Since its discovery, it has received broad attention in the context of various research field. This workshop aims at offering the opportunities for the researchers interested in SSD to convene and exchange ideas on the subject.

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

Event Official Language: Japanese

## Colloquium

### The 9th MACS colloquium

July 12 at 16:15 - 18:50, 2019

Dr. Makoto Fujita (Professor, Department of Applied Chemistry, The University of Tokyo)

Dr. Kazutoshi Mori (Professor, Department of Biophysics, Kyoto University, Graduate School of Science)

The 9th MACS colloquium supported by iTHEMS. It will be broadcasted to Wako, but if you can join the colloquium physically in Kyoto, that would be better. iTHEMS provides good confectionery at Kyoto!

Venue: Lecture room #401, Graduate School of Science Building No 6, Kyoto University

Event Official Language: Japanese

## External Event

### Interstellar Memes

July 25 at 20:00 - 21:30, 2019

Dr. Don Warren (Research Scientist, iTHEMS)

Memes are to cultures what genes are to people: ideas, behaviors, or styles that are transmitted within the culture and can propagate or die out. The universe is a big place. How much of it knows about Grumpy Cat? Tale of Genji? Earth?

Cost: JPY1,500 including a drink

Venue: Good Heavens Bar (2F 5-32-5 Daizawa, Setagaya-ku, Tokyo 155-0032)

Event Official Language: English

## Workshop

### RIMS-iTHEMS joint WS on "Math of Jets"

July 29 - 31, 2019

Co-hosted by RIMS Kyoto University and iTHEMS RIKEN.

Venue: Kyoto University, Main Campus Research Bldg No 15, #201

Event Official Language: Japanese

## Lecture

### SUURI-COOL (Kyushu) Lecture

July 31 - August 2, 2019

Dr. Takumi Doi (Senior Research Scientist, iTHEMS)

SUURI-COOL (Kyushu) at the Ito-campus of Kyushu Univ. will be launched on July 31, 2019. As a first event at SUURI-COOL (Kyushu), the following lecture by Takumi Doi (RIKEN Nishina Center/iTHEMS) will be held. Feel free to join if you will be around Ito-campus.

Venue: SUURI-COOL (Kyushu), #A717, West Zone 1, Ito Campus, Kyushu University

Event Official Language: English

## Workshop

### Math-Life Workshop

August 19 - 20, 2019

Organizers

Masaharu Nagayama (MSC, Hokkaido Univ.)

Tetsuo Hatsuda (iTHEMS, RIKEN)

Hiroshi Suito (AIMR, Tohoku Univ.)

Takayuki Sakajyo (SACRA, Kyoto Univ.)

Venue: 1F Seminar Room, Frontier Research in Applied Sciences Building, Hokkaido Univ.

Event Official Language: Japanese

# Upcoming Visitors

July 1 - 31, 2019 ## Prof. Pei-Ming HoDepartment of Physics, National Taiwan University Visiting Place: #158, 1F, Main Research Building |

July 5 - 11, 2019 ## Dr. Shinsei RyuThe University of Chicago, USA Visiting Place: #157, 1F, Main Research Building |

# Featured Paper of the Week

## Rigidity of the mod 2 families Seiberg-Witten invariants and topology of families of spin 4-manifolds

2019-07-04

After the early 1980s, gauge theory has been used by mathematicians to study 4-dimensional spaces (manifolds). The hottest mathematical subject studied by gauge theory is a sort of difference between the shape of topological (continuous) 4-dimensional manifold and that of smooth 4-dimensional manifold. On the other hand, in most of mathematical areas, it is quite significant to understand symmetry of a given mathematical object, such as a manifold. However, about the space of all symmetries of a 4-dimensional manifold, only few things have been known. In this paper, we study the spaces of symmetries of 4-dimensional manifolds. We revealed that gauge theory (more precisely Seiberg-Witten theory) can extract some difference between the shape of the space of symmetries of a topological 4-dimensional manifold and that of a smooth 4-dimensional manifold. In addition to gauge theory, we also used some classical but deep results in higher-dimensional topology invented 50 years ago. Such a combination of gauge theory with classical results in topology is also a new and interesting direction of this paper.

Reference:

Tsuyoshi Kato, Hokuto Konno, Nobuhiro Nakamura

"Rigidity of the mod 2 families Seiberg-Witten invariants and topology of
families of spin 4-manifolds"

arXiv: 1906.02943

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