Graduate School of Mathematics

NAGOYA UNIVERSITY

Welcome to theWorld of Mathematics
Updated information can be found at the
department’s web page.
http://www.math.nagoya-u.ac.jp/en/index.html

Particularly for up to date information
regarding entrance exams, please see
the link below.
http://www.math.nagoya-u.ac.jp/en/education/index.html
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Grad.Sch.of Math.

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Information

MuseumGraduate School of Mathematics Nagoya University
Chikusa-ku,Nagoya 464-8602 JAPAN TEL（052）789-2429 FAX（052）789-2829

Graduate School of Mathematics
Department of Mathematics, School of Science

NAGOYA UNIVERSITYAn Invitation to Mathematics

Education and Research
at Department of Mathematics,
School of Science/
Graduate School of Mathematics
in Nagoya University
Mathematics research as a base for study in science/an independent style graduate school education
Among all the progress and development made in academics in the 20th century one of the most remarkable contributions is that of the basic principles ofmathematics to a broad variety of fields of science. Now mathematics serves
not only as a common language among natural sciences, but also in sociology
and anthropology, serving as the language of expression for phenomenon
across these fields.

Mathematics as a field of study
What image of mathematics exists in society today? Whatwould one learn from mathematics in university? What is themathematics researched in universities like? Hasn’t a subject
such as mathematics been fully investigated and researchedalready? What are the unsolved problems remaining in thefield of mathematics? These and others are the questions that
we find students wondering about.

A tradition of freedom that bares high level research
The predecessor of this program with its tradition of study in pure mathematics has been recognized internationally as a place for high level learning. With
the goal of carrying on this tradition of high level research on an international
scale, we have expanded our learning environment to include experts from avariety of fields such as mathematical physics.
This program also maintains the tradition of conducting seminars that promote
the expression of ideas from all members, regardless of relative status, amongprofessors, associate professors, and students. We are proud of the fact thatseveral mathematicians who spent their younger years here in Nagoya
University’s math department then went on to make world renowned achievements.

Mathematics as the common language
among sciences
With Newton’s theory forming the base for differential
integral calculus in the 17c, the application of mathematics
as the common language bringing sciences together began.
Since that time, whether the topic at hand is nature or
society, mathematics has been applied as the common
language. Contrary to common perception, mathematics isclosely related to many other fields, and because of this it isoften applied successfully to progress other fields. A recent
example is the internet, which has come to represent modern
communication. Today we cannot survive without it, but it
only came about as a result of code theory, for which theunpredictable application of whole number theory has
proven very important.

A flexible system of education“High level research makes high level education possible”. This is our conviction at Nagoya University. With this concept as our guide, all teaching staff arededicated to covering the basic courses of students from their first year,
including the following: basic mathematical education, undergraduate courses
in the School of Sciences and more specialized courses in the Graduate Schoolof Mathematics, and the role of advisor for students in both the undergraduate
and graduate programs.
The educational approach of this graduate school is to prioritize each student’s
desire for their own educational course. Highlighting students’ interests facilitates the necessary motivation for students to progress smoothly in their studies and research. The “level system” was introduced to act as a pillar amonga broader program of flexibility. This aspect of the program is particularly
aimed at students educated in another learning environment or university,
facilitating their smooth transition to our school’s curriculum.

Mathematics within science
Research in mathematics is not nearly as complex or
overwhelming as is thought. Most of the important ideas in
the field of mathematics can be found in the interaction
around us in nature and society. As the common language ofscience mathematics has led to many discoveries, serving as
an invaluable tool to other field’s development. We expectthat mathematics will continue to develop in its own right, as
it continues to be applied to other science fields.

Nurturing specialists in mathematical scienceswith great independence and broad vision

Education and Research at Department of Mathematics , school of science/

Graduate Program for Doctoral Degree (Ph. D.)・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・ 12

Graduate School of Mathematics in Nagoya University・・・・・・・・・・・・・・・・・・・・・・・・・・ 01

Tuition and Other Information・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・ 14

Gathering together in Nagoya to pursue the study and research of mathematics・・・・ 02

A Message from our Teaching Faculty・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・ 16

An Original Program Fostering Creativity in Mathematics・・・・・・・・・・・・・・・・・・・・・・・ 06

Research Activities at Graduate School of Mathematics・・・・・・・・・・・・・・・・・・・・・・・・ 17

Undergraduate Program・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・ 08

Introduction of Teaching Faculty・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・ 20

Graduate Program for Master’s degree・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・ 10

Support for education and research・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・ 24

The educational goal of the school of mathematical sciences and graduate
school of mathematics is to nurture human resources with the mathematicalscience skills required to solve problems and the ability to apply them independently. In order to achieve this one must acquire the skills to think logically, view problems with a broad perspective, and conduct complex expression. It is for this purpose that various mechanisms and programs have been
introduced. For example, to ensure that the basic skills are mastered at a highlevel, the “core curriculum” has been introduced. In order to promote thereceiving of advice from numerous professors several programs were introduced as follows: multiple advisor system, office hours, and to promote careful selection of research topics and their practical application, “student project” was introduced.

1Graduate School of Mathematics NAGOYA UNIVERSITY

Gathering together in Nagoya
to pursue the study
and research of mathematics

Shoji Toshiaki

Lars Hesselholt

Kohji Matsumoto

Yoshifumi Kimura

Jacques Garrigue

Tetsuya Tate

Dean, Professor

Professor

Professor

Matthew Clarke
Visiting Researcher

2

Professor

Associate Professor

JungHun Leefrom Korea

Associate Professor

YanYan Wang
from P. R. China

Shoji: I am the dean of this school. My area ofspecialty is algebra and I focus mainly on representation theory. As dean I do not currently
teach many courses, but in my seminar I enjoy
researching with my students very much.
Today we are discussing why one shouldchoose Japan or Nagoya University to pursue
studies so let us speak frankly.
Clarke: I am Matthew Clarke. I am studying at
Cambridge University and have just arrived in
Nagoya this summer.
Matsumoto: I am Matsumoto. My area of specialty is number theory. Recently I am surprised to realize that I have become a real old
face here in the graduate school.
Garrigue: I am Jacques Garrigue. Computer
Science is my expertise. I am originally from
France but have been in Japan for 18 years
now.
Park: My name is Park Hyunmi and I comefrom Korea. After finishing high school in
Korea I came to Japan’s Niigata University forundergraduate studies, and then Nagoya University for graduate studies. My research
focus is representation theory and combinatorics.
Tate: My name is Tate Tatsuya. My area ofspecialty is global analysis.
Kimura: My name is Kimura and I teach here.
My specialties are fluid dynamics and numerical analysis of differential equations. In thepast, I had the experience of living abroad fora long period.
Hesselholt: My name is Hesselholt and I am
from Denmark. My research focus is algebraic K-theory and I have been in Japan forabout 5 years. Before coming to Japan I was in
the U.S. for about 15 years. Nice to meet you.
Lee: I am Lee JungHun and I come from
Korea. I am currently a second year
undergraduate student studying mathematics.
Wang: I am Chinese and my name is Wang
YanYan. I come from Shandong. I came here
after completing my studies at China’s Ocean
University. I am currently here on a scholarship from the Chinese Government, for study
abroad. My advisor at home had studied
abroad at Nagoya University so after hearing
about his experience, I decided to come here
myself.

Matsumoto: Firstly, for those who came to
Japan from abroad, would you please tell us
what your first impression was upon
arriving?
Garrigue: Well, it has been over 15 years now
so I really don’t remember. Ha ha…
Lee: The first time I came to Japan was for aninterview, but my overall impression wasgood. At that time, after my interview, I went
to the campus cafeteria. I saw many students
happily enjoying their studies and thought tomyself, “studying could be fun if I camehere”. My impression has not changed sincethen.
Park: I think Japanese students are very
serious about their work. I have never been toa Korean university so I cannot say for sure,but I have the impression that it is a place tolearn only for one’s future career. That
impression was created through listening to
my friends who study there. I really wanted
to study seriously at university.
Shoji: Are there many students like you who
decide to come from Korea to Japan to study
mathematics?
Park: No, there are not so many, perhaps
more studying biology or natural sciences.
For me though rather than English, Japanese
language seems close to Korean so I thought
studying here would somehow work out
better.
Lee: The grammar is almost the same, so you
really just need to exchange the words
between the two languages and it usuallyworks out. (smile)
Shoji: Where did you study Japanese?
Lee: I studied in Korea and sat for the
Examination for Japanese University
Admission for International Students. After
passing, I sat for the entrance exam at
Nagoya University. Last year I took basic
education courses, and studied Japanese on
my own.
Park: When I first arrived in Japan I found it
exhausting to sit through a full day of lectures.
Now that I am used to it, I can manage withjust a bit of study time following class. I findJapanese easier to follow than English now.
Wang: I studied Japanese a bit in China, butmainly since coming here. I just came to

Japan last year so my Japanese is not very
good yet. Japanese sentence structure andvocabulary are difficult. For example, thecharacters read as “daijoubu” in Japanese
language, mean something different in
Chinese. “Tegami” (meaning letter inJapanese) is also different. The meaning in
Chinese is.., well, it may be better not to say.
Ha ha..
Clarke: Many students in my same study
room invite me to lunch often, and also teachme Japanese words. Everyone is friendly andkind. We even went out collecting “kabuto”
beetles together before.
Tate: Forgive me, but I’ve been wanting to
ask this question. Inside your head do you
think about mathematics in your native
language or in Japanese?
Park: It depends on the situation. Things thatcome to mind in Korean, I think about in
Korean, but things that quickly come to mind
in Japanese, I think of in Japanese. Linear
functions, for example, I studied thoroughly
in Korea so when I take notes related to that I
find it quicker to write “function” in Korean
language. When I look at my notes fromlecture I see Korean, Japanese, and English
all mixed, and think how I’d be a bit
embarrassed to share them with others.
Lee: In my experience it is divided between
high school and university. Things I learned
in my Korean high school, I tend to think ofin Korean. While things I learned inuniversity, I think of in Japanese. When
professors study and research in English, do
you translate everything into Japanese inyour head before you think it through?
Matsumoto: No. In such situations my head
has already transformed into English mode.
When it comes to writing articles in English,of course I am concerned about using proper
grammar but when writing proofs on theblackboard in class in English, I don’t worry
about correct grammar.
Garrigue: When I was teaching first year
students calculus it was rather difficult.
Apparently students cannot read my writingin roman letters (smile). But the way ofwriting functions is altogether different.

Hyunmi Park
from Korea

3

Graduate School of Mathematics NAGOYA UNIVERSITY

Matsumoto: What’s your impression of
Nagoya?
Lee: It’s great. It is rather quiet here andprices and rent are cheaper than other cities.
The only thing is that the humidity level insummer is high so your skin feels rather
sticky, and I don’t like that part much.
Park: I am from Jeju Island in Korea where
the climate is quite warm. But, the wind there
is strong so it never feels as hot as this.
Niigata was never this humid so Nagoya
really feels hot to me.
Wang: Nagoya is a beautiful city. But it isalso hot.
Hesselholt: I love the climate in Japan. It’s
good for me because I prefer it to be hotrather than cold.

4

Matsumoto: Are there differences that you
notice in daily life here compared to yourhome country?
Park: In my case I have gotten too used toJapan perhaps, so that when I go home if I
run into someone I often say “sumimasen” or“excuse me” in Japanese. When talking withfriends back home, sometimes I get excitedabout our discussion and phrases come out inJapanese. This always surprises my friends.
Matsumoto: Do you have any problem withthe food here?
Park: No, not at all. I don’t have any allergies
and I really love soba (buckwheat noodles).
Lee: I even like “natto”. I think it is truly
delicious, but when I recommended it to afriend, they didn’t seem to believe me at all. I
told them I pitied them for not being able toenjoy such a wonderful food. Ha ha.
Shoji: Well, even some Japanese people
cannot eat “natto”. (smile) Where do you alllive now?
Lee: I am living in a dormitory that theuniversity introduced me to in Nagoya’s port
area called Nagoya International Student
Center. There is also a foreign student
resident hall on the Higashiyama Campus,
but there is a 6 month limit for living there.
The residence hall in the port area allows
students to stay one year, with the possibilityof extension if rooms are available.
Kimura: How do you commute to campus,
by subway?
Lee: I often come by bicycle.
Shoji: That should be good for your health!
Park: I do get a bit sun burned along the way

though. Ha ha.
Lee: In summertime I think I’d fall over fromthe heat, so I try to commute by train. (smile)
Matsumoto: What is your plan for after
studying mathematics here?
Park: If possible I’d like to continue studying,but I’ll really have to write a good masterthesis in order to do that.
Shoji: In our system it is possible to enter the
doctor course without such a high level oforiginality in your master thesis.
Park: Yes, perhaps that is true but I still feel I
want to aim high. If I feel that continuing myeducation here is best for me, I would like tobe able to do that. That is why I am studying
hard now. If I do not manage to enter the
doctor course, then I will seek a job.
Lee: I am also really enjoying myself here so
I hope to finish a master degree, then doctor
degree, then move on to become a professor.
But, in Korea we are required to serve in the
military, due to conscription laws, so I willprobably return to Korea to carry out myservice after finishing my master degree. I do
not know what I will do after that.
Matsumoto: If you want to become aprofessor, would you like to do so in Korea
or Japan?
Lee: Ideally I’d like to be a professor
throughout the world, moving around. But if
it is between Japan and Korea, I’d choose
Japan because students are more serious.
(smile)Park: I’d like to be in either Korea or Japan. I
don’t know any other enjoyable place to be.
(smile) But if I were to return to Korea, I’dfeel I was giving up a good opportunity here,
so I think I’d prefer to be in Japan.
Wang: I’d like to become a professor in
China. It is a difficult goal, but if you havestudied abroad in the U.S. or Japan they say it
is easier to become a teacher.
Park: I think Japan is a great environment forforeign students to study in. There are fewer
foreign students in math than in engineering
fields, so there are more opportunities to getscholarships. Currently I am receiving a
JASSO (Japan Student Services Organization) scholarship. If you are able toconfidently sell yourself and your abilities,
you’ll likely find a way.
Lee: Same for me. I was introduced to thescholarship by the office staff of this school.
Shoji: On campus there is a center for foreign
students. It is a good place to seek information about Japanese language study and daily
life from various coordinators. Sometimes
they hold events. Please feel free to contact
them anytime.
Lee: In May after entering the university I
was invited to a party at the International
Residence Hall. There I exchanged contact
information with various students and when I
have time we meet up, or get in touch when I
go home.
Shoji: Even among the national universities
Nagoya University has a high number ofstudents from China and Korea. We have alarger number of doctor course students sentfrom Chinese universities than even Tokyo or
Kyoto University.

Park: I have a question I’d like to ask our
professors. Why did you choose Nagoya
University to work at?
Matsumoto: Among Japanese universities
Nagoya University provides a very good
research environment. There are great
facilities and brilliant staff.
Garrigue: I was originally at Kyoto University. At that time an excellent student came tous from Nagoya University and I thought tomyself, “I want to teach computer science tobrilliant students such as this”. (smile)
Hesselholt: How do you find Nagoya University courses? Are they easy?
Wang: No, I don’t find them to be easy. If
you don’t study on your own you cannot
keep up. It is rather difficult, but courses areinteresting.
Lee: The reason that I chose Nagoya is thesame as was just mentioned, the cost of living
is low. (smile) I also found Nagoya University professors to be especially kind to
students. “Café David”is a good example ofthis, where students have a great opportunity
to talk to professors. I haven’t taken
advantage of this enough yet, so I’d like to doso more in the future.
Park: When I was attending Niigata University, I wanted to study representation theory
and combinatorics. Nagoya University wasamong those recommended to me by aprofessor I consulted. The day after I passed
the entrance exam here all the professors
were gathered at the school and carefully
explained the details of the program. So my

impression of them was very good. I thought
to myself, “communication with these
professors seems really comfortable”. Niigata
University is also a nice place, but there are
relatively few graduate students and few
opportunities to exchange ideas about
research. I found this to be a waste. In thisschool’s doctoral program I’ve found senior
students to be very intelligent and willing toteach you many things. I find this to be
stimulating, and it makes me glad that I chose
Nagoya University.
Shoji: I hope in the future you will continue
to feel free to consult us about anything thatarises. Let us all enjoy our studies, researchand lives here together.

5

Education Programs

Graduate School of Mathematics NAGOYA UNIVERSITY

An Original Program
Fostering Creativity in Mathematics

Level system and educational program
In this way students can pursue
a purpose-centered education
suited to their area of inquiry
and unfettered by their official
school year.

Self-study / Research

Self
Study

Research

Colloquium / Researcher’s Seminar
Project
Academic
Support for
LearningandResearch

Weekly Office Hour / Café David
Small Group
Instruction
LectureExercise / Group Study
Level 0
U1

Level 1
U2

Graduate Small Group Small Group
Research
Class
Class

Level 2

U3

U4

Department of Mathematics

M1

Level 3
M2

Master Course

D1

D2

D3

Doctor Course

Level System
The Level System is our central mechanism for classifying programs of study into educational purposes, organizing both undergraduate
and graduate degree curriculums as a coherent whole. Thus, all lectures and small group classes fall into a certain level.
Level 0Level 2All science major students work together in the initial disciplinary phase of
the art of science level 0 classes and learn subjects including calculus andlinear algebra.

The scope of level 2 classes embraces various areas of advanced concepts.
These classes provide scholarly training in logical, abstract and systematic
approaches commonly used in mathematics through a wide diversity ofsubjects. This level is intended for fourth year undergraduates and graduate
students. It is advisable to complete the set of classes within two years.

Level 1
Level 1 classes deal with basic concepts, which all science-majored students
need to comprehend. This level corresponds to curricula for undergraduatesin the second and third years. These classes encourage students to apply andconnect mathematical concepts with other fields of science, such as physics,
and to develop intuitive, logical and abstract thinking.

Level 3
Level 3 classes serve as advanced courses, and are designed based upon theelemental portions of the curriculum up to level 2, the so-called coreprogram. These are intended for all 2nd year or above graduate students andshould be completed over three or four years.

Basic Principles
An Emphasis on Basic Skills and Broad Minds

Connecting Mathematicians through Cafe DavidThe idea of studying mathematics brings images to mind of large lecture halls and rigorous self-study.
These traditional methods of study are indeed important, but there are also dynamic alternatives.
One of those is to gather various thinkers together to debate and discuss mathematics. The above photo isof our own weekly event, “Café David”. Here, undergraduate students, graduate students, and teachingfaculty gather in a casual café meeting style, to chat over both academic and less formal questions.
The well known mathematician often said to represent the 20th century David Hilbert is whom we havenamed our “Café David” after. As the name suggests, delicious coffee is on offer for department members
in attendance. Discussions here allow many to overcome common barriers that exist between undergraduate and graduate students, or between students and faculty, or among academic areas or schools, strengthening relationships and intellectual understanding at the same time. In addition, graduate students join
“Café David” as teaching assistants, offering a comfortable environment to answer tough questions fromlectures. Faculty provide assistance here in the form of office hours and students can learn from interactionin this active public learning space.
Wouldn’t you like to come take a look at our diverse learning styles of mathematics?

6

Cafe DavidThe Department of Mathematics and the Graduate School of Mathematics aim to cultivate self-motivated individuals,
who can successfully navigate inquiry, reflection, and discovery based upon scholarly training in mathematics. Ourcommitment is to maintaining an enlightening environment for problem-conscious students where, together with scholars
and fellow students, they can refine their ideas and apply logical reasoning in seeking solutions to problems.
Prospective students should know that in the mathematics department:
Research planning, pursuit of research and regular reporting of results are expected.
The education in the department is designed to support students’ self-motivation.
Research is pursued in dialogue with active researchers and fellow students.

Emphasizing Independent Will
The aim of the doctoral program is to foster researchers with multiple talents in mathematical sciences who are also
capable of working in various fields. In the Graduate School of Mathematics we offer doctoral students an active andglobal work place in order that students enrich their knowledge by working together with younger researchers.
Mathematical scientists are not only those who work in a university or a laboratory but include those competent to solve
problems of any field of the mathematical sciences. Therefore, we encourage you to take a broad perspective in considering your career options after graduation.
7

Education Programs

Graduate School of Mathematics NAGOYA UNIVERSITY

Undergraduate Program
You will learn differential calculus and linear algebra through examples and by working on exercises.
These are the "raw material" of modern mathematics. You will be asked to carry out explicit computations,which will give you access to computational skill, and will foster proper intuition for mathematical concepts.
It is of utmost importance that you work through as many problems as possible, gaining exposure tomathematics.

Level 0 Semester Lecture(Freshmen)

SmallGroup Class

SummerCalculus of one variable/ Linear algebra/ Overview of mathematics

Seminar on
mathematics

WinterCalculus of several variables/ Linear algebra/ Overview of mathematics

Seminar on
mathematics

First differential calculus and linear algebra will be reworked rigorously in the language of modern
mathematics --sets and maps. Totally new concepts, such as complex function theory and topological spaces
will enter the scene. The learning curve is steep, and you will be required to put in a lot of effort and yourpatience will be taxed, but the reward will be high: an entrance ticket to modern mathematics.

Level 1 Semester Lecture(Sophomore)

Small
Group Class

SummerSets and mappings/ Linear space and linear mappings/ Calculus of one variable

Seminar on
mathematics

WinterCalculus of several variables/ Topological spaces/ Complex function theory
Normal forms of matrices/ Introduction to information sciences

Seminar on
mathematics

You will be introduced to mathematics that was developed in the early 20th century. Level 1 ends with theintroduction of the Lesbesgue integrals and its application to Fourier analysis, curves and surfaces which
generalize circles and spheres, groups and rings that are algebraic abstraction of numbers, polynomials andmaps. There will be "Omnibus lectures" on how mathematics relates to the real world, and what lies aheadof all this, "group study" where you pick the text of your choice, discuss the content with your fellow
students, give talks, and give a poster presentation.

Level 1 Semester Lecture(Junior)

Small
Group Class

SummerIntroduction to group theory/ Introduction to curves and surfaces
Introduction to differential equations/ Lebesgue integrals and measure theory

Seminar on
mathematics

WinterRings and polynomials/ Introduction to differential forms
Introduction to functional analysis/ Omnibus lectures/ Group study

Group study

Lectures for seniors at Level 2 are all open to seniors and graduate students. The subject matter of theselectures differ by year. A list of courses offered during the academic year 2008 is given below. There arealso numerous "crash courses" , which typically last for a week, designed to give an overview of researchat the forefront. Courses at this level emphasizes the diversity and universality of mathematics that can
only be appreciated by taking a higher viewpoint. You are not only expected to learn from these courses,
but also to develop your own viewpoint/taste for mathematics. Reading courses under faculty supervision
are offered, where you will learn how to read a book or a research article, how to formulate your thoughts ina mathematical way, and how to discuss mathematics.

Level 2 Semester Lecture(Senior)

Learning and Lecture Content
The following is a brief description of what is offered at Nagoya University for mathematics majors.
8

SummerFields and Galois theory/ Manifolds/ Functional analysis/ Introduction
to probability theory/ Introduction to mechanics/
Introduction to numerical analysis/ Omnibus lectures

WinterElliptic curves/ The heat kernel and the index theorem/ Introduction to partial
Differential equations/ Electromagnetic theory/
Methods in applied mathematics(offered in English)/ Functional
programming languages

SmallGroup Class

Seniorreading course

9Education Programs

Graduate School of Mathematics NAGOYA UNIVERSITY

Graduate Program for
Master’s degree
Intensive
LectureCourses

Small
Group
Class

Teaching
Assistants(TA)

Fostering Scholars who Investigate,
Think and Discover on their Own
The Graduate School of Mathematics aims to cultivate self-motivated individuals, who can successfully navigate
inquiry, reflection, and discovery based upon scholarly training in mathematics. Our commitment is to maintaining an
enlightening environment for problem-conscious students where, together with scholars and fellow students, they canrefine their ideas and apply logical reasoning in seeking solutions to problems.
10

Intensive courses are those conducted by lecturers from other universities or
institutions, intensively, over short periods of time. Content ranges widelyfrom those of an introductory nature, that require no prior technical knowledge at all, to those that focus more narrowly on the most cutting edge
findings in a specific field. Not only are the mathematical fields of Algebra,
Geometry, Analysis to Applied Mathematics and Mathematical Physics
covered, but lecturers are brought in to offer various perspectives, includingthat of the corporate world and practical applications. To find out more
information about intensive lectures conducted in 2008 and the small groupclasses explained below, please see our graduate school’s web page, under“Education & Job Search”.

Small Group Class is a two-semester seminar intended to develop reading,critical thinking and discussion skills. In the seminar class students expand
upon their learning from faculty lectures and identify their specific focus ofinterest /research from within areas presented in lectures. Within the chosen
subject area, classes offer multifaceted lectures guided by student interest.
The pace of the lectures is tailored to participating students’ needs. As seenfrom the chart above, students can both improve their skills and explore theirchosen field in the small group class. MA students will belong to a creditearning seminar each year. At the same time they are strongly advised toattend another seminar. Students who attend regularly and submit successful
assignments will be awarded at most 1 credit over 2 years in addition to thecredits from other classes for which they are registered.

Teaching assistant positions are filled primarily by first year MA course
students. They are hired to aid professors with lectures and seminars forundergraduate students of first, second, and third year in the science department, as well as others, and to assist with Café David. Duties of a TA include
designing and correcting class exercises, writing interpretations, and attending to all Q & A in and out of class. These duties offer graduate students anopportunity to join the backstage of university lectures. Experiencing
lectures from the standpoint of a teacher allows TAs an invaluable opportunity for their future, to learn now what it is to teach. In addition, as TA, one
can understand many of the typical problems that students repeat, as well as
those of beginning instructors and how to avoid them. Wages are paid to TAs,
but many past TAs say that the real value in this assistant position is theopportunity to enhance one’s own learning and future research.

11

Education Programs

Graduate School of Mathematics NAGOYA UNIVERSITY

Graduate Program for
Doctoral Degree (Ph. D.)

Active Student Body
Our current doctoral students are involved in student organized seminars on campus, as well as the planning and organizing of national academic conferences for young scholars. This is in addition to active independent research of their own.
We believe this combination of activities results in the high quality research output our department’s doctoral students
produce. Among other activities, Student Project receives strong support from our department, as well as from theProgram for Enhancing Systematic Education in Graduate Schools since 2007.
Student Project Titles of 2011
1

Combinatorial representation theory and related topics

2

Studies in commutative rings of positive characteristic from the view
point of F-purity

3

Algebraic topology and algebraic K-theory

4

Interplay between topology and logic

5

Who killed the prime factorization again?

6

Dynamical systems and geometry

7

Arithmetic geometry and related topics

8

Fuchsian groups and Kleinian groups

9Interdisciplinary number theory

10

The Dixmier-Douady class11

Cluster algebras and related topics

12

Analytic geometry on Harnack inequalities

13

The variation of reproducing kernels

RA（Research Assistant）

Fostering the Next Generation of Young Scholars
The primary goal of our doctor course is to foster the next generation of young mathematicians. To understand the necessary broad range of skills involved in mathematical sciences and be prepared to apply them appropriately to various
problems. The doctoral course in particular requires self-driven learning, including discovering problems on one’s own
and building the skills necessary to solve them. Sending our PhD holders equipped with these skills as competitive professionals out into society is the ultimate goal.

C O L U M N
Paving the way for passage to Germany
One of the great mathematicians of the nineteenth century, G. Lejiune
Dirichlet, was born in Düren (Germany) and made notable contributions tomodern number theory and calculus. Following precedent, Yoshitaka
Sasaki, a graduate student in our department of mathematics, chose thesame country and field as Dirichlet when considering location and theme forattendance of a mathematical conference with the financial support of Good
Practice (GP). Mr. Sasaki, as a leader of the GP project team “Comprehensive Approaches of zeta- and L-functions”, successfully embarked on hisacademic career internationally, and paved the way for progress in his areaof specialty.
Having experienced various academic presentations, Mr. Sasaki and his
team have spent much time conjecturing their outline of the GP project. He

12also has shown great devotion to his specialty, paving the way for thisproject, and hosting many seminars. His latest activity includes giving a talkabout D. Goldfield and J. Hoffstein in a lecture titled, “Introduction ofMultiple Dirichlet Series”, in August 2008. “I believe that the principle ofzeta–functions remains its possible application to various mathematicalfields has much yet to be investigated, such as application to algebra,
geometry and analysis; and that new approaches to it should be sought.” Mr.
Sasaki also said, “I am interested in understanding these characteristics ofzeta- and L-functions, and that is the main objective in establishing our teamproject.”
After collecting information about conferences hosted both domesticallyand abroad, within the limitations of the expenses covered by GP, he and his
team members finally selected the conference titled, “New Directions in the
Theory of Universal zeta- and L-functions” held from October 6 to 10, 2008

Many doctoral students may be employed as research assistants (RA) to help them develop their research skills and toprovide opportunities for participation in various research groups in the Graduate School of Mathematics. The RA system
has been financially supported by the Program for Enhancing Systematic Education in Graduate Schools since 2007.
Grants-in-Aid for Scientific Research also helps to support doctoral students as research students. There were 15 RAs in
2007, 12 in 2008, 14 in 2009,9 in 2010,and 12 in 2011,65 in total.

JSPS Fellows
This program was established by JSPS（Japan Society for the Promotion of Science）to assist promising and highly qualified students wishing to conduct research in universities or institutions. Fellowships are awarded for a period of two to
three years with monthly research-related expenses and Grants-in-Aid for Scientific Research. Detailed information isprovided at: HYPERLINK "http://www.jsps.go.jp/english/index.html

at Würzburg University in the northern area of Bayern, Germany. They
hoped to gain inspiration and further understanding of advanced study ofnumber theory. This well-timed conference was also complementary totheir academic needs; their specialty, number theory, involves other fields
of mathematical knowledge and this conference dealt with application
studies of probability theory, whose field has progressed remarkably inrecent days.
Consequently, Mr. Sasaki said that his days at Würzburg were intellectually enjoyable. The first day at the university Mr. Sasaki presented his
paper “Multiple Zeta Values for Coordinate-wise Limits at Non-positive
Integers”, to which, as a result, host Professor J. Steuding gave favorable
comments. “I was nervous during my presentation, so relieved to hear his
positive feedback. I was afraid of hearing something like “it is logicallywrong!” said Mr. Sasaki. The problem session was scheduled on the third

day and it provided his team a good opportunity to exchange information.
An excursion to a beautiful area of historical heritage beside a river called
residenz, on the last day helped all participants from Japan to relax and get
acquainted with graduate students and professors from various countries.
Mr. Sasaki observed after returning from Germany that he was grateful forthe opportunity to have made the project proposal and carry it out because
he could look for the best academic institution, most suitable for their
purpose across the globe and carry out the plan with financial assistance.
Sasaki said, “There are still only few institutions that will initiate use ofacademic grants for students.” Being confident and encouraged, he is now
busy preparing for other mathematical conferences in Japan, coming up in
the next few months. He is sure that this academic venture to Germany will
become one of the most important building blocks of his future study.

13

Graduate School of Mathematics NAGOYA UNIVERSITY

Tuition and Other Information
Tuition and Other Fees（as of April, 2011）
Student Status

Degree-Seeking
Student（undergraduate）
Degree-Seeking
Student（graduate）
Research Student, Graduate
School Research Student
Special Audit Student, Graduate
School Special Audit Student

Advising & Counseling Services (ACS)

Application（¥）

Registration（¥）

Tuition（¥）

17,000282,000

535,800 per year

30,000282,000

535,800 per year

9,800

84,60029,700 per month
14,800 per credit

Special Research Student

29,700 per month

Traning Course in Japanese

9,900

43,50030,200 per month

Training Course in Japanese Lang．
& Culture

9,800

84,60029,700 per monthfrom HANDBOOK for International Students 2011-2013, Nagoya University

Fee Exemptions
Independently-financed degree-seeking students, who demonstrate excellent academic records and are in need of financial assistance, are eligible to be considered for exemptions from half or the entire tuition．However, as the possibility ofobtaining an exemption is small, it is advisable to prepare to pay the necessary fees．The application process for fee
exemptions takes place each semester．Applications for the spring semester are generally accepted from the end of February to March, and for the fall semester, from the end of August to the middle of September．Please pay close attention tothese deadlines．Students should contact the office of their school for further information．

http://www.isa.provost.nagoya-u.ac.jp/en/

ECIS(ACS Office) is a university-wide office to assist international students with issues or problems they may have. We
provide information and advices to international students about academic and personal matters, as well as cross-culturaladjustment and psychological issues. If you have any difficulties or concerns while you are in Japan, please feel free tocontact us. We will keep our discussions confidential.
Office Hours and Staff

As of November 2008, Nagoya University is currently home to 1,360 international students, 69.8% of them independently financed．A variety of financial support is available to these students. Information about scholarships is posted on
the school bulletin board．Students are advised to check the boards daily.

Ms. Machiko MATSUURA / Director（Professor）

OfficeRoom742 West wing, IB Building

Office Hours

Mon

Tue

Wed

Thu

Fri

10:00-12:00

-

○

○

-

○

13:00-16:00

○

○

-

○

○

AdvisorMs. Makiko TADOKORO / International Student Advisor & Counselor（Associate Professor）

OfficeRoom740 West wing, IB Building

Office Hours

Mon

Tue

Wed

Thu

Fri

10:00-12:00

○

○

○

○

○

13:00-16:00

○

○

-

○

○

Scholarships
For information on the scholarships provided by The Japan Student Service Organization (JASSO), please visit the website:http: //nupace.ecis.nagoya-u.ac.jp/en/life/jasso.html

AdvisorAdvisorMs. Naomi BANNO / International Student Advisor & Counselor（Associate Professor）

OfficeRoom738 West wing, IB Building

Office Hours

Mon

Tue

Wed

Thu

Fri

10:00-12:00

○

○

○

autumn only○

13:00-16:00

○

○

○

autumn only○

From Monday to Friday: 10:00-12:00, 13:00-16:00
TEL : 052-788-6117 E-mail: isa@ecis.nagoya-u.ac.jp

ACS Office

Room739 West wing, IB Building
from Advising & Counseling Services , Nagoya University

Japanese Language Programs
The Education Center for International Students, Nagoya University offers the following Japanese language courses．

University-Wide Japanese Language Programs(1) Standard Courses in Japanese/Intensive Courses in Japanese(2) Online Japanese Courses(3) Kanji Course(4) Introductory Lectures in Japanese Studies

2．Special Japanese Programs
ECIS offers four types of Special Japanese Programs．Enrollment in these courses is limited．
(1) Intensive Program in Elementary Japanese(2) Intensive Program in Advanced Japanese(3) Japanese Language Classes for International Undergraduate Students(4) Introductory Program for Korean Engineering Students
14

After graduating from our school students pursue the following【Undergraduate】【Master’s Course】

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（ persons ）15

A Message from our Teaching Faculty

Graduate School of Mathematics NAGOYA UNIVERSITY

Research Activities at Graduate School of Mathematics

Iyama, Osamu

A message from the fjord country, Norway / Osamu Iyama
When I got off a connecting flight to Trondheim from Copenhagen, I foundmy breath turning into a white smoke in the cold air. It reminded me that
Norway had low temperatures even in August. I often travel to Trondheim,
Norway’s third largest city, for academic purposes, and this was my fifth
visit. Having just attended a summer conference in Poland, I thought I
already knew what the weather would be like in Norway. I should havebrought along my warmer outfits! Thinking of what it would cost to buy anappropriate jacket here, I sighed deeply again turning the air into a smoky
vapor.
After leaving the airport, I enjoyed the beauty of the Nidelva River on theway to the Norwegian University of Science and Technology (NTNU). I
was looking forward to seeing a familiar face in a certain office on theeighth floor at the university. When I got to the office, my face waswreathed in smiles. Dr. Reiten and I were delighted with this reunion. She
was waiting there with a spare sweater and scarf ready for me. What awonderful person she is! It was a series of papers that Professor Idun Reiten
wrote during the 1970s that inspired my own choice of research.

minutely as the editing process neared its end. Even a slight change canmake the entire article sound more sophisticated. We were also surprised tofind a few conflicting statements. In the process of choosing the academic
journals which to submit the paper, we spent days discussing its contents.
This also entailed exchanging e-mails with a mathematician in the U.K., alsoa co-author. It took two busy weeks for us to complete the final draft.
I dined out with Professor Reiten the last day before my departure for Japan.
We ate our usual fare, a famous fish soup. In the restaurant, I talked about
topics my students in Japan are working on. She was cheerful, joking“Osamu, you were born in the very same year in which Almost Split Exact
Sequence was discovered.” A memorial was held celebrating the sixty-fifthbirthday of this surprisingly energetic woman in May 2007. On the flightback to Japan, I found myself wondering how much further mathematics
will advance while she is still a working scholar. I returned to Nagoya thefollowing day to continue with my research, revitalized by the days in
Norway.

I am always relaxed when I chat with her in English, because she has neverpounced on my grammar mistakes. I couldn’t wait to tell her the latest
results of my research. The details of the discoveries I had omitted in
e-mails from Japan I found easy to articulate here, face-to-face. I am
particularly grateful to her for showing genuine pleasure in my findings.
Students come to NTNU from all over the world. I believe her presencehelps to explain why.

International Conference by Graduate School of Mathematics

These pictures were taken at the 7th Nagoya International Conference. The Graduate School of Mathematics has beensponsoring this conference annually since 2001 with a revolving theme. In 2007, we invited Professor Toshikazu Sunada
who had long worked for our department, from 1974 to 1991 and is currently a professor at Meiji University, to the conference “Spectral Analysis in Geometry and Number Theory” that was organized mainly by young researchers. While amember of our department he honed his originality and creativity, making many honorable achievements that would go on
to shape his future research. We are proud to say our deparment has produced many such mathematicians known globally.

The main purpose of this particular visit was to complete the finial draft ofa paper we had collaborated on. It required examining the contents

Kawamura, Tomomi

Before arriving here, to be honest, I was worried about working in such ahuge institution. I thought that it may be overwhelming. But fortunately it
did not take much time to adjust to the Graduate School of Mathematics here
in Nagoya University. I thank the students and entire staff who welcomed me.
I found the relationships among students and staff to be very good, no matter
their position or status. They both are full of willingness to discover theworld of mathematics with their enriched knowledge!
Various lectures and seminars taking place throughout the year allow bothstudents and professors exposure to diverse research. Education seminars
provide a good opportunity to learn about new research we would ordinarily
not come into contact with, therefore expanding our vision in general. I havefound this to be one of the great benefits of joining such a large department
and feel grateful for the opportunity to participate.
What made me the most surprised was the Office Hour System that isparticular to our department: Cafe David and Ladies’ Lunch. The system hasa cooperative nature not common to universities and has become an
important part of this department. In general, office hours have meant for
students a severe moment. It is normally understood as a time slot when
professors wait for students’ with enough courage to visit their office, asking
any questions relevant to the professor’s course. Some students knock on thedoor awkwardly or hesitate and just turn away. On the contrary, our officehour takes place in an area where students often pass by casually. This is the
key! We have arranged such a setting in order to get students to come andask us questions freely.
I participate in 2 different types of office hours. First, there is Cafe David
that is organized by younger researchers and certain graduate students called
TAs. The objective is to answer academic questions over a cup of coffee inan open lounge environment. But actually, many students and staff end up
using it as an enjoyable opportunity to communicate with others in thedepartment. I sometimes find that an area which I am not very strong or
knowledgeable of will be discussed at Cafe David, and as a result I takeaway a new perspective on the topic, changing my impression of it altogether.
Another one is Ladies’ Lunch. As female students remain the minority in our

16

department one of my colleagues, Professor Yukari Ito, planned this weekly
event to create a space where girls can exchange information easily. They get
together over lunch boxes where they can chat freely about some of theunique worries that female students often face. Although these students arenormally cheerful members of our department, I do hope they can talk about
concerns here, and reduce any existing related stress.
During both office hours, I find that rather than giving something to thestudents, I tend to learn from their strong desire and passion towards
mathematics. I can say that these moments fuel my drive for my own
research.
I guess the good attendance of students in our lectures is the result of an
educational environment in which students and faculty can communicate
openly. All members of our department community are encouraged to
exchange and challenge ideas openly. As a result students and professors feela unique level of comfort with each other. This environment motivates not
only students but also faculty. That’s why I tell myself every day “Ok, let’s
do it together!” regarding our pursuit of research in mathematics. I hope thistype of comfortable communication, high research quality, and our vision for
future learning, continue to evolve bringing positive opportunities for all.

From September 1-5, 2008 our 8th annual International Nagoya Mathematics Conference titled, “Combinatrics andRepresentation Theory” was held. At this time, we aimed at focusing not only on our main theme of interaction of combinatorics and representation theory, but also at including the most recent research outcomes from the relevant areas ofprobability theory, mathematical physics, geometry, while also hoping to achieve meaningful international exchange andcommunication among scholars. With over 100 conference participants we invited about 20 researchers to present from:
United States, France, Australia, England, Denmark, Poland, and Italy, and this time, many younger researchers including
graduate students participated, too. At the conference representation theories such as classical group, Hecke Algebra, andquantum group, and those that follow such as combinatorics, enumeration problems of combinatorial objects such asplane partitions were the central themes of the addresses given by 10 Japanese and 14 foreign presenters. Starting withthe lecture by Professor A. Ram entitled, “Two boundary Hecke algebras and tantalizer algebras” and ending with Professor J. Stembridge’s lecture “Admissible W-graphs”, a heated discussion drew in broad participation and debate among
the many in attendance.

Past Conference Titles●2011（11th）Topology and Analysis of Foliation●2010（10th）
Representation Theory of Algebraic Groups
and Quantum Groups'10●2009（9th）Harmonic Analysis and Partial Differential
Equations●2008（8th） Combinatorics and Representation Theory●2007（7th） Spectral Analysis in Geometry andNumber Theory●2006（6th） Representation Theory of Algebraic Groups
and Quantum Groups’06

17

Research Activities at Graduate School of Mathematics

Graduate School of Mathematics NAGOYA UNIVERSITY

The Global 30 Project - Bringing Nagoya University to the World

Academic Cooperation Programs

In July 2009, the selection results of the 2009 Project for Establishing Core Universities for Internationalization (Global 30) were announced,
with Nagoya University standing out as one of the Global 30 leaders.

Our Graduate School has several academic exchange programs sharedwith worldwide institutions to promote and develop cooperation in thefield of mathematical sciences through the following activities:

The objectives of Global 30 are to strengthen the international competitiveness of Japanese higher education and to offer an education withstandards that appeal to foreign students while, through creating an environment where Japanese students work together with international
students, fostering highly educated individuals who can be active internationally. The project comprehensively supports a plan to create
universities that act as bases for internationalization by providing both the high level of education expected from universities andenvironments that make studying in Japan more accessible for overseas students.

(1) Exchange of faculty and students.
(2) Exchange of publications and other academic materials.
(3) Bilateral symposia and workshops.
(4) Meetings to improve mutual research and educational
programs.
(5) Mutual student managed projects.

To lead Japan's universities toward internationalization, Nagoya University must transform itself into a "university of the world". This meansbuilding a new environment in which Japanese and international students work side by side. In this way, the high standards of undergraduate
and graduate education Nagoya University has achieved will be more widely accessible to students from overseas, and the University will beable to educate individuals with the ability to interact on the world stage.

Here is the list of institutions in cooperation agreement as of
May 2012:● Department of Mathematics, Nanjing University since 2012.
● Department of Mathematical Sciences, Soel National University since 2012.
● Faculty of Mathematics, Ruhr Universit t Bochum since 2011.
● Universite Paris 7 -Denis Diderot since 2004.
● The Korean Institute for Advanced Study (KIAS) since 2004.

SIGNING CEREMONY Memorandum of Understanding on Academic Cooperation

Here are some of the strategic measures being taken to realize this goal.
from http://www.nagoya-u.ac.jp/en/international/edu-act/g30/

Mathematics without Borders
Mathematics has no borders. No matter what nationality they are, mathematicians around the world strive each day through their research toprogress the development of mathematics. Among them there are always researchers out there somewhere pursuing answers to the sameproblems. Therefore, it can be said that the exchange of information regarding research is extremely important. In order to exchange this up
to date information our school works hard to promote and offer various conferences, intensive courses, seminars and workshops.
In this vein, in 2004 we established a formal academic alliance between Korean Institute for Advanced Study (KIAS) and Paris 7 Denis
Diderot University. With them we have conducted cooperative research workshops and the exchange of graduate students as research
assistants.

Department of Mathematics, NANJING UNIVERSITY andGraduate School of Mathematics,
NAGOYA UNIVERSITYMarch 2, 2012, Graduate School of Mathematics, Nagoya University

Exchange beyond Fields
Mathematics has historically influenced other fields, and at the sametime evolved itself, from the influence of other research fields.
Nowadays, working towards a goal of broad global exchange is notenough. Conducting research with a vision beyond our own narrow
fields is also required. Our department makes a unique effort to strive
towards working with scholars of interdisciplinary research, and alsowith the Graduate School of Information Science, in order to further
this goal.

International Lounge
International Lounge is now open, which is a room speciallyarrangedto activate international exchanges and partnership in various
occasions.

Mathematicians shouldering a tradition
K. Yosida : 1942 - 1953 at Nagoya University
Created the theory of semi-groups of operators. His book
"Functional Analysis" is read all over the world.
T. Nakayama : 1942 - 1964 at Nagoya University
One of the original members of the department of mathematics,
his studies on modular representation theory of symmetric groups
and non-commutative rings are world-famous.
K. Ito : 1943 - 1952 at Nagoya University, and then to Kyoto
University
His formula on stochastic differential equations, applied tomathematical finance, is world-famous. He received the first
Gauss Prize on 2006.
M. Kuranishi : Graduated from Nagoya University then was on
our staff from 1949 - 1963, and from there, went to Columbia
University (U.S.).
Decisive work on deformation theory of complex structures is hisarea of focus.

18

M. Nagata : Graduated from Nagoya University and was on our
staff from 1950 - 1953, then moved on to Kyoto University.
He did world-famous work on the theory of commutative rings andthe foundation of algebraic geometry.
T. Kubota : Graduated from Nagoya University then worked here
from 1952 - 1993.
He created the theory of p-adic zeta-functions with Leopoldt.
M. Kashiwara : 1974 - 1977 at Nagoya University, then to RIMS,
Kyoto University
Decisive work on the theory of D-modules and its application torepresentation theory.
K. Aomoto : 1978 - 2002 at Nagoya Unviersity
Created the theory of multi-variable hypergeometric functions,
independently of Gel'fand.
S. Mori : 1980 - 1990 at Nagoya University, then on to RIMS,
Kyoto University
Completed the classification theory of 3 dimensional algebraic
varieties. He also received the Fields Prize in 1990.

19

Introduction of Teaching Faculty

Graduate School of Mathematics NAGOYA UNIVERSITY

Awata, Hidetoshi

Hashimoto, Mitsuyasu

Ishi, Hideyuki

Kawamura, Tomomi

keywords

keywords

keywords

keywords

integrable model, conformal field theory

commutative ring,invariant theory

homogeneous space,unitary representation

knot theory, topology

My current subject is the quantum field theory with infinite-dimensional
symmetry such as Virasoro algebra, for example, the string theory,
conformal field theory and two-dimensional integrable model.

I am mainly interested in commutative ring theory. I mainly study
commutative rings with group actions such as determinantal rings. In
particular, ring theoretic properties of invariant subrings under the actionof algebraic groups are very interesting for me.

I study geometry and analysis on a manifold whose symmetry is not sosmall but not so large. I am interested in how a 'strain' of the manifold isreflected on function spaces over the manifold.

I mainly research the relations between diagrams and invariants of knots
and links. It is amazing that a lot of formulas are proved using advanced
theories, though some of them seem to be very easy.

Fujiwara, Kazuhiro

Hayashi, Masahito

Ito, Kentaro

Kimura, Yoshifumi

keywords

keywords

keywords

keywords

Number theory, Arithmetic geometry,non-commutative class field theory

quantum information, information theory

Hyperbolic geometry, Kleinian groups

Fluid Mechanics, vortex motion,
Turbulence

I am trying to understand a very primitive but basic object "integers" viathe modern aspects such as automorphic forms and Shimura varieties(non-commutative class field theory). Algebraic and geometricmethods (including cohomology theory) are mainly used in my approach.

In order to ravel the mistery of quantum theory, I have studied quantum
information teory based on the information theoretical aspect.
My study treats this topic from the view points of information theory andrepresentation theory.

My research interest is the theory of Kleinian groups. In this area,
hyperbolic geometry, Riemann surfaces and low-dimensional topology
are closely related each other. I am studying deformation spaces ofKleinian groups, which have fractal boundaries.

My research specialty is theoretical and computational fluid mechanics. I
am interested in studying various mathematical aspects of flow problems.
In particular, I am concerned with the nonlinear dynamics of vortices andwaves in flows including turbulence.

Furusho, Hidekazu

Hayashi, TakahiroIto, Yukari

Kobayashi, Ryoichi

keywords

keywords

keywords

keywords

number theory, arithmetic geometry,motivic fundamental groupquantum group, Hopf algebra,
tensor category

crepant resolution, quatient singularity,
McKay correspondence

Diophantine Geometry

I am working on (p-adic) periods and (p-adic) differential equations
associated with motivic fundamental groups. I am also working on
structures on special types of quantum groups associated with the
KZ-equations.

The field I am working in is quantum groups and their representations. In
particular I am interested in generalized quantum groups and theirrelations to other area of mathematics, such as classical representation
theory and integrable systems.

I am studying quotient singularities by finite groups. I am interested in
the geometric and algebraic structure of them and their correspondences.
They are also related with the super string theory in physics.

Diophantine geometry of minimal surfaces is a new reserach area which
combines two classical subjects. A mysterious geometry emerges fromthis coupling, in which I am recently most interested in.

Garrigue, JacquesHesselholt, Lars

Iyama, Osamu

Kondo, Shigeyuki

keywords

keywords

keywords

Programming languages, Type theory.

Homotopy theory, algebraic K-theory,p-adic arithmetic geometry

Representation theory, Auslander-Reiten theory,
Derived category, Cluster theory

Algebraic Geometry, Moduli,
Automorphic Forms

I am studying the theory underlying functional programming languages.
For more than 15 years, I have been working at fitting types onto theworld, but the job is far from finished.

My research focuses on the study of automorphisms of high dimensional
manifolds through homotopy theory, algebraic K-theory, and topologicalcyclic homology. In this investigation, invariants and constructions in
p-adic arithmetic geometry naturally appear.

The theory of categorical structure of modules over associative algebras
was initiated by Auslander, Gabriel, Ringel and others. This active
research area has a strong impact on other fields of mathematics andphysics, and requires fresh ideas from young students.

I'm studying geometry of the moduli spaces of some varieties byapplying the theory of periods of K3 surfaces and Borcherds theory on
automorphic forms.

Geisser, Thomas

Hishida, Toshiaki

Kanno, Hiroaki

keywords

keywords

Kubo, Masashi

keywords
Algebraic K-theory, motivic cohomology, higher
Chow groups

Partial Differential Equations,
Navier-Stokes Flow

Quantum Field Theory, Supersymmetric Gauge,
String Theory, Integrable Systemsource coding, channel coding

I work on algebraic K-theory and motivic invariants of varieties, andtheir applications to arithemetic algebraic geometry. This includes classfield theory of schemes, the Tate-Beilinson conjectures, and theBeilinson-Soule vanishing conjecture.

Interests are focussed on the existence, uniqueness, regularity, stability
and asymptotic behavior of the Navier-Stokes flow in several unboundeddomains. Functional- and real-analytic methods are often employed.

I am working on quantum geometry underlying the web of dualities
among supersymmetric gauge/string theories. Representation theory andintegrable systems are powerful tools for the investigation of quantum
invariants in such a geometry.

My research field is the information theory. They includes many topics,and I study especially source coding and channel coding. Those topics
treat of rate of data compression and channel capacity respectively. They
are based on the theory of stochastic processes.

Gyoja, AkihikoHora, Akihito

Kato, Jun

Ma, Shohei

keywords

keywords

keywords

keywords

keywords

keywords

representation theory,
algebraic groupprobability theory, harmonic analysis,
asymptotic representation theory.

Nonlinear Partial Differential Equations,
Fourier Analysis

Algebraic Geometry / moduli space /rationality problem

I am working to formulate "(unknown) invariant theory" which should
associate to infinite dimensional representations, mainly using algebraic
analysis, algebraic geometry, and representation theory.

I am studying probability theory and harmonic analysis, particularlyinterested in hierarchies of limit theorems. Such a point of view is appliedalso to asymptotic theory for group representations.

My research field is nonlinear partial differential equations relevant to
the wave propagation phenomena, and related topics. I have been
studying the solvability of such equations by using functional analysis,
Fourier analysis, etc.

I am interested in moduli spaces of special algebraic varieties.
Especially, I am studying the rationality problem for such moduli spaces.

Hamanaka, Masashi

Inahama, Yuzuru

Kawahira, Tomoki

Matsumoto, Kohji

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mathematical physics, elementary particle physics,
noncommutative solitons

Stochastic processes describe random
motions of paticles, etc.

Complex Dynamics,
Hyperbolic GeometryZeta-functions, L-functions

I am interested in mathematical structure behind law of nature,especially, elementary particle physics and string theory. Now I study
noncommutative solitons and integrable systems related to N=2 string
theory and twistor theory.

Among them, solutions of stochastic differential equations (SDEs) aremost important examples. I am now studying these processes by using
rough path theory, which is a generalization of SDE theory.

Dynamical systems in complex variables, as analogues of Kleiniangroups and 3-dimensional hyperbolic geometry

Studying distribution of values and analytic properties of various zeta
and L-functions such as the Riemann zeta-function, automorphic
L-functions, and multiple zeta-functions.

2021

Introduction of Teaching Faculty
Matsumoto, Sho

Graduate School of Mathematics NAGOYA UNIVERSITY

Nakanishi, Tomoki

Sasahara, YasuhiroTate, Tatsuya

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symmetric function,
representation theory

quantum integrable systems,
quantum groups

Global analysis, Calculus of variations

Global Analysis,
Geometric Asymptotic Analysis.

There are a lot of probability measures derived from representation
theory of symmetric groups and classical groups. I study them and their
asymptotic behaviour by using symmetric functions and calculus fordeterminants.

I study (i) the integrable systems in quantum dynamics and field theories,(ii) the algebraic structures and their representation theories behind themsuch as quantum groups and Lie algebras, and (iii) the interplay of (i) and(ii).

I am studying variational problems which appear in geometry andmathematical physics. In particular, I'm interested in problems which do
not result in solving differential equations.

I am interested in asymptotic properties of quantities and functions
appearing naturally in partial differential equations, geometry andrepresentation theory such as eigenfunctions and eigenvalues of elliptic
operators, multiplicities of group representations and matrix integrals.

Minami, Kazuhiko

Nayatani, Shin

Sasahira, Hirofumi

Tsugawa, Kotaro

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solvable lattice model, statistical mechanics,
quantum structure

nonpositively curved metric spaces,
rigidity of discrete groups, harmonic maps

Topology, Gauge theory

well-posedness, Fourier restriction norm,
I-method

I am mostly working in theories of quantum and statistical structure oflattice models. Within these areas one can work on problems involving
solvable lattice models, its algebraic structures, critical phenomena andapplications to magnetic materials

I am interested in themes of differential geometry such as conformal
geometry and geometry of nonpositively curved metric spaces. Recently
I study rigidity of actions of discrete groups on such metric spaces using
methods of harmonic maps, discrete geometry and random groups.

I study three and four dimensional topology using gauge theory. This
theory has been developing with relations to various fields. For example,
algebraic geometry, knot theory and physics. The geometry of three andfour dimensions is very different from higher dimensions and interesting.

I have interests in partial differential equations. My current focus is on
the study of the Cauchy problem of nonlinear dispersive equations byharmonic analysis.

Moriyama, Sanefumi

Ohira, Toru

Sato, Takeshi

Uzawa, Tohru

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String Theory, Gauge Theory,
Mathematical Physics

Mathematical Biology and Physiology /Delayed Stochastic Systems

modular equation / pi / periodgroup theory, representation theory,geometry

String theory is the most promising candidate for a unified description of
all particle interactions. My research concerns the underlying beautiful
mathematical structure of string theory and its physical implications.

My interest lies in creating mathematical models of various physical,
biological and social phenomena. Systems with feedbacks andinteractions under the influence of noise / fluctuations and delays are ofparticular focus.

I study special functions (hypregeometirc functions, modular function
e.t.c.), especially period relations and (iterative and series) approximations to pi.

Representation theory deals with symmetries in vector spaces. It is anextremely active field, with connections with various fields, pure andapplied.

Moriyoshi, Hitoshi

Ohsawa, Takeo

Sugimoto, Mitsuru

Yamagami, Shigeru

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Noncommutative Geometry,
The Atiyah-Singer Index Theorem

L2 extension theorem

Partial differential equations,
Fourier Analysis

operator algebra, tensor category

Noncommutative Geometry is a new framework in Mathematics
proposed by A. Connes. The Atiyah-Singer Index Theorem is a central
theme in Noncommutative Geometry, which is my current researchsubject.

There is a situation where the structure of an equation becomes simpler if
one makes a transformation by introducing extra variables. The L2
extension theorem due to Takegoshi and myself serves as an lemma inperforming such a strategy.

I am studying various properties of solutions to partial differential
equations by means of "estimates". Fourier analysis is the main tool, but
it is also an important object of study in itself.

Main interests are mathematical structures, which have origins in quantum
physics, such as representations of quantum algebras, quantum symmetries in operator algebras and quantum analysis in tensor categories.
Related fields in functional analysis are also in the research range.

Nagao, Kentaro

Ohta, Hiroshi

Suzuki, Hiroshi

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Algebraic geometry ,Donaldson-Thomas theory

symplectic geometry,gauge theory, Floer theory

algebraic number theory, capitulation
problemI have been studying 3-dimensional Calabi-Yau categories. Propeties of
the category induce various geometric/algebraic phenomena. In this area,
you may enjoy harmony of spectacular general theory and rich examples.

Recently, I am mainly studying two subjects: One is Floer cohomology
theory in symplectic geometry based on certain homotopical algebra (socalled A -algebra), and the other is to study some relationship between
singularity theory and symplectic/contact geometry.

When I calculate some groups, Hamiltonian graphs, Schur polynomials,
etc., I feel that this is not a number theory, and I sometimes remember
NaN.

Nagao, Taro

Okada, Soichi

Takahashi, Ryo

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random matrices,semiclassical theory

enumerative and algebraic combinatorics,
combinatorial representation theory

commutative algebra/representation theory of algebras

number theory

Random matrices are matrices with random number elements. Using themethods such as the semiclassical analysis, I multilaterally study randommatrices from the viewpoints of the fundamental theory and various
applications.

My research interests are in combinatorcs and its connection with otherfields such as algebra, representation theory, and integrable systems.
More specific topics of interest are related to Young diagrams, symmetricfunctions, alternating sign matrices, classical groups, etc.

I have been studying the boundary between commutative algebra andrepresentation theory of algebras, that is, representation theory ofcommutative rings. The main purpose is to understand the structure offinitely generated modules over a commutative noetherian ring.

I am studying arithmetic geometry over function fields of characteristic p.

Naito, Hisashi

Saito, Hiroshi

Tanigawa, Yoshio

Martin, Herschend

Designated Associate Professor（G30）
Fabien Trihan

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Differential Geometry, Variational Problem,
Computer Network System

algebraic geometry, algebraic cycle.

analytic number theory, zeta-function

Representation theory, Quivers,
Auslander-Reiten theory

My research subject are geometric variational problems and non-linear
partial differential equations. Recently, I also research an authentication
system of computer network.

My research interest is in algebraic geometry, especially in algebraic
cycles such as normal cones as key ingredients of intersection theory inview of Chow bivariant intersection theory and related topologicalinvariants such as vanishing cycles.

From the point of view of the modular relation, I am trying to generalize
the functional equations of the zeta functions and to apply it to the studyof arithmetical functions. I am also interested in multiple zeta functions.

My research is in representation theory of finite dimensional algebras. In
particular, I’m interested in homological methods and connections toalgebraic geometry, such as those appearing in higher dimensional
Auslander-Reiten theory.

22

23

Support for education and research

Graduate School of Mathematics NAGOYA UNIVERSITY

Staff from across many sections and areas are involved in the life and operationof the School of Science and Department of Mathematics.
The sections introduced here are an important part of our support structures.

Nagoya Mathematical Journal
Mathematics Library
A fully developed library is a quintessential element inproviding quality mathematics education, and thus ourmathematics library has served us well as the “face” ofour department. The library houses over 100,000 volumes
related to mathematical science and more than 1,400 kindsof periodicals, 90% of which are published overseas. Oneof our highlights is the Hilbert Collection, where copies ofnearly 10,000 academic papers that the greatest mathematician, David Hilbert (1862-1943), had owned. It has
become a valuable resource for research. Books ofreference including textbooks are found in the student
reference section in order to promote easy access to facilities for students. Online search catalogs are fully
equiped for easy access to books and electronic journals, and librarians offer support to users seeking further
information.

Known as a comprehensive academic journal for mathematics,
Nagoya Mathematical Journal (NMJ) has long been highly
evaluated internationally, since its first edition published by ourdepartment in June of 1950. All back numbers are available aselectronic archives, and can be accessed through a databasecalled Project Euclid by the library of Cornell University. Whilereviewing many creative mathematical papers submitted to thejournal from around the world, editing committees make anelaborate effort to maintain its scholastic quality. We firmly
believe that the academic value of NMJ depends on the advanced
level of mathematics with which our department deals. We areproud of NMJ as proof of the depth of its history and its
excellence shown by mathematicians in Nagoya.

Computers and Networks
Electronic journals and e-mail are part of the modern
indispensable tool of computer networking for researchers ofmathematical science. Computer laboratories are located in
Science Building I (2 rooms) and in Science Building A (1room). All PCs are connected to the intra-campus network(NICE), which offers reliable high-speed access to theInternet. This computer network environment corresponds tothe needs of both graduate students and faculty for exchanging various scholastic information. Our department iscommitted to enhancing our information technology environment as a research tool not only as a scaffold of numericalanalysis and information science, but also for theoreticaldevelopment by installing various mathematical software.

Office of Academic Affair

24

The Office of Academic Affairs was established in 2003, inorder to provide specific services needed by students andfaculty. In 2008, it was reorganized to deal with all
educational affairs. For students and faculty, the officeprocesses research grants (Grants-in-Aid for Scientific
Research) and student aid to attend workshops, andmanages study rooms and locker keys. In assisting department activities the office edits mathematical journals,
publishes information in the form of brochures and updates
web sites, prepares to hold international conference, suchas Nagoya International Conference, and hosts foreign
visitors. The office aims at creating better academic
surroundings with prompt service responding to department needs, with a friendly atmosphere as their motto.

http://projecteuclid.org/Dienst/Ul/1.0/Journal?authority=euclid.nmj

Office of Mathematics
Department
The Office of Mathematics Department supports faculty
and students by maintaining campus facilities, purchasing
office supplies, and arranging research and business trips.
The office, for example, takes care of air-conditioning forcomputer laboratories and classrooms. Its constant effort
provides faculty and students with a cozy environment toresearch and study, and the smooth arrangement of facility
use and meetings. Accordingly, the office plays animportant role for both faculty and students, helping them
to focus on their business within a comfortable campus,
doing its best to offer speedy and accurate service.

25

Graduate School of Mathematics

NAGOYA UNIVERSITY

Welcome to theWorld of Mathematics
Updated information can be found at the
department’s web page.
http://www.math.nagoya-u.ac.jp/en/index.html

Particularly for up to date information
regarding entrance exams, please see
the link below.
http://www.math.nagoya-u.ac.jp/en/education/index.html
JR Chuo Line

Bldg.C

Subway Meijo Line
Hisaya-odori

Ozone

Bldg.B

Marunouchi
Chikusa

NagoyaNakamura
Kuyakusho

Fushimi Sakae

Motoyama

SubwayHigashiyama Line

ImaikeNagoyaUniversity

Exit No.3

GokisoTakabata

JR Shinkansen

TsurumaiKanayama

Subway Sakuradori Line

Kamimaezu

YagotoSubwayTsurumai Line

Meitetsu Line
JR Shinkansen

ToyodaAuditorium

Exit No.2

Exit No.1

Aratamabashi
Nagoyako

Grad.Sch.of Math.

Bldg.A

Tokushige

Information

MuseumGraduate School of Mathematics Nagoya University
Chikusa-ku,Nagoya 464-8602 JAPAN TEL（052）789-2429 FAX（052）789-2829

Graduate School of Mathematics
Department of Mathematics, School of Science

NAGOYA UNIVERSITY