Hirofumi Nakai

Profile Information

Affiliation: Associate Professor, Tokyo City University

Degree: (BLANK)(Osaka City University)

J-GLOBAL ID: 200901061241026172
researchmap Member ID: 5000008709

External link

I am interested in the structure of the stable homotopy category of spectra, and I have been working on it using some gadgets like Adams or Adams-Novikov spectral sequence. Of course, the relevant computations are very hard as much as ``Tour de France''. Then, our lack of knowledge on behavior of Adams differentials is crucial. Instead, many researchers are exploring the Hurewicz image to coefficient groups of some generalized homology theories nowadays. I also have been studying such topics past few years.

Research Interests

Research Areas

Natural sciences / Geometry / algebraic topology, homotopy theory

Research History

2020 - Present

Faculty of Science and Engineering, Department of Natural Sciences, Tokyo City University
Apr, 2009 - Mar, 2020

Faculty of Knowledge Engineering, Department of Natural Sciences, Tokyo City University
Apr, 2008 - Mar, 2009

准教授, 知識工学部リテラシー学群自然科学系列, 武蔵工業大学
Apr, 2007 - Mar, 2008

講師, 知識工学部リテラシー学群自然科学系列, 武蔵工業大学
Sep, 2006 - Mar, 2007

講師, 工学部教育研究センター, 武蔵工業大学
Oct, 2001 - Aug, 2006

General Education Division, Oshima National College of Maritime Technology
Apr, 2001 - Sep, 2001

Faculty of Science, Himeji Institute of Technology

Education

Apr, 1995 - Mar, 2000

Osaka City University
Apr, 1993 - Mar, 1995

Osaka City University
Apr, 1989 - Mar, 1993

Tottori University

Papers

The method of infinite descent in stable homotopy theory II

Hirofumi Nakai, Douglas C. Ravenel

New York Journal of Mathematics, 30(1) 231-269, Feb, 2024 Peer-reviewed
A Simple Formula for Doomsday

Hirofumi Nakai

The Mathematical Intelligencer, 45(2) 131-132, Dec 2, 2022 Peer-reviewedLead author
On the Stable Homotopy Groups of Certain James Constructions

7(1) 111-120, Mar, 2014
ラムダ代数を用いたAdams $E_{2}$項の元の表示

中井洋史

東京都市大学共通教育センター紀要, 6(1) 81-93, Mar, 2013
Chromatic method in motivic homotopy category

5(1) 43-56, Mar, 2012
トポロジーの工学への応用（現状と展望）

中井洋史

東京都市大学共通教育センター紀要, 4(1) 91-103, Mar, 2011
Solution of Kervaire invariant problem, and some remaining problems

Journal of General Education Center, 3(1) 23-34, Mar, 2010
超楕円曲線に随伴する形式群とモジュライスタック

中井洋史

武蔵工業大学共通教育センター紀要, 2(1) 24-39, Mar, 2009
On beta-elements in the Adams-Novikov spectral sequence

Hirofumi Nakai, Douglas C. Ravenel

JOURNAL OF TOPOLOGY, 2(2) 295-320, 2009 Peer-reviewed
代数トポロジーにおける数論的方法

中井洋史

武蔵工業大学共通教育センター紀要, 1(1) 16-30, Mar, 2008
AN ALGEBRAIC GENERALIZATION OF IMAGE J

Hirofumi Nakai

HOMOLOGY HOMOTOPY AND APPLICATIONS, 10(3) 321-333, 2008
On the homotopy groups of $E(n)$-local spectra with unusual invariant ideals

Hirofumi Nakai, Katsumi Shimomura

Geometry & Topology Monographs, 10(1) 319-332, Jun, 2007 Peer-reviewed
The structure of the general chromatic $E_1$-term $Ext_{\Gamma(2)}^{0}(M_{2}^{1})$ at the prime $2$

Hirofumi Nakai, Daichi Yoritomi

Hiroshima Mathematical Journal, 33(1) 137-156, Jan, 2003 Peer-reviewed
On the generalized Novikov first Ext group modulo a prime

H Nakai, DC Ravenel

OSAKA JOURNAL OF MATHEMATICS, 39(4) 843-865, Dec, 2002 Peer-reviewed
The chromatic $E_{1}$-term $H^{0}M_{1}^{2}$ for $p=3$

Hirofumi Nakai

Memoirs of the Faculty of Science, Kochi University, 23(1) 27-44, Mar, 2002 Peer-reviewed
The chromatic Ext groups Ext(Gamma)(0)(m+1) (BP*, M-2(1))

Ichigi, I, H Nakai, DC Ravenel

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 354(9) 3789-3813, 2002 Peer-reviewed
On the Adams-Novikov $E_2$-terms for Smith-Toda spectra $V(n)$

NAKAI Hirofumi

Department of Mathematics, Graduate School of Science, Department of Mathematics, Mar, 2000 Peer-reviewed
The chromatic $E_{1}$-term $H^{0}M_{1}^{2}$ for $p>3$

Hirofumi Nakai, Zen-ichi Yosimura

New York Journal of Mathematics, 6(1) 21-54, Jan, 2000 Peer-reviewed
The quasi $KO_{*}$-types of spectra $X$ with $KU_{*}X = Z/2^{m} \oplus Z/2^{n}$

Hirofumi Nakai, Zen-ichi Yosimura

Memoirs of the Faculty of Science, Kochi University (Mathematics), 17(1) 111-140, Mar, 1996 Peer-reviewed

Books and Other Publications

世界を読み解くリテラシー

井上健, 山本史華, 中井洋史, 井上健, 山本史華, 中井洋史 (Role: Joint editor)

萌書房, May 10, 2010 (ISBN: 4860650549)
近代ホモトピー論 (1940年代から1960年代まで) /土屋昭博述, 中井洋史記

土屋昭博, 中井洋史

Graduate School of Mathematical Sciences, the University of Tokyo, 2009

Presentations

Real Johnson-Wilson homology groups of few cell spectra

Hirofumi Nakai, Zen-ichi Yosimura

Sep 24, 2020
同変一般コホモロジー論における双対性の周辺

中井洋史

高知ホモトピー論談話会, Dec 26, 2019
Toward the united Johnson-Wilson theory

NAKAI Hirofumi

Dec, 2019 Invited
On the structure maps of united Johnson-Wilson theory

NAKAI Hirofumi

Mar 31, 2019
A variant of Johnson-Wilson theory

中井洋史

高知ホモトピー論談話会, Dec 27, 2018
On the self map of real Johnson-Wilson theory

中井洋史

高知ホモトピー論談話会, Dec 27, 2017
An Introduction of motivic periodic and nilpotent phenomena

中井洋史

新居浜代数トポロジーワークショップ, Sep, 2017
On the cohomology of moduli stack of hyperelliptic curves

Hirofumi Nakai

The symposium of “Johnson homomorphisms and related topics”, May, 2017 Invited
On the structure of the motivic stable homotopy category

中井洋史

高知ホモトピー論談話会, Dec, 2016
On the singularity of hyperelliptic curve and Weierstrass Hopf algebroid

中井洋史

代数曲線論シンポジウム, Dec, 2016 Invited
ホモトピー論における最近の動向

中井洋史

鳥取大学数学談話会, Sep, 2016
Recent progress on the motivic stable homotopy groups of spheres

中井洋史

高知ホモトピー論談話会, Dec, 2015
ホモトピー論の系譜

中井洋史

高知ホモトピー論小談話会2015, Jul, 2015
The mathematical works of Katsumi Shimomura

中井洋史

高知ホモトピー論談話会, Dec, 2013
On the stable homotopy groups of $T(m)_{(j)}$

Hirofumi Nakai

5th East Asian Conference of Algebraic Topology, Dec, 2013 Invited
Adams型のスペクトル系列「(コ)ホモロジーからホモトピーへの架け橋」「解決した問題, 未解決の問題」

中井洋史

代数的トポロジー信州春の学校, Mar, 2013 Invited
Behren’s $Q(N)$ spectra and Shimomura’s $\beta$-elements

中井洋史

高知ホモトピー論談話会, Dec, 2012
Exact functor theorems and Elliptic cohomologies

中井洋史

SGAD2012, Nov, 2012 Invited
Toward understanding the motivic chromatic phenomena

中井洋史

高知ホモトピー論談話会, Dec, 2011
On $p$-torsion delta-elements in the Adams-Novikov spectral sequence

中井洋史

日本数学会秋期会, Sep, 2010

Professional Memberships

Apr, 1998 - Present

The Mathematical Society of Japan
American Mathematical Society

Research Projects

球面のホモトピー群の周期的元に関する研究

科研費, Apr, 2010 - Mar, 2013

中井洋史
BP理論を用いた有限スペクトラムの安定ホモトピー群の研究

科研費, Apr, 2004 - Mar, 2007

中井洋史
Formal group laws and Hopf algebroids associated to algebraic curves, and those relations with generalised cohomology theories
Homotopy groups of finite CW complex from the viewpoints of Brown-Peterson theory

Social Activities

授業改善に向けたデータの読み取りと活用等について

Lecturer

世田谷区教育委員会, 夏季教科等研修, Aug 23, 2018