Research keywords (8):
loop space
, operad
, discrete Morse theory
, homotopy group
, model category
, classifying space
, category and functor
, homology
Research theme for competitive and other funds (23):
2022 - 分野を超えて数学を語るコミュニティを創りたい!
2016 - 2021 結び目と3次元多様体の量子トポロジー
2020 - ホプフォロジカル代数のホモトピー論的研究
2020 - 2021 Homotopy theory of Hopfological algebra
2015 - 2019 Construction of a new model for configuration spaces by means of discrete Morse theory
2015 - 2017 Research on homotopy theory and reconstruction of spaces using categories
2013 - 2016 2-categorical covering theory for algebras
2013 - 2016 Homotopy noncommutativity of loop spaces
2011 - 2016 Iterated integrals, geometric structures of configuration spaces and applications to quantum topological invariants
2010 - 2014 Topological complexity and L-S theory
2011 - 2014 Combinatorial mathods in the study of topology of configuration spaces and their applications
2007 - 2010 gauge theory and homotopy theory
2005 - 2008 On unstable higher periodicity phenomena in model categories
2002 - 2004 高次懸垂写像の組み合わせ論的モデルによるホモトピー群の大域的構造の研究
2002 - 2004 The study of global structure of unstable homotopy groups by higher EHP sequence
1997 - 1998 THE INTEGRAL REPRESENTATION OF INFINITELY DIVISIBLE RANDOM FIELDS WITH ITS APPLICATION TO THE PROBLEM OF LAW EQUIVALENCE
1997 - 1998 Geometric reserch of closed differential forms on manifolds
1996 - 1996 Little cubeの空間のホモロジーとそのホモトピー論への応用
1995 - 1995 ループ空間のホモロジーとそのホモトピー論への応用
1995 - 1995 同変写像の分類と、その存在・非存在について
1994 - 1994 ループ空間のMorava K-理論とそのホモトピー論への応用
The study of the $v_n$-Bockstein operations on the homology of loop spaces
Construction of spectral sequences for loop spaces
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Papers (17):
Yasuhide Numata and Yusuke Takahashi and Dai Tamaki. Faces of directed edge polytopes. Australasian Journal of Combinatorics. 2023. 88. 1. 77-96
Dai Tamaki, Hiro Lee Tanaka. Stellar stratifications on classifying spaces. Trends in Mathematics. 2019. 287-313
Vidit Nanda, Dai Tamaki, Kohei Tanaka. Discrete Morse theory and classifying spaces. Advances in Mathematics. 2018. 340. 723-790
Dai Tamaki. Cellular stratified spaces. Combinatorial and Toric Homotopy: Introductory Lectures. 2017. 35. 305-435