An intrinsically linked simplicial $n$-complex

Ryo Nikkuni

Algebraic & Geometric Topology, to appear, 2027 Peer-reviewed
Intrinsic linking of a simplicial $n$-complex embedded in $\mathbb{R}^{2n}$

Ryo Nikkuni

Archiv der Mathematik, 127(2) 205-214, Aug, 2026 Peer-reviewed
A short proof of the generalized Conway-Gordon-Sachs Theorem

Ryo Nikkuni

Journal of Knot Theory and Its Ramifications, 34(12) 2550057, Jun 27, 2025 Peer-reviewed
Converses to generalized Conway-Gordon type congruences

Ryo Nikkuni

Tokyo Journal of Mathematics, 47(2) 353-364, Dec, 2024 Peer-reviewed
Crossing numbers and rotation numbers of cycles in a plane immersed graph

Ayumu Inoue, Naoki Kimura, Ryo Nikkuni, Kouki Taniyama

Journal of Knot Theory and Its Ramifications, 31(11) 2250076, Aug 30, 2022 Peer-reviewed

Misc.

Topology of spatial graphs and their intrinsic properties

Ryo Nikkuni

76(1) 1-26, Jan, 2024 Peer-reviewedInvited
空間グラフのトポロジー

新國亮

数理科学, 617 13-19, 2014 Invited

Books and Other Publications

空間グラフのトポロジー : Conway-Gordonの定理をめぐって

新國亮

サイエンス社, Jul, 2022 (ISBN: 9784781915487)

Presentations

Intrinsic linking of a simplicial $n$-complex embedded in $\mathbb{R}^{2n}$

新國亮

研究集会「3次元と4次元のトポロジー」, Sep 15, 2026 Invited
On intrinsically linked simplicial $n$-complexes

Ryo Nikkuni

International Workshop on Spatial Graphs 2026, Aug 12, 2026 Invited
An intrinsically linked simplicial $n$-complex

Ryo Nikkuni

39th Summer Topology and Its Applications Conference, Aug 12, 2025 Invited
Conway-Gordon type theorems and its applications

Ryo Nikkuni

Joint meeting of the NZMS, AustMS and AMS, Dec 10, 2024 Invited
Capturing knots and links in spatial graphs

Ryo Nikkuni

Knots and Spatial Graphs 2024, Nov 7, 2024 Invited
Conway--Gordon の空間7頂点完全グラフをめぐって

新國亮

研究集会「結び目理論」, Feb 14, 2024 Invited
空間グラフの内在的性質に関する最近の話題

新國亮

ミニシンポジウム「グラフ理論とその関連分野」，Japanese Conference on Combinatorics and its Applications 2023, Aug 28, 2023 Invited
Converses to generalized Conway-Gordon type congruences

Ryo Nikkuni

Knots and Spatial Graphs 2023, Jun 16, 2023, KAIST Invited
Capturing links in spatial complete graphs

Ryo Nikkuni

AMS Sectional meeting (2021 Fall Southeastern Sectional Meeting, formerly at the University of South Alabama), Nov 20, 2021 Invited
Conway-Gordon theorems and Vassiliev invariants

Ryo Nikkuni

Workshop on Knot Theory, Sep 4, 2021 Invited
Intrinsic knotting and linking on complete graphs

Ryo Nikkuni

Mini-symposium on Knot Theory, Japanese Conference on Combinatorics and its Application 2020, Aug 19, 2020 Invited
Linear spatial complete graphs and generalized Conway-Gordon theorems

Ryo Nikkuni

Knots and Spatial Graphs 2020, Feb 18, 2020 Invited
n-Flat Graphs

Ramin Naimi (Speaker), Ryo Nikkuni, Yukihiro Tsutsumi, Hedda Zhao

AMS Sectional meeting (2019 Fall Western Sectional Meeting), Nov 10, 2019 Invited
Generalizations of the Conway-Gordon theorems and intrinsic knotting on complete graphs

Hiroko Morishita, Ryo Nikkuni

AMS Sectional meeting (2019 Fall Western Sectional Meeting), Nov 9, 2019 Invited
Topology of Spatial Graphs - Extrinsic properties and Intrinsic properties - 3

NIKKUNI Ryo

Summer School on Mathematical Physics 2019, Aug 25, 2019 Invited
Topology of Spatial Graphs - Extrinsic properties and Intrinsic properties - 2

NIKKUNI Ryo

Summer School on Mathematical Physics 2019, Aug 24, 2019 Invited
Topology of Spatial Graphs - Extrinsic properties and Intrinsic properties - 1

NIKKUNI Ryo

Summer School on Mathematical Physics 2019, Aug 23, 2019 Invited
On re finements and generalizations of the Conway-Gordon theorems

NIKKUNI Ryo

The 66th Topology Symposium, Aug 10, 2019 Invited
A preorder in the set of genus two irreducible handlebody-knot table with up to 6 crossings (joint work with Y. Ozawa and M. Suzuki)

NIKKUNI Ryo

Handlebody-knots and Related Topics 12, Jul 15, 2019 Invited
On generalizations of the Conway-Gordon theorems

NIKKUNI Ryo

Intelligence of Low-dimensional Topology 2019, May 22, 2019 Invited
Non-existence of epimorphisms between certain genus two handlebody-knot groups

NIKKUNI Ryo

Claremont Topology Seminar, Mar 7, 2019 Invited
Generalization of the Conway-Gordon theorems and intrinsic knotting on complete graphs

NIKKUNI Ryo

Seminar on Geometric Topology of dimension 3, Jun 26, 2018
Intrinsic knotting on spatial complete graphs on 8 vertices

NIKKUNI Ryo

N-KOOK Seminar, May 19, 2018 Invited
Random linear embeddings of spatial graphs and configurations of Mobius ladders

Erica Flapan, Kenji Kozai (Speaker), Ryo Nikkuni

AMS Sectional Meetings (2018 Spring Eastern Sectional Meeting), Apr 21, 2018 Invited
Conway-Gordon type theorems for Hamiltonian knots in spatial complete graphs

Ryo Nikkuni

An invited talk at Hanyang University, Feb 26, 2018 Invited
Regular isotopy on spatial graphs and adjusted diagrams

Ryo Nikkuni

School of Spatial Graph Theory, Jan 23, 2018 Invited
On adjusted diagrams of spatial graphs

Ryo Nikkuni

Knots in Ryukyus 2017, Jan 21, 2018
Conway-Gordon Type Theorems

Ryo Nikkuni

Session on Spatial Graph Theory, MAA MathFest 2017, Jul 27, 2017 Invited
A regular isotopy between two spatial graphs which are ambient isotopic

Ryo Nikkuni

Friday Seminar on Knot Theory, May 12, 2017 Invited
Generalized Simon invariants of spatial graphs

Erica Flapan (Speaker), Will Fletcher, Ryo Nikkuni

AMS Sectional Meetings (2017 Spring Southeastern Sectional Meeting), Mar 10, 2017 Invited
Linear embeddings of a graph into the 3-space and Conway-Gordon type theorems

Ryo Nikkuni

International workshop on Topology and graphs in polymer chemistry, Aug 6, 2016 Invited
Free differential calculus and classical and twisted Alexander invariants of spatial graphs

Ryo Nikkuni

International Workshop on Spatial Graphs 2016, Aug 5, 2016
A calculation of the difference of the Jones polyomials for a certain pair of knots

Ryo Nikkuni

Knots in Ryukyus 2016, Feb 20, 2016
On calculations of the twisted Alexander ideals for spatial graphs, handlebody-knots and surface-links

Atsushi Ishii, Ryo Nikkuni, Kanako Oshiro

AMS Sectional Meetings (2015 Fall Western Sectional Meeting), Oct 24, 2015 Invited
Calculation of Alexander invariants of spatial graphs

Ryo Nikkuni

Handlebody-knots and related topics VIII, Sep 27, 2015 Invited
Common factors of Jones polynomials for links and Vassiliev invariants

Ryo Nikkuni

Extended KOOK Seminar 2015, Aug 20, 2015
On calculations of the twisted Alexander ideals for spatial graphs, handlebody-knots and surface-links

Ryo Nikkuni

Friday Seminar on Knot Theory, May 1, 2015 Invited
Conway-Gordon Type Theorems and its Applications II, III

Ryo Nikkuni

The 4th HYU MATH-Workshop: Low Dimensional Topology, Oct 24, 2014 Invited
Conway-Gordon Type Theorems and its Applications I

Ryo Nikkuni

The 4th HYU MATH-Workshop: Low Dimensional Topology, Oct 23, 2014 Invited
Reduced Wu and generalized Simon invariants for spatial graphs

Erica Flapan, Speaker, Will Fletcher, Ryo Nikkuni

AMS Sectional Meetings (2014 Western Spring Sectional Meeting), Apr 6, 2014 Invited
On a generalization of the Simon invariant

Ryo Nikkuni

Knots in Ryukyus 2013, Sep 12, 2013
On reduced Wu invariants of spatial graphs

Ryo Nikkuni

International Workshop on Spatial Graphs 2013, Aug 13, 2013
Conway-Gordon type theorem for the complete four-partite graph $K_{3,3,1,1}$

Ryo Nikkuni

Spatial Graphs Conference, Jun 8, 2013
On reduced Wu invariants of spatial graphs and the intrinsic chirality

Ryo Nikkuni

Tokyo Woman's Christian University Topology Seminar, May 11, 2013 Invited
A homotopy classification of two-component spatial graphs up to neighborhood equivalence

Ryo Nikkuni

Claremont Topology Seminar, Feb 26, 2013 Invited
Capturing a knot in a spatial intrinsically knotted graph

NIKKUNI Ryo

Knots in Ryukyus 2017, Sep 4, 2012
△Y-exchanges and Conway-Gordon type theorems

Ryo Nikkuni

Knots and Spatial Graphs 2012, Aug 15, 2012 Invited
On the Heawood graph as an intrinsically knotted graph

NIKKUNI Ryo

University of Tsukuba Topology Seminar, Jul 4, 2012 Invited
△Y-exchanges and Conway-Gordon type theorems

Ryo Nikkuni

Intelligence of Low-dimensional Topology, May 16, 2012 Invited
On invariants of knots and links in a spatial complete four-partite graph $K_{3,3,1,1}$

Ryo Nikkuni

The Eighth East Asian School of Knots and Related Topics, Jan 10, 2012

Professional Memberships

Mathematical Society of Japan

Research Projects

空間グラフの内在的性質の研究とその応用

科学研究費助成事業, 日本学術振興会, Apr, 2025 - Mar, 2028

新國亮
Research of the topology of spatial graphs and their intrinsic properties

Grants-in-Aid for Scientific Research, Japan Society for the Promotion of Science, Apr, 2022 - Mar, 2025

Ryo Nikkuni
Geometric and algebraic aspects of Dehn surgery

Grants-in-Aid for Scientific Research, Japan Society for the Promotion of Science, Apr, 2019 - Mar, 2024

MOTEGI Kimihiko
Research of hierarchy structures of spatial graphs and algebraic invariants

Grants-in-Aid for Scientific Research, Japan Society for the Promotion of Science, Apr, 2019 - Mar, 2024
Geometric structures and combinaorial structures of 3-manifolds

Grants-in-Aid for Scientific Research, Japan Society for the Promotion of Science, Apr, 2015 - Mar, 2020

Sakuma Makoto

Social Activities

トポロジーの視点と発想

Lecturer

東京女子大学, 東京女子大学模擬授業 (情報数理科学科模擬授業), Jul 23, 2025 - Present
○と◇を同じと見る数学〜トポロジーの考え方

Lecturer

FROMPAGE, 夢ナビライブ2012, Jul 14, 2012
紐を結んで数学を

Lecturer

武蔵野市, 武蔵野地域五大学共同講演会, Nov 1, 2011

Media Coverage

夢みる数学～東京女子大学現代教養学部数理科学科編～

講談社, Rikejo, vol. 32, pp.56--57, Feb 9, 2015 Newspaper, magazine

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