Rchr
J-GLOBAL ID：201801005069396631
Update date: Jul. 07, 2023
Hikami Kazuhiro
ヒカミ カズヒロ | Hikami Kazuhiro
Affiliation and department：
Homepage URL (1)：
https://sites.google.com/view/khikami
Research field (3)：
Mathematical physics and basic theory
, Algebra
, Geometry
Research theme for competitive and other funds (22)：
- 2022 - 2027 量子モジュラー形式の深化と展開
- 2020 - 2025 幾何的漸化式に基づく量子トポロジーと弦の場の量子構造の数理の究明
- 2020 - 2024 Asymptotic behaviors of quantum invariants of knots and three-manifolds
- 2016 - 2021 Studies on Mock Modular Forms and Quantum Invariants
- 2017 - 2020 行列模型に基づくファットグラフの分子生物学への応用
- 2017 - 2020 結び目群の表現と量子不変量の漸近挙動
- 2014 - 2017 Quantum invariants of knots and representations of knot groups
- 2011 - 2016 Study of modular/quasimodular forms and multiple zeta values appearing in various aspects of mathematics and physics
- 2012 - 2015 Geometry of Quantum Dilogarithm Function
- 2011 - 2015 Quantum Topology and Modular Forms in Mathematical Physics
- 2010 - 2012 Volume Conjecture and its generalizations
- 2009 - 2011 Studies on topological quantum computation
- 2007 - 2010 Studies on modular and quasimodular forms arising in various contexts in mathematics and physics
- 2007 - 2008 Research of number theoretic properties of quantum invariants of knots and 3-manifolds and its application
- 2006 - 2008 Geometry of Quantum Invariants of Knots and 3-Manifilds, and Its Applications to Physics
- 2005 - 2006 Research of relation among quantum invariant and number theoretic invariants and modular forms
- 2003 - 2005 結び目の量子不変量の物理的研究
- 2000 - 2003 Mathematics in ultradiscrete integrable systems
- 1997 - 1999 Studies of Nonlinear Waves and Nonlinear Dynamical Systems
- 1996 - 1996 可積分系における長距離力と境界条件の効果・およびその物性物理への応用
- 1995 - 1995 ハルデイン・シャストリー型スピン系の代数的構造の解析
- 1995 - 1995 長距離相互作用をもつ系の解析とその物性物理への応用
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Papers (81)：
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Anna Beliakova, Kazuhiro Hikami. Non-semisimple invariants and Habiro’s series. Topology and Geometry. 2021. 161-174
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Kazuhiro Hikami. DAHA and skein algebra of surfaces: double-torus knots. Letters in Mathematical Physics. 2019
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Kazuhiro Hikami. Note on Character Varieties and Cluster Algebras. SIGMA. 2019. 15. 003
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Kazuhiro Hikami, Jeremy Lovejoy. Hecke-type formulas for families of unified Witt en-Reshetikhin-Turaev invariants. COMMUNICATIONS IN NUMBER THEORY AND PHYSICS. 2017. 11. 2. 249-272
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Kazuhiro Hikami, Jeremy Lovejoy. Torus knots and quantum modular forms. Research in the Mathematical Sciences. 2015. 2. 2
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MISC (1)：
Lectures and oral presentations (19)：
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3-manifodls and quantum modular forms
(AMS spring western virtual sectional meeting: special session "q-series, number theory, and quantum topology" 2022)
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Quantum invariants, q-series, DAHA
(Number Theory, Strings, and Quantum Physics 2021)
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モックモジュラー形式と量子モジュラー形式
(東北大学理学部数学科談話会 2021)
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Braid Group and Cluster Algebra
(GeMAT Seminar (Geometric Methods in Algebra and Topology) 2020)
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DAHA and skein algebra on surface
(Zoom Cluster Seminar 2020)
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Professional career (1)：
Association Membership(s) (2)：
American Mathematical Society
, 日本物理学会
