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Hikita, Tatsuyuki
Research Institute for Mathematical Sciences (RIMS) Assistant Professor
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Last Updated :2025/05/27
Basic Information
Affiliated programs (koza)
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Last Updated :2025/05/27
Research
Research Topics, Overview of the research
Research Topics
Geometric representation theoryOverview of the research
We propose a concept of canonical bases in equivariant K-theory or equivariant elliptic cohomology for conical symplectic resolutions and try to apply them to algebraic geometry, representation theory, or hypergeometric functions.
Research Areas
Papers
- Abelian and non-abelian elliptic stable envelopesTatsuyuki Hikita第8回Algebraic Lie Theory and Representation Theory 報告集, Jan. 2024
- Non-toric examples of elliptic canonical basesTatsuyuki Hikita第6回 Algebraic Lie Theory and Representation Theory 報告集, 2021
- On an algebro-geometric realization of the cohomology ring of conical symplectic resolutionsTatsuyuki Hikita第60回代数学シンポジウム報告集, 2015, Invited
- Elliptic canonical bases for hypertoric varieties疋田 辰之第5回 Algebraic Lie Theory and Representation Theory 報告集, 2019
- Canonical bases in equivariant K-theory of conical symplectic resolutions疋田 辰之第3回 Algebraic Lie Theory and Representation Theory 報告集, Oct. 2017
- An Algebro-Geometric Realization of the Cohomology Ring of Hilbert Scheme of Points in the Affine PlaneTatsuyuki HikitaINTERNATIONAL MATHEMATICS RESEARCH NOTICES, Apr. 2017, Peer-reviewed
- Affine Springer fibers of type A and combinatorics of diagonal coinvariantsTatsuyuki HikitaADVANCES IN MATHEMATICS, Oct. 2014, Peer-reviewed
Misc.
- On an algebro-geometric realization of the cohomology ring of conical symplectic resolutions (Combinatorial Representation Theory and Related Topics)疋田 辰之数理解析研究所講究録, Apr. 2016
- Affine Springer fibers of type A and combinatorics of diagonal coinvariants (Combinatorial Representation Theory and Related Topics)Hikita TatsuyukiRIMS Kokyuroku, Dec. 2013
Presentations
- K-theoretic canonical bases and their elliptic analoguesTatsuyuki Hikita2022年度日本数学会年会代数学分科会特別講演, 28 Mar. 2022, Invited
- Remarks on canonical bases in equivariant K-theoryTatsuyuki HikitaGeometric Representation Theory, 13 Oct. 2016, Invited
- On the cohomology of conical symplectic resolutionsTatsuyuki Hikita日本数学会2016年度秋季総合分科会無限可積分系特別講演, 16 Sep. 2016, Invited
- On an algebro-geometric realization of the cohomology ring of conical symplectic resolutionsTatsuyuki HikitaWorkshop on Algebraic Lie Theory and Symplectic Geometry, 24 Mar. 2016, Invited
- On an algebro-geometric realization of the cohomology ring of conical symplectic resolutionsTatsuyuki HikitaAlgebraic Geometry in East Asia 2016, 18 Jan. 2016, Invited
- On an algebro-geometric realization of the cohomology ring of conical symplectic resolutionsTatsuyuki Hikita代数幾何学シンポジウム, 20 Oct. 2015, Invited
- On an algebro-geometric realization of the cohomology ring of conical symplectic resolutionsTatsuyuki HikitaCombinatorial Representation Theory and Related Topics, 19 Oct. 2015
- On an algebro-geometric realization of the cohomology ring of conical symplectic resolutionsTatsuyuki HikitaThe 60th Algebra Symposium, 03 Sep. 2015, Invited
- An algebro-geometric realization of the cohomology ring of Hilbert scheme of points in the affine planeTatsuyuki HikitaRepsentation theory and Related Topics, 17 Feb. 2015, Invited
- On a theorem of DeConcini-ProcesiTatsuyuki HikitaShanghai Workshop on Representation Theory, Dec. 2014, Invited
- Rational shuffle conjecture and affine Springer fibers of type ATatsuyuki Hikita第17回代数群と量子群の表現論, 02 Jun. 2014
- Affine Springer fibers of type A and combinatorics of diagonal coinvariantsTatsuyuki HikitaCombinatorial Representation Theory and Related Topics, Oct. 2012
- Affine Springer fibers of type A and combinatorics of diagonal coinvariantsTatsuyuki HikitaGeometric/categorical aspects of representation theory, 21 Feb. 2012, Invited
- A proof of the Stanley-Stembridge conjectureTatsuyuki HikitaCombinatorics on flag varieties and related topics 2025, 12 Feb. 2025, Invited
- A proof of the Stanley-Stembridge conjectureTatsuyuki Hikita名古屋組合せ論・表現論セミナー, 06 Dec. 2024, Invited
- A proof of the Stanley-Stembridge conjectureTatsuyuki Hikita2024 TALKS IN COMBINATORICS, Beijing Institute of Technology, 29 Nov. 2024, Invited
- (q,t)-chromatic symmetric functionsTatsuyuki HikitaGeometry and Mathematical Physics, 22 Nov. 2024, Invited
- A proof of the Stanley-Stembridge conjectureTatsuyuki Hikita東京科学大学表現論セミナー, 22 Nov. 2024, Invited
- Non-toric examples of elliptic canonical basesTatsuyuki HikitaElliptic Integrable Systems, Representation Theory and Hypergeometric Functions, 01 Aug. 2023, Invited
- Abelian and non-abelian elliptic stable envelopesTatsuyuki HikitaAlgebraic Lie Theory and Representation Theory 2023, 15 May 2023
- Elliptic bar involutions for quiver varietiesTatsuyuki HikitaRepresentation theory and geometry of loop spaces, 12 Jan. 2023, Invited
- Non-toric examples of elliptic canonical basesTatsuyuki HikitaMS seminar, IPMU, 11 Nov. 2021, Invited
- Non-toric examples of elliptic canonical basesTatsuyuki HikitaAlgebraic Lie Theory and Representation Theory, 26 Jun. 2021
- Elliptic canonical bases for toric hyper-Kahler manifoldsTatsuyuki Hikita東大京大代数幾何セミナー, 17 Jun. 2020, Invited
- Highest weight categories arising from equivariant coherent sheaves on toric hyper-Kahler manifoldsTatsuyuki Hikita阪大オンライン代数幾何学セミナー, 08 Jun. 2020, Invited
- Elliptic canonical bases for toric hyper-Kahler manifoldsTatsuyuki HikitaGeometric Representation Theory and Quantum Field Theories, 19 Dec. 2019, Invited
- Elliptic and K-theoretic canonical bases for hypertoric varieties疋田 辰之Representation Theory of Algebraic Groups and Quantum Groups, 24 Oct. 2019, Invited
- Elliptic canonical bases for hypertoric varietiesTatsuyuki HikitaAlgebraic Lie Theory and Representation Theory, 24 May 2019
- シンプレクティック双対性入門疋田 辰之数学入門公開講座, 30 Jul. 2018
- Canonical bases in equivariant K-theory of conical symplectic resolutionsTatsuyuki HikitaAlgebraic Lie Theory and Representation Theory, 10 Jun. 2017, Invited
Awards
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Last Updated :2025/05/27
Education
Teaching subject(s)
- From 01 Apr. 2024, To 31 Mar. 2025Calculus with Exercises AN149, Spring, Institute for Liberal Arts and Sciences, 3
- From 01 Apr. 2023, To 31 Mar. 2024Mathematical Theory of SymmetriesN177, Fall, Institute for Liberal Arts and Sciences, 2
- From 01 Apr. 2023, To 31 Mar. 2024Linear Algebra with Exercises AN151, Spring, Institute for Liberal Arts and Sciences, 3
- From 01 Apr. 2022, To 31 Mar. 2023Invitation to Modern Mathematics and Mathematical SciencesN114, Spring, Institute for Liberal Arts and Sciences, 2
- From Apr. 2020, To Mar. 2021Invitation to Modern Mathematics and Mathematical Sciences - Basic concepts and their role in various sciencesSpring, 全学共通科目
- From Apr. 2021, To Mar. 2022Invitation to Modern Mathematics and Mathematical Sciences - Basic concepts and their role in various sciencesSpring, 全学共通科目
