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Name: Hisashi Kasuya

Information:

Position:Associate Professor 

Affiliation: Osaka Univ.

email: kasuya   @  math.sci.osaka-u.ac.jp

CURRICULUM VITAE

Education

Employment and Fellowships

・October 2016--present: Associate Professor, Department of Mathematics, Graduate School of Science, Osaka University 

・November 2015-October 2017 : PD-Fellow, Institut de Mathtématiques de Jussieu – Paris Rive Gauche Paris France)

・April 2013–September 2016  Assistant Professor, Department of Mathematics Tokyo Institute of Technology

・ April 2010–March 2013 JSPS Research Fellow (DC1)

Grants

                  

・2019-04-01 – 2024-03-31 Grant-in-Aid for Scientific Research (B)

・ April 2015--March 2019  the Grand-in-Aid for Young Scientists (B) JSPS

・ October 2013--March 2015 the Grand-in-Aid for Research Activity Start-Up from JSPS

・ April 2010--March 2013 JSPS Research Fellowships for Young Scientists, DC1

Publications:

(1) H. Kasuya, Cohomologically symplectic solvmanifolds are symplectic, J. Symplectic Geom. 9 (2011) no. 4, 429-434

(subject: symplectic geometry, topology)

(2) H. Kasuya, Coeffective cohomology of symplectic aspherical manifolds. Proc. Amer. Math. Soc. 140 (2012), 2835--2842

(subject: symplectic geometry, Hodge theory, Non-Kahler geometry)

(3) H. Kasuya, Formality and hard Lefschetz properties of aspherical manifolds, Osaka J. math. 50 (2013) no. 2 439-455

(subject: Solvable Lie algebra, de Rham homotoy, symplectic geometry, Hodge theory, Non-Kahler geometry)

(4) H. Kasuya, Algebraic hulls of solvable groups and exponential iterated integrals on solvmanifolds , Geom. Dedicata 162 (2013), 263--270.

(subject: de Rham homotoy, solvable group)

(5) H. Kasuya, Minimal models, formality and hard Lefschetz properties of solvmanifolds with local systems, J. Differential Geom., 93, (2013), 269--298.

(subject: Solvable Lie algebra, de Rham homotoy, symplectic geometry, Hodge theory, Non-Kahler geometry, local system cohomology)

(6) H. Kasuya, Vaisman metrics on solvmanifolds and Oeljeklaus-Toma manifolds. Bull. London Math. Soc. (2013) 45 (1): 15--26.

(subject: complex geometry, LCK geometry, Non-Kahler Hermitian geometry, discrete subgroup of solvable Lie group)

(7) H. Kasuya, Techniques of computations of Dolbeault cohomology of solvmanifolds. Math. Z. 273 (2013), no. 1-2, 437--447.

(subject: complex geometry, Non-Kahler geometry)

(8) H. Kasuya, Geometrical formality of solvmanifolds and solvable Lie type geometries. RIMS Kokyuroku Bessatsu B 39, "Geometry of Transformation Groups and Combinatorics" 21-34

(subject: Riemannian geometry, de Rham homotory)

(9) H. Kasuya, The Frolicher spectral sequences of certain solvmanifolds. J. Geom. Anal. 25 (2015), no. 1, 317--328.

(subject: complex geometry, Non-Kahler geometry, Hodge theory)

(10) H. Kasuya, Hodge symmetry and decomposition on non-Kahler solvmanifolds. J. Geom. Phys. 76 (2014), 61--65.

(subject: complex geometry, Non-Kahler geometry, Hodge theory)

(11) A. Fino, H. Kasuya, L Vezzoni , SKT and tamed symplectic structures on solvmanifolds. Tohoku Math. J. (2) 67 (2015), no. 1,

(subject: complex geometry, Non-Kahler Hermitian geometry)

(12) H. Kasuya, de Rham and Dolbeault Cohomology of solvmanifolds with local systems.

(subject: topology, complex geometry, local system cohomology) .Math. Res. Lett. 21, (2014) No. 781--805..

(13) H. Kasuya, Lefschetz coincidence numbers of solvmanifolds with Mostow conditions. Arch. Math. (Brno) 50 (2014), no. 1, 27--37

(subject: topology, fixed point theory)

(14) D. Angella, H. Kasuya, Hodge theory for twisted differentials. Complex Manifolds 1 (2014), Art. 5.

(subject: complex geometry, Non-Kahler geometry, Hodge theory, Local system cohomology)

(15) H. Kasuya, Flat bundles and Hyper-Hodge decomposition on solvmanifolds.  Int. Math. Res. Not. IMRN 2015, no. 19, 9638–9659.

(subject: complex geometry,Kahler and Non-Kahler geometry, Hodge theory, local system cohomology)

(16)H. Kasuya, Examples of non-Kahler solvmanifolds admitting hodge decomposition. Real and Complex Submanifolds, Springer Proceedings in Mathematics & Statistics 106 (2014), 211--227.

(subject:, Non-Kahler geometry, Hodge theory)

(17) A. Fino, H. Kasuya, Tamed symplectic structures on compact solvmanifolds of completely solvable type. Ann. Sc. Norm. Super. Pisa, Cl. Sci. (5) 16, No. 3, 971-979 (2016).

(subject: symplectic geometry, Non-Kahler Hemitian geometry )

(18) H. Kasuya, Singularity of the varieties of representations of lattices in solvable Lie groups. J. Topol. Anal. 8 (2016), no. 2, 273–285.

(subject: Topology, representation of discrete group, deformation theory, solvable group, singularity of algebraic variety)

(19) H. Kasuya, Central theorems for cohomologies of certain solvable groups.  Trans. Amer. Math. Soc. 369 (2017), no. 4, 2879–2896.

(subject: group cohomology, algebraic group, solvable group)

(20) H. Kasuya, Cohomologies of Sasakian groups and Sasakian solvmanifolds.

Ann. Mat. Pura Appl. (4) 195 (2016), no. 5, 1713–1719.

(subject: Sasakian geometry, Hodge theory, local system cohomology) arXiv:1410.5183

(21) D. Angella, S. Calamai, H. Kasuya Cohomologies of generalized complex manifolds and nilmanifolds.  J. Geom. Anal. 27 (2017), no. 1, 142–161.

(subject:Generalized complex geometry

(22) S. Console, A. Fino, H. Kasuya, On de Rham and Dolbeault Cohomology of Solvmanifolds

Transform. Groups 21 (2016), no. 3, 653–680.

(subject: topology, complex geometry, discrete subgroup of solvable Lie group)

(23)H. Kasuya, Generalized deformations  and holomorphic poisson cohomology  of  solvmanifolds.  Ann. Global Anal. Geom. 51 (2017), no. 2, 155–177.

(subject: complex geometry,generalized complex geometry , deformation theory, holomorphic Poisson geometry)

(24)H. Kasuya, An extention  of  Nomizu's Theorem --A user's guide--

 Complex Manifolds 3 (2016), 231–238

(25) D. Angella, H. Kasuya, Cohomologies of deformations of solvmanifolds and closedness of some properties.North-Western European Journal of Mathematics 3 (2017), 75--105

(subject: complex geometry, Non-Kahler geometry, Hodge theory, deformation theory)

(26) H. Kasuya, Mixed Hodge structures and Sullivan's minimal models of Sasakian manifolds.  Ann. Inst. Fourier (Grenoble) 67 (2017), no. 6, 2533–2546.

(subject: Sasakian geometry, Hodge theory, de Rham homotopy)

(27) D. Angella, H. Kasuya, Bott-Chern cohomology of solvmanifolds. Ann. Global Anal. Geom. 52 (2017), no. 4, 363--411.

(subject: complex geometry, Non-Kahler geometry, Hodge theory, homological algebra)

(28) H. Kasuya,  Techniques of Constructions of Variations of Mixed Hodge Structures. Geom. Funct. Anal. 28 (2018), no. 2, 393–442.

(Kahler Geometry, Hodge theory)

(29)

H. Kasuya,

A differential geometric viewpoint of mixed Hodge structures.

Contemporary perspectives in differential geometry and its related fields. Proceedings of the 5th international colloquium on differential geometry and its related fields, Veliko Tarnovo, Bulgaria, September 6--10, 2016. Hackensack, NJ: World Scientific

(30) H. Ishida, H. Kasuya

Transverse Kähler structures on central foliations of complex manifolds . Ann. Mat. Pura Appl. (4) 198 (2019), no. 1, 61–81. (subject: complex geometry, de Rham homotopy, Hodge theory)

(31) D. Angella, H. Kasuya, Symplectic Bott-Chern cohomology of solvmanifolds. J. Symplectic Geom. 17(2019), no. 1, 41-91

( subject: symplectic geometry, Non-Kahler geometry, Hodge theory, local system cohomology)

(32)  H. Kasuya, Twisted Lefschetz numbers of infra-solvmanifolds and algebraic groups. J. Algebra 546 (2020), 457–466.

(subject: fixed point theory, local system cohomology, algebraic group, group cohomology)

(33) H. Kasuya, Remarks on Dolbeault cohomology of Oeljeklaus-Toma manifolds and Hodge theory

 Proc. Amer. Math. Soc. 149 (2021), no. 7, 3129–3137. 

(34) H. Kasuya,

Morgan's mixed Hodge structures and nonabelian Hodge structures

 Comm. Algebra 49 (2021), no. 6, 2655–2678.

(35)I.  Biswas, H. Kasuya,  Higgs Bundles and Flat Connections Over Compact Sasakian Manifolds. Comm. Math. Phys. 385 (2021), no. 1, 267–290.

( subject: differential geometry, metrics on vector bundles, sasakian geometry)

(36) H. Kasuya, Extended  simplicial rational Nomizu's Theorem  and Sullivan's minimal models for non-nilpotent groups

Geom Dedicata 216, 30 (2022).

( subject: Rational homotopy, group cohomology)

(37) H. Ishida, H. Kasuya,   Non-invariant deformations of left-invariant complex structures on compact Lie groups. Forum Math. 34, No. 4, 907-918 (2022).

( subject: deformation theory, compact Lie group,  representation of  semi-simple Lie algebra )

(38) H. Kasuya, Developments in non-K\”ahler Geometry--various examples and structures, Hodge theory and deformation theory-- 

(Japanese)  accepted by  Sugaku

非ケーラー幾何学の広がり―多様な例と構造，ホッジ理論および変形理論―   数学 掲載予定

(39) H. Kasuya, J. Stelzig, Frölicher spectral sequence and Hodge structures on the cohomology of complex parallelisable manifolds.  Transformation Groups 28, 1595–1606 (2023). 

( subject: Complex geometry,  Homogeneous space, Non-Kahler Hodge theory)

(40) H. Kasuya, Almost-formality and deformations of representations of the fundamental groups of Sasakian manifolds. Ann. Mat. Pura Appl. (4) 202 (2023), no. 4, 1793{1801.


(41)H. Kasuya,   Cohomology of holomorphic line bundles and Hodge symmetry on Oeljeklaus-Toma manifolds.

Eur. J. Math. 9, No. 3, Paper No. 50, 15 p. (2023).

(42) H. Kasuya, N. Miyatake  Uniformizations of compact Sasakian manifolds, accepted by Int. Math. Res.Not. IMRN , Volume 2024, Issue 10 8313-8328 

(43)   I Biswas, H. Kasuya

Higgs bundles and flat connections over compact Sasakian manifolds, II: quasi-regular bundles

accepted by  Annali della Scuola Normale Superiore di Pisa,

(44)  H. Kasuya, J. Stelzig

Complex non-Kähler manifolds that are cohomologically close to, or far from, being Kähler

accepted by  Math Res Let


Preprints:



(1) H. Ishida, H. Kasuya

Double sided torus actions and complex geometry on 

SU(3)


(2) H. Kasuya  

Categories of complex variations of Hodge structure over compact K"ahler manifolds


(3) H.Kasuya, D. Popovici

Partially Hyperbolic Compact Complex Manifolds

(4) I Biswas, H. Kasuya

Sasakian geometry and Heisenberg groups

(5) K. Hasegawa, H. Kasuya,

Cartan Flat Non-degenerate CR Lie Groups

Video Talks

H.Kasuya, Results and problems on cohomology of solvmanifolds Geometry and TACoS “Nilmanifold and Solvmanifold Techniques in Complex Geometry” https://www.youtube.com/channel/UCeHQo5ia5gCj5EnCUfY3Obw 

Organizing:

Mini-workshop on Higgs bundles, Osaka University (Japan), 27-28th/May/2024.

New developments in Kobayashi–Hitchin correspondence and Higgs bundles, Osaka Metropolitan University (Japan), 5-9/Aug/2024.





Recent Talks

8 Sep. 2015 H Kasuya: Extensions of Nomizu’s Theorem,  "Braids, Configuration Spaces and Quantum Topology" Tokyo, Japan

7 Mar 2016: H. Kasuya: Extensions of Nomizu's Theorem, Aula Tricerri, DiMaI, Firenze, Italy

25 Mar 2016: H. Kasuya: Extensions of Nomizu's Theorem,  The 4th Workshop "Complex Geometry and Lie Groups" Nara Japan

8 Sep. 2016: H. Kasuya: Morgan's mixed Hodge structures and geometric structures "Fifth International Colloquium on Differential Geometry and its Related Fields"  Veliko Tarnovo, Bulgaria

21 Mar. 2018 H. Kasuya: Techniques of constructions of variations of mixed Hodge structures "ANALYTIC AND ALGEBRAIC GEOMETRY" ICTS, Bangalore India.

28 Mar. 2018 H. Kasuya: Techniques of constructions of variations of mixed Hodge structures

"Complex analytic geometry" Tata Institute of Fundamental Research, Mumbai, India.

11 June 2018 -- Techniques of constructions of variations of mixed Hodge structures

The 5th workshop "Complex Geometry and Lie Groups" Florence Italy

28 Aug. 2018 "Techniques of constructions of variations of mixed Hodge structures and points"

第65幾何学シンポジウム 東北大 仙台

15. Nov. 2018  "DGA-Models and constructions of variations of mixed Hodge structures"

The 24th Symposium on Complex Geometry Kanazawa 2018

8 Dec. 2018  "Morgan's mixed Hodge structure and Hain's mixed Hodge structure" 第45回 変換群論シンポジウム 熊本

5. Jan. 2019 "DGA-Models of Variations of Mixed Hodge Structures"

Workshop on Global Aspects of Projective and Kähler Geometry, Sanya, China

18. Mar. 2019"DGA-Models of Variations of Mixed Hodge Structures" International Conference on Analytic & Algebraic Geometry

Kerala School of Mathematics, India

25. jun.2019 DGA-Models of Variations of Mixed Hodge Structures"

Interaction Between Algebraic Geometry and QFT.Moscow Institute of Physics and Technology ＭＩＰＴ Russia

13. July  2021 "Non-invariant deformations of left-invariant complex structures on compact Lie groups"

 2021 Pacific Rim Complex & Symplectic Geometry Conference 

22. July 2021 "Hodge theory on Oeljeklaus-Toma manifolds —number theory, complex geometry and group symmetry" 

HAYAMA Symposium on Complex Analysis in Several Variables XXII

6. Oct. "Higgs bundles in odd-dimensions"

Workshop on Toda equations, parabolic Higgs bundles, and related topics