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G₂ Manifolds

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Published papers and preprints (most recent listed first)

• [29] Spiro Karigiannis and John Loftin; "Octonionic-algebraic structure and curvature of the Teichmüller space of G₂ manifolds"; in preparation.
• [28] Xenia de la Ossa, Spiro Karigiannis, and Eirik Eik Svanes; "Geometry of general U(m)-structures: Kähler identities, the dd^c lemma, and Hodge theory"; in preparation.
• [27] Thomas A. Ivey and Spiro Karigiannis; "Cohomogeneity one solitons for the isometric flow of G₂-structures"; Geometriae Dedicata 218 (2024), 102, 35pp. DOI: doi.org/10.1007/s10711-024-00954-8
• [26] Anton Iliashenko and Spiro Karigiannis; "A special class of k-harmonic maps inducing calibrated fibrations"; Mathematical Research Letters, to appear.
• [25] Shubham Dwivedi, Panagiotis Gianniotis, and Spiro Karigiannis; "Flows of G₂-Structures, II: Curvature, torsion, symbols, and functionals"; submitted for publication.
• [24] Spiro Karigiannis and Lucía Martín-Merchán "Extrinsic geometry of calibrated submanifolds"; Mathematische Zeitschrift 307 (2024), 33, 26pp. DOI: doi.org/10.1007/s00209-024-03503-x
• [23] Benjamin Aslan, Spiro Karigiannis, and Jesse Madnick; "Calibrated geometry in hyperKähler cones, 3-Sasakian manifolds, and twistor spaces"; Canadian Journal of Mathematics, published online, print version to appear. DOI: doi.org/10.4153/S0008414X24000282
• [22] Max Chemtov and Spiro Karigiannis; "Observations about the Lie algebra g₂ ⊂ so(7), associative 3-planes, and so(4) subalgebras"; Expositiones Mathematicae 40 (2022), 845-869. DOI: doi.org/10.1016/j.exmath.2022.10.004
• [21] Da Rong Cheng, Spiro Karigiannis, and Jesse Madnick; "A variational characterization of calibrated submanifolds"; Calculus of Variations and Partial Differential Equations 62 (2023), 174, 38pp. DOI: doi.org/10.1007/s00526-023-02513-7
• [20] Thomas A. Ivey and Spiro Karigiannis; "Twisted-Austere Submanifolds in Euclidean Space"; Symmetry, Integrability and Geometry: Methods and Applications 17 (2021), 023, 31pp. DOI: doi.org/10.3842/SIGMA.2021.023
• [19] Spiro Karigiannis and Jason Lotay; "Bryant-Salamon G₂ manifolds and coassociative fibrations"; Journal of Geometry and Physics 162 (2021), 104074, 60pp. DOI: doi.org/10.1016/j.geomphys.2020.104074
• [18] Spiro Karigiannis; "Introduction to G₂ geometry"; Lectures and Surveys on G₂ manifolds and related topics; Fields Institute Communications, vol 84. Springer, New York, NY. (EXPOSITORY) DOI: doi.org/10.1007/978-1-0716-0577-6_1
• [17] Da Rong Cheng, Spiro Karigiannis, and Jesse Madnick; "Bubble tree convergence of conformally cross product preserving maps"; Asian Journal of Mathematics 24 (2021), 903-984. DOI: doi.org/10.4310/AJM.2020.v24.n6.a1
• [16] Shubham Dwivedi, Panagiotis Gianniotis, and Spiro Karigiannis; "A gradient flow of isometric G₂ structures"; The Journal of Geometric Analysis 31 (2021), 1855-1933. DOI: doi.org/10.1007/s12220-019-00327-8
• [15] Ki Fung Chan, Spiro Karigiannis, and Chi Cheuk Tsang; "The L_B-cohomology on compact torsion-free G₂ manifolds and an application to "almost" formality"; Annals of Global Analysis and Geometry 55 (2019), 325-369. DOI: doi.org/10.1007/s10455-018-9629-x
• [14] Ki Fung Chan, Spiro Karigiannis, and Chi Cheuk Tsang; "Cohomologies on almost complex manifolds and the ∂∂-lemma"; Asian Journal of Mathematics 23 (2019), 561-584. DOI: doi.org/10.4310/AJM.2019.v23.n4.a2
• [13] Spiro Karigiannis and Dominic Joyce; "A new construction of compact torsion-free G₂ manifolds by gluing families of Eguchi-Hanson spaces"; Journal of Differential Geometry 117 (2021), 255-343. DOI: doi.org/10.4310/jdg/1612975017
• [12] Spiro Karigiannis and Jason Lotay; "Deformation theory of G₂ conifolds"; Communications in Analysis and Geometry 28 (2020), 1057-1210. DOI: doi.org/10.4310/CAG.2020.v28.n5.a1
• [11] Spiro Karigiannis and Nat Chun-Ho Leung; "Deformations of calibrated subbundles of Euclidean spaces via twisting by special sections"; Annals of Global Analysis and Geometry 42 (2012), 371-389. DOI: doi.org/10.1007/s10455-012-9317-1
• [10] Spiro Karigiannis, Ben McKay, and Mao-Pei Tsui; "Soliton solutions for the Laplacian coflow of some G₂-structures with symmetry"; Differential Geometry and its Applications 30 (2012), 318-333. DOI: doi.org/10.1016/j.difgeo.2012.05.003
• [09] Spiro Karigiannis; "What is… a G₂-manifold?"; Notices of the American Mathematical Society 58 (2011), 580-581. (EXPOSITORY)
• [08] Spiro Karigiannis; "Desingularization of G₂ manifolds with isolated conical singularities"; Geometry and Topology 13 (2009), 1583-1655. DOI: doi.org/10.2140/gt.2009.13.1583
• [07] Spiro Karigiannis; "Flows of Spin(7)-structures"; Proceedings of the 10th Conference on Differential Geometry and its Applications: DGA 2007; World Scientific Publishing, (2008), 263-277. DOI: doi.org/10.1142/9789812790613_0023
• [06] Spiro Karigiannis and Naichung Conan Leung; "Hodge theory for G₂-manifolds: Intermediate Jacobians and Abel-Jacobi maps"; Proceedings of the London Mathematical Society (3) 99 (2009), 297-325. DOI: doi.org/10.1112/plms/pdp004
• [05] Spiro Karigiannis; "Flows of G₂-structures, I."; Quarterly Journal of Mathematics 60 (2009), 487-522. DOI: doi.org/10.1093/qmath/han020
• [04] Spiro Karigiannis; "Some notes on G₂ and Spin(7) geometry"; Recent Advances in Geometric Analysis; Advanced Lectures in Mathematics, Vol. 11; International Press, (2010), 129-146.
• [03] Spiro Karigiannis and Maung Min-Oo; "Calibrated sub-bundles in non-compact manifolds of special holonomy"; Annals of Global Analysis and Geometry 28 (2005), 371-394. DOI: doi.org/10.1007/s10455-005-1940-7
• [02] Marianty Ionel, Spiro Karigiannis, and Maung Min-Oo; "Bundle constructions of calibrated submanifolds in R⁷ and R⁸"; Mathematical Research Letters 12 (2005), 493-512. DOI: doi.org/10.4310/MRL.2005.v12.n4.a5
• [01] Spiro Karigiannis; "Deformations of G₂ and Spin(7) structures on manifolds"; Canadian Journal of Mathematics 57 (2005), 1012-1055. DOI: doi.org/10.4153/CJM-2005-039-x

• List of all my articles available on the arXiv.
• My author/reviewer page on MathSciNet. (Subscription to MathSciNet required.)

Harvard University PhD Thesis

• Deformations of G₂ and Spin(7) Structures on Manifolds

Harvard University Minor Thesis

• The Inverse Scattering Transform and Integrability of Nonlinear Evolution Equations

Undergraduate Expository Papers

• Generalized Symmetries, Conservation Laws, and Noether's Theorem in Classical Mechanics
• Quasi-Exactly Solvable Systems in Quantum Mechanics
• Variational Symmetries of the Willmore Functional (Coming someday...)