MODULAR FORMS

• Mirror Symmetry for Lattice Polarized Del Pezzo Surfaces. Charles Doran, Alan Thompson. Communications in Number Theory and Physics 12 (2018) Number 3, 543-580.
• ​​Calabi-Yau Threefolds Fibred by High Rank Lattice Polarized K3 Surfaces. Charles Doran, Andrew Harder, Andrey Novoseltsev, Alan Thompson. Mathematische Zeitschrift (2019). https://doi.org/10.1007/s00209-019-02279-9
• Hodge Numbers from Picard-Fuchs Equations. Charles Doran, Andrew Harder, Alan Thompson. SIGMA 13 (2017), 045, 23 pages.
• Picard-Fuchs Uniformization of Modular Subvarieties. Brent Doran, Charles Doran, Andrew Harder. In Uniformization, Riemann-Hilbert Correspondence, Calabi-Yau Manifolds, and Picard-Fuchs Equations, Institut Mittag-Leffler, Advanced Lectures in Mathematics, Volume 42, 21-54.
• Vertical D4-D2-D0 Bound States on K3 Fibrations and Modularity. Vincent Bouchard, Thomas Creutzig, Duiliu-Emanuel Diaconescu, Charles Doran, Callum Quigley, Artan Sheshmani. Communications in Mathematical Physics, Volume 350, Issue 3, 1069-1121 (2017).
• Calabi-Yau Manifolds Realizing Symplectically Rigid Monodromy Tuples. Charles Doran and Andreas Malmendier. Advances in Theoretical and Mathematical Physics, Volume 23, Issue 5.
• Humbert Surfaces and the Moduli of Lattice Polarized K3 Surfaces. Charles Doran, Andrew Harder, Hossein Movasati, Ursula Whitcher; 2016; In String-Math 2014, American Mathematical Society, Proceedings of Symposia in Pure Mathematics 93, 124-155.
• String-Math 2014, Vincent Bouchard, Charles Doran, Stefan Méndez-Diez, Callum Quigley, Eds.; 2016; American Mathematical Society, Proceedings of Symposia in Pure Mathematics 93, 396 pages.
• The 14th Case VHS via K3 Fibrations. Adrian Clingher, Charles Doran, Jacob Lewis, Andrey Novoseltsev, Alan Thompson; 2016; In Recent Advances in Hodge Theory: Period Domains, Algebraic Cycles, and Arithmetic, Cambridge University Press, London Mathematical Society Lecture Note Series 427, 165-227.
• Geometrization of N-Extended 1-Dimensional Supersymmetry Algebras, I; Charles Doran, Kevin Iga, Jordan Kostiuk, Greg Landweber, Stefan Méndez-Diez; 2015; Advances in Theoretical and Mathematical Physics, Volume 19 (2015) Number 5, pp. 1043-1113.
• Families of Lattice Polarized K3 Surfaces with Monodromy; Charles Doran, Andrew Harder, Andrey Novoseltsev, Alan Thompson; 2015; International Mathematics Research Notices, 2015 (23): 12265-12318.
• Algebraic Cycles and Local Quantum Cohomology; Charles Doran, Matt Kerr; 2014; Communications in Number Theory and Physics, Volume 8 (2014), Number 4, pp. 703-727.
• Automorphic Forms for Triangle Groups; Charles Doran, Terry Gannon, Hossein Movasati, Khosro Shokri; 2013; Communications in Number Theory and Physics, Volume 7 (2013), Number 4, pp. 689-737.
• Modularity of Fano Varieties. Charles Doran, Andrew Harder, Ludmil Katzarkov, Jacob Lewis, Victor Przyjalkowski.  37 pages.
• Lattice Polarized K3 Surfaces and Siegel Modular Forms; Adrian Clingher, Charles Doran; 2012; Advances in Mathematics, Volume 231, Issue 1, 10 September 2012, Pages 172–212.
• Algebraic K-Theory of Toric Hypersurfaces; Charles Doran, Matthew Kerr; 2011; Communications in Number Theory and Physics, Vol. 5, No. 2, pp. 397-600.
• Note on a Geometric Isogeny of K3 Surfaces. Adrian Clingher, Charles Doran; 2011; International Mathematics Research Notices, 2011 (16): 3657-3687.
• Yau's Work on Moduli, Periods, and Mirror Maps for Calabi-Yau Manifolds. Charles Doran; 2010; In Geometry and Analysis, Volume I. Editor L. Ji. Pages 93-102.
• Normal Forms, K3 Surface Moduli, and Modular Parametrizations. Adrian Clingher, Charles Doran, Jacob Lewis, Ursula Whitcher; 2009; In Groups and Symmetries, proceedings of the CRM conference in honor of John McKay. CRM Proceedings & Lecture Notes, 47, 81-98.
• Modular Forms and String Duality, Noriko Yui, Helena Verrill, Charles Doran, Eds.; 2008; Fields Institute Communications, 54, 297 pages.
• Modular Invariants for Lattice Polarized K3 Surfaces. Adrian Clingher, Charles Doran; 2007; Michigan Mathematical Journal, 55, Issue 2, 355-393.
• Algebro-geometric Isomonodromic Deformations Linking Hauptmoduls: Variation of the Mirror Map. Charles Doran; 2001; Centre de Recherches Mathematiques: CRM Proceedings and Lecture Notes, 30, 27-35.
• Picard-Fuchs Uniformization and Modularity of the Mirror Map; Charles Doran; 2000; Communications in Mathematical Physics, 212, 625-647.
• Picard-Fuchs Uniformization: Modularity of the Mirror Map and Mirror- Moonshine. Charles Doran; 2000; Centre de Recherches Mathematiques: CRM Proceedings and Lecture Notes, 24, 257-281.