PICARD-FUCHS EQUATIONS
- Hodge Numbers from Picard-Fuchs Equations. Charles Doran, Andrew Harder, Alan Thompson. SIGMA 13 (2017), 045, 23 pages.
- Zeta Functions of Alternate Mirror Calabi-Yau Families. Charles Doran, Tyler Kelly, Adriana Salerno, Steven Sperber, John Voight, Ursula Whitcher. Israel Journal of Mathematics.
- On the Hypergeometric Decomposition of Symmetric K3 Quartic Pencils. Charles Doran, Tyler Kelly, Adriana Salerno, Steven Sperber, John Voight, Ursula Whitcher. 62 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.
- Mirror Symmetry, Tyurin Degenerations, and Fibrations on Calabi-Yau Manifolds. Charles Doran, Andrew Harder, Alan Thompson. String-Math 2015.
- Calabi-Yau Manifolds Realizing Symplectically Rigid Monodromy Tuples. Charles Doran and Andreas Malmendier. Advances in Theoretical and Mathematical Physics, Volume 23, Issue 5.
- 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
- Special Function Identities from Superelliptic Kummer Varieties. Adrian Clingher, Charles Doran, Andreas Malmendier. Asian Journal of Mathematics, Volume 21, Number 5, pp. 909-952, October 2017.
- 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.
- 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.
- Normal Functions, Picard-Fuchs Equations, and Elliptic Fibrations on K3 Surfaces; Xi Chen, Charles Doran, Matthew Kerr, James Lewis; 2014; Journal für die reine und angewandte Mathematik (Crelles Journal), DOI: 10.1515/crelle-2014-0085, November 2014.
- 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.
- Hori-Vafa Mirror Periods, Picard-Fuchs Equations, and Berglund-Hübsch-Krawitz Duality; Charles Doran, Richard Garavuso; 2011; Journal of High Energy Physics, October 2011, 2011:128.
- Modularity of Fano Varieties. Charles Doran, Andrew Harder, Ludmil Katzarkov, Jacob Lewis, Victor Przyjalkowski. 37 pages.
- Algebraic K-Theory of Toric Hypersurfaces; Charles Doran, Matthew Kerr; 2011; Communications in Number Theory and Physics, Vol. 5, No. 2, pp. 397-600.
- 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.
- Families of Quintic Calabi-Yau 3-Folds with Discrete Symmetries; Charles Doran, Brian Greene, Simon Judes; 2008; Communications in Mathematical Physics, Volume 280, Number 2, 675-725.
- On Stokes Matrices of Calabi-Yau Hypersurfaces; Charles Doran, Shinobu Hosono; 2007; Advances in Theoretical and Mathematical Physics, 11, Issue 1, 147-174.
- Mirror Symmetry and Integral Variations of Hodge Structure Underlying One Parameter Families of Calabi-Yau Threefolds. Charles Doran, John Morgan; 2006; In Mirror Symmetry V, AMS/IP Studies in Advanced Mathematics, 38, 517-537.
- Algebraic and Geometric Isomonodromic Deformations; Charles Doran; 2001; Journal of Differential Geometry, 59, 33-85.
- 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.