HODGE THEORY

• Mirror Symmetry for Lattice Polarized Del Pezzo Surfaces. Charles Doran, Alan Thompson. Communications in Number Theory and Physics 12 (2018) Number 3, 543-580.
• Specialization of Cycles and the K-Theory Elevator. Charles Doran, Matt Kerr, James Lewis, Jaya Iyer, Pedro Luis del Angel, Stefan Müller-Stach, Deepam Patel. 43 pages.
• ​​​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.
• 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 Mirror Quartic K3 Surfaces. Charles Doran, Andrew Harder, Andrey Novoseltsev, Alan Thompson; 2016; Advances in Mathematics, Volume 298, 6 August 2016, 369-392.
• 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.
• Calabi-Yau Threefolds Fibred by Kummer Surfaces Associated to Products of Elliptic Curves. Charles Doran, Andrew Harder, Andrey Novoseltsev, Alan Thompson; 2016; In String-Math 2014, American Mathematical Society, Proceedings of Symposia in Pure Mathematics 93, 278-303.
• 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.
• Short Tops and Semistable Degenerations; Ryan Davis, Charles Doran, Adam Gewiss, Andrey Novoseltsev, Dmitri Skjorshammer, Alexa Syryczuk, Ursula Whitcher; 2014; Experimental Mathematics, Volume 23, Issue 4, 2014, pp. 351-362.
• 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.
• Closed Form Expressions for Hodge Numbers of Complete Intersection Calabi-Yau Threefolds in Toric Varieties. Charles Doran, Andrey Novoseltsev; 2010; In Mirror Symmetry and Tropical Geometry, Contemporary Mathematics, Vol. 527, pp. 1-14.
• 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.
• 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.
• Algebraic Topology of Calabi-Yau Threefolds in Toric Varieties; Charles Doran, John Morgan; 2007; Geometry and Topology, 11, 597-642.
• Modular Invariants for Lattice Polarized K3 Surfaces. Adrian Clingher, Charles Doran; 2007; Michigan Mathematical Journal, 55, Issue 2, 355-393.
• On K3 Surfaces with Large Complex Structure; Adrian Clingher, Charles Doran; 2007; Advances in Mathematics, 215, 504-539.
• 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.