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Calabi-Yau Manifolds

  • Mirror Symmetry for Lattice Polarized Del Pezzo Surfaces. Charles Doran, Alan Thompson. To appear in Communications in Number Theory and Physics.
  • ​​Calabi-Yau Threefolds Fibred by High Rank Lattice Polarized K3 Surfaces. Charles Doran, Andrew Harder, Andrey Novoseltsev, Alan Thompson. 31 pages.
  • Hodge Numbers from Picard-Fuchs Equations. Charles Doran, Andrew Harder, Alan Thompson. SIGMA 13 (2017), 045, 23 pages.
  • K3 Orientifolds. Charles Doran, Andreas Malmendier, Stefan Méndez-Diez, Jonathan Rosenberg. 18 pages.
  • Zeta Functions of Alternate Mirror Calabi-Yau Families. Charles Doran, Tyler Kelly, Adriana Salerno, Steven Sperber, John Voight, Ursula Whitcher. To appear in 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.  
  • Mirror Symmetry, Tyurin Degenerations, and Fibrations on Calabi-Yau Manifolds. Charles Doran, Andrew Harder, Alan Thompson. To appear in String-Math 2015.
  • 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 350, 1069-1121 (2017).
  • Calabi-Yau Manifolds Realizing Symplectically Rigid Monodromy Tuples. Charles Doran and Andreas Malmendier. 94 pages. arXiv:1503.07500
  • Equivalences of Families of Stacky Toric Calabi-Yau Hypersurfaces. Charles Doran, David Favero, Tyler Kelly. 15 pages. To appear in Proceedings of the American Mathematical Society.
  • 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.
  • Toric Degenerations and Laurent Polynomials related to Givental's Landau-Ginzburg Models; Charles Doran, Andrew Harder; 2016; Canadian Journal of Mathematics, Volume 68 (2016), 784-815. 
  • 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.
  • String Theory on Elliptic Curve Orientifolds and KR-Theory; Charles Doran, Stefan Méndez-Diez, Jonathan Rosenberg; 2015; Communications in Mathematical Physics, April 2015, Volume 335, Issue 2, pp. 955-1001.
  • 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.
  • T-Duality for Orientifolds and Twisted KR-Theory; Charles Doran, Stefan Méndez-Diez, Jonathan Rosenberg; 2014; Letters in Mathematical Physics, November 2014, Volume 104, Issue 11, pp. 1333-1364.
  • 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.
  • 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.
  • From Polygons to String Theory; Charles Doran, Ursula Whitcher; 2012; Mathematics Magazine, Volume 85, Number 5, December 2012, pp. 343-360.
  • 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.
  • 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.
  •  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.
  • Algebraic Topology of Calabi-Yau Threefolds in Toric Varieties; Charles Doran, John Morgan; 2007; Geometry and Topology, 11, 597-642.
  • Crosscaps in Gepner Models and the Moduli Space of T2 Orientifolds; Brandon Bates, Charles Doran, Koenraad Schalm; 2007; Advances in Theoretical and Mathematical Physics, Volume 11, Number 5, 839-912.
  • 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.
  • A Periodic Table for Supersymmetric M-Theory Orbifolds. Charles Doran, Michael Faux; 2003; Journal of Mathematical Physics, 44, 2853-2873.
  • Four-Dimensional N = 1 Super Yang-Mills Theory from an M-Theory Orbifold. Charles Doran, Michael Faux, Burt Ovrut; 2003; Advances in Theoretical and Mathematical Physics, 6, 329-355.
  • Intersecting Branes in M-Theory and Chiral Matter in Four Dimensions; Charles Doran, Michael Faux; 2002; Journal of High Energy Physics, JHEP08, 024.
  • 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.