General Information

Research Interests

I study the geometry and topology of complex algebraic varieties. My research focuses on Hodge theory, especially on the study of Hodge loci and normal functions, and on applications of mixed Hodge modules. Recently, I am also thinking about holonomic D-modules on complex abelian varieties and their Fourier-Mukai transforms. I am a member of the algebraic geometry group.

Mathematical Biography

I received my Ph.D. from Ohio State University in 2008, with Herb Clemens; after that, I was a postdoc at the University of Illinois at Chicago and at Kavli IPMU near Tokyo. Since 2012, I have been working as an assistant professor at Stony Brook University. During the academic year 2013/14, I am on leave at the University of Bonn.

Coordinates

Mailing Address

Department of Mathematics
Stony Brook University
Stony Brook, NY 11794-3651

Contact Information

Office: Math Tower 3-117 (map)
Phone: (631) 632-8618
E-Mail: cschnell@math.sunysb.edu

Preprints

  1. The Cremmer-Scherk Mechanism in F-theory Compactifications on K3 Manifolds
    [with M. Douglas and D. Park]
  2. The extended locus of Hodge classes

Published Papers

  1. Holonomic D-modules on abelian varieties
    To appear in Inst. Hautes Études Sci. Publ. Math.
  2. Kodaira dimension and zeros of holomorphic one-forms
    Ann. of Math. 179 (2014), 1–12
    [with M. Popa]
  3. Torsion points on cohomology support loci: from D-modules to Simpson's theorem
    To appear in Recent Advances in Algebraic Geometry (Ann Arbor, 2013)
  4. Weak positivity via mixed Hodge modules
    To appear in Hodge Theory and Complex Algebraic Geometry (Columbus, 2013)
  5. Generic vanishing theory via mixed Hodge modules
    Forum of Mathematics, Sigma 1 (2013), e1, 60pp.
    [with M. Popa]
  6. Moduli of products of stable varieties
    Compositio Math. 149 (2013), 2036–2070
    [with B. Bhatt, Z. Patakfalvi and W. Ho]
  7. The zero locus of the infinitesimal invariant
    Fields Inst. Commun. 67 (2013), 589–602
    [with G. Pearlstein]
  8. The fundamental group is not a derived invariant
    Derived Categories in Algebraic Geometry, 279–285. EMS Ser. Congr. Rep. 8 (2011)
  9. Canonical cohomology as an exterior module
    Pure Appl. Math. Quart. 7 (2011), no. 4, 1529–1542
    [with R. Lazarsfeld and M. Popa]
  10. Residues and filtered D-modules
    Math. Annalen 354 (2012), no. 2, 727–763
  11. Complex-analytic Néron models for arbitrary families of intermediate Jacobians
    Invent. Math. 188 (2012), no. 1, 1–81
  12. A variant of Néron models over curves
    Manuscripta Math. 134 (2011), no. 34, 359–375
    [with M. Saito]
  13. Derived invariance of the number of holomorphic 1-forms and vector fields
    Ann. Sci. Éc. Norm. Supér (4) 44 (2011), no. 3, 527–536
    [with M. Popa]
  14. Local duality and polarized Hodge modules
    Publ. Math. Res. Inst. Sci. 47 (2011), no. 3, 705–725
  15. Primitive cohomology and the tube mapping
    Math. Z. 268 (2011), no. 3–4, 1069–1089
  16. The locus of Hodge classes in an admissible variation of mixed Hodge structure
    C. R. Acad. Sci. Paris, Ser. I 348 (2010), 657–660
    [with P. Brosnan and G. Pearlstein]
  17. Two observations about normal functions
    Clay Math. Proc. 9 (2010), 75–9

Unpublished Papers

  1. Surfaces with big anticanonical class
    [with D. Chen]
  2. Canonical extensions of local systems
  3. Idempotent ultrafilters and polynomial recurrence

Ph.D. Thesis

Lecture Notes

Miscellaneous

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