Christian Schnell

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, and about pluricanonical bundles and their properties. I am a member of the algebraic geometry group.

Fall 2016 Teaching

This semester, I am teaching MAT 313.

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 was on leave at the University of Bonn. I am currently supported by a Centennial Fellowship from the American Mathematical Society.

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.stonybrook.edu

Preprints

1. Viehweg's hyperbolicity conjecture for families with maximal variation
   [with M. Popa]
2. Hodge modules on complex tori and generic vanishing for compact Kähler manifolds
   [with G. Pareschi and M. Popa]
3. Graded duality for filtered D-modules
   [with M. Saito]
4. The extended locus of Hodge classes

Published Papers

1. Fields of definition of Hodge loci
   To appear in Recent Advances in Hodge Theory (Vancouver, 2013)
   [with M. Saito]
2. On Saito's vanishing theorem
   Math. Res. Lett. 23, No. 2 (2016), pp. 499–527
3. On direct images of pluricanonical bundles
   Algebra Number Theory 8 (2014), no. 9, 2273–2295
   [with M. Popa]
4. The Cremmer-Scherk Mechanism in F-theory Compactifications on K3 Manifolds
   J. High Energ. Phys. 1405, 135 (2014)
   [with M. Douglas and D. Park]
5. Holonomic D-modules on abelian varieties [Erratum]
   Inst. Hautes Études Sci. Publ. Math. 121 (2015), no. 1, 1–55
6. Kodaira dimension and zeros of holomorphic one-forms
   Ann. of Math. 179 (2014), no. 3, 1109–1120
   [with M. Popa]
7. Torsion points on cohomology support loci: from D-modules to Simpson's theorem
   London Math. Soc. Lecture Note Ser. 417 (2015), 405–421
8. Weak positivity via mixed Hodge modules
   Contemp. Math. 647 (2015), 129–137
9. Generic vanishing theory via mixed Hodge modules
   Forum Math. Sigma 1 (2013), e1, 60pp.
   [with M. Popa]
10. Moduli of products of stable varieties
    Compositio Math. 149 (2013), no. 12, 2036–2070
    [with B. Bhatt, Z. Patakfalvi and W. Ho]
11. The zero locus of the infinitesimal invariant
    Fields Inst. Commun. 67 (2013), 589–602
    [with G. Pearlstein]
12. Residues and filtered D-modules
    Math. Annalen 354 (2012), no. 2, 727–763
13. Complex-analytic Néron models for arbitrary families of intermediate Jacobians
    Invent. Math. 188 (2012), no. 1, 1–81
14. The fundamental group is not a derived invariant
    EMS Ser. Congr. Rep. 8 (2011), 279–285
15. Canonical cohomology as an exterior module
    Pure Appl. Math. Quart. 7 (2011), no. 4, 1529–1542
    [with R. Lazarsfeld and M. Popa]
16. 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]
17. A variant of Néron models over curves
    Manuscripta Math. 134 (2011), no. 34, 359–375
    [with M. Saito]
18. Local duality and polarized Hodge modules
    Publ. Math. Res. Inst. Sci. 47 (2011), no. 3, 705–725
19. Primitive cohomology and the tube mapping
    Math. Z. 268 (2011), no. 3–4, 1069–1089
20. 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]
21. Two observations about normal functions
    Clay Math. Proc. 9 (2010), 75–79

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

• The boundary behavior of cohomology classes and singularities of normal functions
  [Ohio State University, 2008]

Lecture Notes

• A graduate course on Basic topology (Stony Brook, 2014)
• A talk on Zeros of holomorphic one-forms (Paris, 2014)
• Two lectures on Mixed Hodge modules (Sanya, 2013)
• A graduate course on the Generic vanishing theorem (Stony Brook and Bonn, 2013)
• Five lectures on Absolute Hodge classes (Trieste, 2010)
  [with F. Charles]
• A graduate course on Complex manifolds (Chicago, 2010)
• Two lectures on Mumford-Tate groups (Trento, 2009)
• A seminar on Deformations of complex structure (Columbus, 2005)
• A seminar about Picard-Fuchs equations (Columbus, 2004)
• A talk on the Gauss-Bonnet theorem (Columbus, 2004)
• A lecture on the De Giorgi-Nash-Moser estimates (Columbus, 2002)

Miscellaneous

• The set of (-1)-curves on a certain class of elliptic surfaces
• A condition for an ideal in a power series ring to be generated by constants
• The Serre construction in codimension two
• Stable approximations of certain vector bundles
• Hypersurfaces containing a given subvariety
• Computing cohomology of local systems

Past Events

• Complex, p-adic, and logarithmic Hodge theory and their applications
  Simons Center, March 6 to April 29, 2016
• AGNES Yale 2016
  Yale University, April 8 to April 10, 2016
• Local and Global Methods in Algebraic Geometry
  UIC, May 12 to May 15, 2016
• Topology of complex algebraic varieties
  Luminy, May 30 to June 3, 2016
• Higher dimensional algebraic geometry
  University of Utah, July 18 to July 26, 2016