Jens  Funke

Office: CM 310
Phone: +44-(0)191-334-3063
email: jens.funke@durham.ac.uk

Teaching

Research

Areas of Interest: Number theory, automorphic and modular forms, representation theory, cohomology of arithmetic groups

Research Topics: I am interested in cohomology classes of arithmetic quotients of orthogonal and unitary symmetric spaces which arise from certain naturally embedded submanifolds.  Furthermore, I am also interested in the corresponding arithmetic situation, when these submanifolds occur as the complex points of certain cycles in Shimura varieties of this type. I study these cycles by realizing them via the theta correspondence as Fourier coefficients of Siegel and Hermitian modular forms. Click here for a more detailed description of my research. My research was 2007-2011 supported by NSF-grant DMS-0701228 of the United States National Science Foundation.

Publications

• Regularied theta liftings and periods of modular fucntions (joint with Jan Bruinier and Ozlem Imamoglu), 48 pages, preprint
• The geometric theta correspondence for Hilbert modular surfaces (joint with John Millson), 35 pages, preprint
  
• Spectacle cycles with coefficients and modular forms of half-integral weight (joint with John Millson), in: Arithmetic Geometry and Automorphic Forms, in honor of Stephen S. Kudla. Higher Eduction Press and International Press (2011).
  
• Boundary behavior of special cohomology classes arising from the Weil representation (joint with J. Millson, revised version), 58 pages, to appear in Math Juisseau Journal.
• On the injectivity of the Kudla-Millson lift (joint with J.Bruinier), in Moonshine: The First Quarter Century and Beyond. London Math. Soce. Lecture Notes 372, Cambridge University Press (2010).
  
• Special cohomology classes arising for the Weil representation  in Proceedings of the RIMS Symposium on Automorphic Representations, Automorphic forms, L-functions, and related topics, Kyoto, Jan. 2008.
• CM points and weight 3/2 modular forms, 21 pages, to appear in the proceedings of the Gauss-Dirichlet conference, Goettingen, 2005. Clay Mathematics Proceedings 7, AMS (2008).
  
• Traces of CM values of modular functions (joint with J. Bruinier), J. Reine Angew. Math. 594, 1-33 (2006)
• Cycles with local coefficients for orthogonal groups and vector-valued Siegel modular forms (joint with J. Millson),  American J. Math.  128, 899-948 (2006)
• On two geometric theta lifts (joint with J. Bruinier), Duke Mathematical Journal 125 (2004), 45-90.
• Cycles in hyperbolic manifolds of non-compact type and Fourier coefficients of  Siegel modular forms (joint with J. Millson), Manuscripta Mathematica 107 (2002),  409-449.
• Heegner divisors and non-holomorphic modular forms, Compositio Mathematica 133 (2002), 289-321.
• Trace operator and theta series (joint with S. Boecherer, R. Schulze-Pillot), Journal of Number Theory 78 (1999), 119-139

Workshop: Durham Days on Modular Forms