Jens  Funke

Department of Mathematical Sciences

New Mexico State University

Jens Funke

Assistant Professor

New Mexico State University

Department of Mathematical Sciences

P.O.Box 30001

Department 3MB

Las Cruces, NM 88003-8001

USA

Office: Walden Hall 205
Phone: 505-646-2406
email: jfunke@nmsu.edu 

I am on leave for 2007/08. I can be reached by email.

Research

Areas of Interest: Number theory, automorphic and modular forms, representation theory, arithmetic geometry and Arakelov theory

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 is supported by NSF-grants DMS-0305448 and DMS-0701228. 

Publications

• Boundary behavior of special cohomology classes arising  from the Weil representation (joint with J. Millson), 42 pages, preprint. (in revision)

• 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 (2007).

• On the injectivity of the Kudla-Millson lift (joint with J. Bruinier), 23 pages, to appear in the proceedings of the Workshop on the Moonshine Conjectures and Vertex Algebras, Edinburgh 2004. London Math. Soce. Lecture Notes, Cambridge University Press (2007).

• 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