Jens Funke

Professor Jens Funke

Department of Mathematical Sciences  

Science Laboratories 

South Rd 

DURHAM DH1 3LE

UNITED KINGDOM

Office: CMS 2047
Phone: +44-(0)191-334-3063
email: jens dot funke at durham dot ac dot uk 

Teaching

2024-2025:  

Courses: (for details consult our internal pages/ultra)

Topics in Algebra and Geometry IV (Modular Forms) (Term 1)

Analysis I (Term 2)

Projects: 

Project III:  Partitions

Project IV:  The finite Weil representation

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.

Publications

• Indefinite Theta Series: The case of an N-gon  (joint with Steve Kudla), Accepted by Pure and Applied Mathematics Quarterly (2022).
• The construction of Green currents and singular theta lifts for unitary groups (joint with Eric Hofmann), Trans. AMS 374, 2909-2947 (2021).
  
• Modularity of generating series of winding numbers (joint with J Bruinier, O Imamoglu, Y Li) (2017), Research in the Mathematical Sciences (2018) 5:23.
• On some incomplete theta integrals (joint with Steve Kudla), Compositio Mathematica 155, 1711-1746 (2019)
• Mock modular forms and geometric theta functions for indefinite quadratic forms (joint with Steve Kudla), Journal of Physics A: Mathematical and Theoretical 50, #40 (2017).
• Degenerate Whittaker Functions for Sp_n(R) (joint with Jan Bruinier and Steve Kudla), Int. Math. Research Notices (2018), no. 1, 1-56; doi:10.1093/imrn/rnw218.
  
• Regularized theta liftings and periods of modular functions (joint with Jan Bruinier and Ozlem Imamoglu), J. Reine Angew. Math. 703 (2015), 43-93.
• The geometric theta correspondence for Hilbert modular surfaces (joint with John Millson), Duke Math. Journal 163 (2014), 65-116.
  
• Boundary behavior of special cohomology classes arising from the Weil representation (joint with J. Millson), Math Juissieu Journal 12 (2013), 571-634.
• 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).
  
• On the injectivity of the Kudla-Millson lift (joint with J.Bruinier), in Moonshine: The First Quarter Century and Beyond. London Math. Soc. 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 (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