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
2022-2023:
Courses: (for
details consult our internal pages/ultra)
Topics in Algebra and Geometry IV
(Modular Forms) (Term 1)
Representation Theory IV (Term
2)
Projects:
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