*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