Associate Professor (Reader)

Department of Mathematical Sciences

UNITED KINGDOM

Office: CM 310

Phone: +44-(0)191-334-3063

email: jens *dot* funke *at* durham* dot* ac *dot*
uk

**Teaching
**

Course:

Representation Theory III/IV (for details consult duo)

Projects:

Project III: A Course in Arithmetic

Project IV: Analytic Number Theory: The Riemann Zeta Function and the Prime Number Theorem

**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**

- Modularity of generating series of winding numbers (joint with J Bruinier, O Imamoglu, Y Li), preprint (2017).
- Theta integrals and generalized error functions II (joint with Steve Kudla), preprint (2017).
- 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,
doi:10.1093/imrn/rnw218 (2016).

- 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
**1****2**(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