Ruprecht-Karls-Universität Heidelberg

My research interests

  • Modular forms, automorphic forms, in particular for unitary groups.
  • Number theory
  • Arithmetic algebraic geometry
My main research area

My research focuses on geometric liftings for modular groups of higher rank, especially unitary groups.

In particular, I work on Borcherds products and related constructions for U(p,1), and more generally on singular theta lifts for U(p,q) and the construction of Green forms for special cycles of the attached modular varieties, the underlying structure here being the dual reductive pair U(p,q) × U(1,1).

Such constructions can be utilized to obtain modularity results for generating series valued in the cohomology of the modular varieties, which is of interest in the context of the Kudla program, situated at the intersection of the two fields of arithmetic geometry and of modular forms.

Preprints & Papers

Habilitationsschrift

My Habilitation was completed on July 14 2021 (see below for my talk).
Here's my Habilitionsschrift (postdoctoral thesis) Geometric Liftings for Unitary Groups, Heidelberg 2021: (pdf).

Preprints & papers

  • The Fourier-Jacobi expansion of the singular theta lift. preprint 2022, arXiv (link)
  • The construction of Green currents and singular theta lifts for unitary groups (joint work with J. Funke)
    preprint 2019, revision 2020 arXiv: (link), Trans. AMS, published electronically: January 27, 2021
    (DOI: https://doi.org/10.1090/tran/8289 )
  • Holomorphic Derivatives of Siegel Modular Forms (joint work with W. Kohnen)
    Bull. Korean Math. Soc 2018 Vol. 55, No. 5, 1621-1625 (link)
  • Course Notes: Liftings and Borcherds Products (2016) revised preprint (August 2017): (pdf)
    L-Functions and Automorphic Forms, Jan Hendrik Bruiner, Winfried Kohnen Hrsg., CMCS 10, Springer 2017
  • Local Borcherds Products for Unitary Groups. preprint (2016), revised version (2017) arXiv (link)
    Nagoya Mathematical Journal 234 (2019): 139-169 (first published online 27 Oct. 2017).
    (DOI doi.org/10.1017/nmj.2017.37)
  • On Products of Fourier Coefficients of Cusp Forms. (2015) (joint work with W. Kohnen)
    arXiv (link) Forum Math. Vol 29, Issue 1, 245 (January 2017)
    (DOI: 10.1515/forum-2015-0175, June 2016)
  • Borcherds Products for U(1,1) (2013),
    minor revision April 2013, on arXiv (link)
    IJNT, Vol. 09, Issue No. 7 (November 2013),
    (DOI: 10.1142/S1793042113500589)
  • Borcherds Products on Unitary Groups (2012),
    revision (2013), on arXiv (link)
    Math. Ann., Vol. 358 (Issue 3), (2014), 799-832 ,
    (DOI: 10.1007/s00208-013-0966-6)

Earlier research projects

A few talks

  • My Habilitionsvortrag on the Collatz conjecture (pdf) (July 14th, 2021) (in German)
  • Prepatory course L-Functions and Automorphic Forms (Heidelberg, February 17th-19th 2016)
    an updated version of my course note: (pdf)
  • Building Bridges: 2nd EU/US Workshop (Bristol, held on July 9th, 2014) (pdf)
  • 27th Automorphic Forms Workshop (UCD Dublin, held on March 13, 2013) (pdf)
  • My PhD defense, February 8, 2011 (pdf) (in German)
  • 27th seminar AKLS, in Aachen, March 3, 2010 (pdf)
  • My poster for the "Nachwuchskonferenz: Young Researchers in Arithmetic and Algebraic Geometry" (October 5, 2010) (pdf)



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