Tobias Berger


Lecturer

University of Sheffield, School of Mathematics and Statistics

E-mail: tberger(at)cantab(dot)net

School of Mathematics and Statistics, University of Sheffield, Hicks Building, Hounsfield Road, Sheffield S3 7RH

Office: J9

Research Interests: Cohomology of arithmetic groups, automorphic forms, Galois representations, Bloch-Kato conjecture

Picture of Tobias Berger


Publications and Preprints

(Note that the versions presented here may differ slightly from the published versions. Please contact me for latest version of preprints.)
  • On the Bloch-Kato conjecture for the Asai L-function, arXiv
  • Theta lifts of Bianchi modular forms and applications to Paramodularity,
    (joint with Lassina Dembélé, Haluk Şengün and Ariel Pacetti, J. of London Math. Soc. 92 (2) (2015), 353–370), arXiv
  • On lifting and modularity of reducible residual Galois representations over imaginary quadratic fields (joint with Kris Klosin,IMRN 20 (2015), 10525-10562), pdf
  • On higher congruences between automorphic forms (joint with Kris Klosin and Ken Kramer, Mathematical Research Letters 21 (2014), no. 1, 71-82), arXiv
  • Arithmetic properties of theta lifts (manuscripta mathematica 143 (2014), 389-417), pdf
  • On deformation rings of residually reducible Galois representations and R=T theorems (joint with Kris Klosin, Mathematische Annalen 355 (2013), no. 2, 481-518.) arXiv
  • The original publication is available at www.springerlink.com - click here to access the published version.
  • An R=T theorem for imaginary quadratic fields (joint with Kris Klosin, Mathematische Annalen 349 (2011), no. 3, 675-703) pdf
  • The original publication is available at www.springerlink.com - click here to access the published version.
  • A deformation problem for Galois representations of imaginary quadratic fields
  • (joint with Kris Klosin, Journal de l'Institut de Math. de Jussieu 8(4) (2009), 669-692) pdf © Cambridge University Press.
  • l-adic representations associated to modular forms over imaginary quadratic fields (joint with Gergely Harcos, Int. Math. Res. Not. 23 (2007), Art. ID rnm113, 16pp.) pdf
  • On the Eisenstein ideal for imaginary quadratic fields (Compositio Mathematica 145(3) (2009), 603-632) pdf
  • Denominators of Eisenstein cohomology classes for GL(2) over imaginary quadratic fields (manuscripta mathematica 125 (2008), 427-470) pdf
  • An Eisenstein ideal for imaginary quadratic fields (PhD thesis, University of Michigan 2005) pdf
  • Erratum: The claim in Theorem 5.1 in my thesis (repeated in Theorem 15 of the Compositio paper) about the perfectness of the Poincare pairing for Dedekind domains is incorrect. This was only used in the proof of Lemma 5.3 (resp. Lemma 16). To prove the latter results one can use instead Pontryagin duality. For details please see pdf.

Education and Experience

  • 2010- Lecturer, University of Sheffield, School of Mathematics and Statistics
  • 2008-2010 College Lecturer and Assistant Director of Studies, Queens' College
  • 2005-2008 Research Fellow, Queens' College, University of Cambridge, England
  • 2005-2006 Post-doc, Max Planck Institute, Bonn, Germany
  • 2000-2005 PhD University of Michigan, Ann Arbor, USA, Advisor: Chris Skinner
  • 1999-2000 Certificate of Advanced Study (Part III), Queens' College, University of Cambridge, England
  • 1996-1999 BA(Hons)/MA Mathematics, Queens' College, University of Cambridge, England

Links


Talks


Teaching

For current courses please see Sheffield teaching links.

PhD thesis of my student Andrew Jones (Modular Elliptic Curves over Quartic CM Fields pdf, Sheffield 2015)