Dr Tobias Berger
School of Mathematical and Physical Sciences
Senior Lecturer in Number Theory
Chair of Examiners
+44 114 222 3791
Full contact details
School of Mathematical and Physical Sciences
J9
Hicks Building
Hounsfield Road
Sheffield
S3 7RH
- Profile
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I received my Ph.D. at the University of Michigan in 2005, studying under Chris Skinner. After a year at the Max-Planck-Institute in Bonn I spent four years at Queens' College, Cambridge, as a Junior Research Fellow and College Lecturer. I joined the University of Sheffield as a lecturer in autumn 2010.
- Research interests
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My research area is algebraic number theory, more precisely the connections between modular forms and Galois representations and applications of this, in particular, to conjectures about special values of L-functions. Establishing the precise links between modular forms (or more generally, automorphic representations) and Galois representations is part of the famous programme designed by Langlands that spans number theory, algebraic geometry and representation theory. My particular focus is the study of automorphic forms and Galois representations over imaginary quadratic fields, an interesting case in which previously developed tools from algebraic geometry are not applicable. This case is therefore an important testing ground for finding new techniques that could apply in the general context of the Langlands programme.
- Publications
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Show: Featured publications All publications
Featured publications
Journal articles
- On Siegel eigenvarieties at Saito–Kurokawa points. Annales de l'Institut Fourier, 72(3), 901-961. View this article in WRRO
- Deformations of Saito-Kurokawa type and the Paramodular Conjecture. American Journal of Mathematics, 142(6), 1821-1875. View this article in WRRO
- Modularity of residual Galois extensions and the Eisenstein ideal. Transactions of the American Mathematical Society. View this article in WRRO
- Theta lifts of Bianchi modular forms and applications to paramodularity. Journal of the London Mathematical Society, 92(2), 353-370. View this article in WRRO
- On Lifting and Modularity of Reducible Residual Galois Representations Over Imaginary Quadratic Fields. International Mathematics Research Notices, 2015(20), 10525-10562. View this article in WRRO
- On higher congruences between automorphic forms. Mathematical Research Letters, 21(1), 71-82. View this article in WRRO
Preprints
All publications
Journal articles
- On Siegel eigenvarieties at Saito–Kurokawa points. Annales de l'Institut Fourier, 72(3), 901-961. View this article in WRRO
- $R=T$ theorems for weight one modular forms. Transactions of the American Mathematical Society.
- Deformations of Saito-Kurokawa type and the Paramodular Conjecture. American Journal of Mathematics, 142(6), 1821-1875. View this article in WRRO
- Modularity of residual Galois extensions and the Eisenstein ideal. Transactions of the American Mathematical Society. View this article in WRRO
- A p-adic Hermitian Maass lift. Glasgow Mathematical Journal, 61(1), 85-114. View this article in WRRO
- Oddness of residually reducible Galois representations. International Journal of Number Theory, 14(5), 1329-1345. View this article in WRRO
- Theta lifts of Bianchi modular forms and applications to paramodularity. Journal of the London Mathematical Society, 92(2), 353-370. View this article in WRRO
- On Lifting and Modularity of Reducible Residual Galois Representations Over Imaginary Quadratic Fields. International Mathematics Research Notices, 2015(20), 10525-10562. View this article in WRRO
- On higher congruences between automorphic forms. Mathematical Research Letters, 21(1), 71-82. View this article in WRRO
- Arithmetic properties of similitude theta lifts from orthogonal to symplectic groups. Manuscripta Mathematica, 143(3-4), 389-417.
- On deformation rings of residually reducible Galois representations and R = T theorems. Mathematische Annalen, 1-38.
- An R = T theorem for imaginary quadratic fields. Mathematische Annalen, 349(3), 675-703.
- A DEFORMATION PROBLEM FOR GALOIS REPRESENTATIONS OVER IMAGINARY QUADRATIC FIELDS. J INST MATH JUSSIEU, 8(4), 669-692.
- On the Eisenstein ideal for imaginary quadratic fields. COMPOS MATH, 145(3), 603-632.
- Denominators of Eisenstein cohomology classes for GL(2) over imaginary quadratic fields. MANUSCRIPTA MATH, 125(4), 427-470.
- l-adic Representations Associated to Modular Forms over Imaginary Quadratic Fields. INT MATH RES NOTICES.
- Irreducibility of limits of Galois representations of Saito-Kurokawa
type. Research in Number Theory.
- Lafforgue pseudocharacters and parities of limits of Galois
representations. manuscripta mathematica.
Preprints
- Lafforgue pseudocharacters and parities of limits of Galois representations, arXiv.
- Irreducibility of limits of Galois representations of Saito-Kurokawa
type, arXiv.
- On Siegel eigenvarieties at Saito-Kurokawa points. View this article in WRRO
- Modularity of residual Galois extensions and the Eisenstein ideal, arXiv.
- Deformations of Saito-Kurokawa type and the Paramodular Conjecture (with
an appendix by Cris Poor, Jerry Shurman, and David S. Yuen), arXiv.
- On lifting and modularity of reducible residual Galois representations
over imaginary quadratic fields, arXiv.
- A $p$-adic Hermitian Maass lift, arXiv.
- Theta Lifts of Bianchi Modular Forms and Applications to Paramodularity, arXiv.
- A deformation problem for Galois representations over imaginary quadratic fields, arXiv.
- An Eisenstein ideal for imaginary quadratic fields and the Bloch-Kato conjecture for Hecke characters, arXiv.
- Denominators of Eisenstein cohomology classes for GL_2 over imaginary quadratic fields, arXiv.
- On Siegel eigenvarieties at Saito–Kurokawa points. Annales de l'Institut Fourier, 72(3), 901-961. View this article in WRRO
- Research group
- Grants
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Current grants, as Principal Investigator
Deformations of Saito-Kurokawa type Galois representations EPSRC Past grants, as Principal Investigator
Paramodularity Conjecture Travel Grant LMS Arithmetic applications of Kudla-Millson theta lifts EPSRC