Dr Haluk Sengun
School of Mathematical and Physical Sciences
Lecturer
Chair of Communications Committee
+44 114 222 3725
Full contact details
School of Mathematical and Physical Sciences
J06a
Hicks Building
Hounsfield Road
91Ö±²¥
S3 7RH
- Profile
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I got my BSc from Istanbul Bilgi University and my PhD from the University of Wisconsin
at Madison. I held post-doctoral positions at Barcelona, Bonn, Essen and Warwick.
- Research interests
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I am interested in the cohomology and K-theory of arithmetic groups, automorphic forms, abelian varieties, Galois representations and the mostly conjectural connections between them as envisioned by the Langlands Programme. I especially study the above objects in the setting where the relevant arithmetic groups live in the Lie group PSL(2,C) (such as "Bianchi groups"). I enjoy developing computer programs and carrying out numerical experiments to explore and gain insight.
I am also involved in the construction of a database on Bianchi modular forms (that is, modular forms for GL(2) over imaginary quadratic fields) and related arithmetic data inside the L-functions and Modular Forms Database (LMFDB).
- Publications
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Show: Featured publications All publications
Featured publications
Journal articles
- . Selecta Mathematica, 30(4).
- . Commentarii Mathematici Helvetici, 93(2), 359-375.
- On the asymptotic Fermat's Last Theorem over number fields. Commentarii Mathematici Helvetici.
- . Duke Mathematical Journal, 165(9), 1629-1693.
Preprints
- , https://arxiv.org/abs/2207.13484.
All publications
Edited books
- K-Theory and Representation Theory. Cambridge University Press.
Journal articles
- . Selecta Mathematica, 30(4).
- . Journal of Noncommutative Geometry, 14(1), 125-189.
- . International Journal of Number Theory, 16(04), 787-802.
- . Annals of K-Theory, 3(4), 631-656.
- Mod p Base Change transfer for GL(2). Journal of the Ramanujan Mathematical Society, 33(3), 297-334.
- . Commentarii Mathematici Helvetici, 93(2), 359-375.
- On the asymptotic Fermat's Last Theorem over number fields. Commentarii Mathematici Helvetici.
- . Duke Mathematical Journal, 165(9), 1629-1693.
- . Journal de Théorie des Nombres de Bordeaux, 28(1), 237-260.
- . Journal of Algebra, 445, 458-502.
- . Journal of the London Mathematical Society, 92(2), 353-370.
- . Proceedings of the London Mathematical Society, 111(2), 484-518.
- , 279-315.
- On level one cuspidal Bianchi modular forms.. LMS J. Comput. Math., 16, 187-199.
- . LMS Journal of Computation and Mathematics, 16, 187-199.
- On The Torsion Homology of Non-Arithmetic Hyperbolic Tetrahedral Groups. Int. Jour. Number Theory., 08(2), 311-320.
- . Experimental Mathematics, 20(4), 487-505.
- . Journal of Number Theory, 129(8), 2010-2019.
- The nonexistence of certain representations of the absolute galois group of quadratic fields. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 137(1), 27-35.
- . Proceedings of the American Mathematical Society, 137(01), 27-35.
- Congruence RFRS towers.
- Torsion in the homology of principal congruence subgroups of Bianchi groups. Annales de l'Institut Fourier.
Chapters
- Arithmetic aspects of Bianchi groups, Computations with Modular Forms Proceedings of a Summer School and Conference, Heidelberg, August/September 2011 (pp. 279-315). Springer
- Group C*-algebras, C*-correspondences and K-theory In Sengun M & Plymen R (Ed.), K-Theory and Representation Theory Cambridge University Press
Conference proceedings papers
- . Operator Theory, Operator Algebras and Their Interactions with Geometry and Topology, Vol. 278 (pp 403-424). Shanghai, China, 23 July 2018 - 27 July 2018.
Preprints
- , https://arxiv.org/abs/2207.13484.
- A K-theoretic Selberg trace formula, arXiv.
- Hecke modules for arithmetic groups via bivariant K-theory, arXiv.
- Mod p Base Change transfer for GL(2), arXiv.
- Hecke operators in KK-theory and the K-homology of Bianchi groups, arXiv.
- On the asymptotic Fermat's Last Theorem over number fields, arXiv.
- Uniformization of modular elliptic curves via p-adic periods, arXiv.
- Darmon points on elliptic curves over number fields of arbitrary
signature, arXiv.
- Theta Lifts of Bianchi Modular Forms and Applications to Paramodularity, arXiv.
- An Introduction to A-polynomials and their Mahler Measures, arXiv.
- Torsion homology growth and cycle complexity of arithmetic manifolds, arXiv.
- Dimension Formulae for Spaces of Lifted Bianchi Modular Forms, arXiv.
- The Nonexistence of Certain Representations of the Absolute Galois Group
of Quadratic Fields, arXiv.
- Arithmetic Aspects of Bianchi Groups, arXiv.
- On the Dimension of Cohomology of Bianchi Groups, arXiv.
- Some Applications of Number Theory to 3-Manifold Theory, arXiv.
- On Level One Cuspidal Bianchi Modular Forms, arXiv.
- On The Torsion Homology of Non-Arithmetic Hyperbolic Tetrahedral Groups, arXiv.
- On the Integral Cohomology of Bianchi groups, arXiv.
- Weight Reduction for Mod l Bianchi Modular Forms, arXiv.
- . Selecta Mathematica, 30(4).
- Research group
- Grants
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Current Grant
A torsion Jacquet-Langlands Transfer via K-theory EPSRC
- Teaching activities
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MAS220 Algebra MAS430 Analytic Number Theory
Links