Dr Haluk Sengun
School of Mathematics and Statistics
Lecturer
Chair of Communications Committee
M.Sengun@shef.ac.uk
+44 114 222 3725
+44 114 222 3725
J06a, Hicks Building
Full contact details
Dr Haluk Sengun
School of Mathematics and Statistics
J06a
Hicks Building
Hounsfield Road
Sheffield
S3 7RH
School of Mathematics and Statistics
J06a
Hicks Building
Hounsfield Road
Sheffield
S3 7RH
- Profile
-
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
- On the asymptotic Fermat’s last theorem over number fields. Commentarii Mathematici Helvetici, 93(2), 359-375. View this article in WRRO
- On the asymptotic Fermat's Last Theorem over number fields. Commentarii Mathematici Helvetici.
- Torsion homology growth and cycle complexity of arithmetic manifolds. Duke Mathematical Journal, 165(9), 1629-1693. View this article in WRRO
Preprints
- Equal rank local theta correspondence as a strong Morita equivalence, https://arxiv.org/abs/2207.13484. View this article in WRRO
All publications
Edited books
- K-Theory and Representation Theory. Cambridge University Press.
Journal articles
- Hecke operators in KK-theory and the K-homology of Bianchi groups. Journal of Noncommutative Geometry, 14(1), 125-189. View this article in WRRO
- Torsion homology growth for noncongruence subgroups of Bianchi groups. International Journal of Number Theory, 16(04), 787-802.
- Hecke modules for arithmetic groups via bivariant K-theory. Annals of K-Theory, 3(4), 631-656. View this article in WRRO
- Mod p Base Change transfer for GL(2). Journal of the Ramanujan Mathematical Society, 33(3), 297-334. View this article in WRRO
- On the asymptotic Fermat’s last theorem over number fields. Commentarii Mathematici Helvetici, 93(2), 359-375. View this article in WRRO
- On the asymptotic Fermat's Last Theorem over number fields. Commentarii Mathematici Helvetici.
- Torsion homology growth and cycle complexity of arithmetic manifolds. Duke Mathematical Journal, 165(9), 1629-1693. View this article in WRRO
- Lower Bounds on the Dimension of the Cohomology of Bianchi Groups via Sczech Cocyles. Journal de Théorie des Nombres de Bordeaux, 28(1), 237-260. View this article in WRRO
- Uniformization of modular elliptic curves via p-adic periods. Journal of Algebra, 445, 458-502. 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
- Darmon points on elliptic curves over number fields of arbitrary signature. Proceedings of the London Mathematical Society, 111(2), 484-518. View this article in WRRO
- Arithmetic Aspects of Bianchi Groups, 279-315.
- On level one cuspidal Bianchi modular forms. LMS Journal of Computation and Mathematics, 16, 187-199. View this article in WRRO
- ON THE TORSION HOMOLOGY OF NON-ARITHMETIC HYPERBOLIC TETRAHEDRAL GROUPS. International Journal of Number Theory, 08(02), 311-320. View this article in WRRO
- On The Torsion Homology of Non-Arithmetic Hyperbolic Tetrahedral Groups. Int. Jour. Number Theory., 08(2), 311-320. View this article in WRRO
- On the Integral Cohomology of Bianchi Groups. Experimental Mathematics, 20(4), 487-505. View this article in WRRO
- Weight reduction for mod ℓ Bianchi modular forms. Journal of Number Theory, 129(8), 2010-2019. View this article in WRRO
- The nonexistence of certain representations of the absolute galois group of quadratic fields. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 137(1), 27-35.
- The nonexistence of certain representations of the absolute Galois group of quadratic fields. Proceedings of the American Mathematical Society, 137(01), 27-35. View this article in WRRO
- Congruence RFRS towers. View this article in WRRO
- 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
- A K-theoretic Selberg trace formula. Operator Theory, Operator Algebras and Their Interactions with Geometry and Topology, Vol. 278 (pp 403-424). Shanghai, China, 23 July 2018 - 27 July 2018. View this article in WRRO
Preprints
- Equal rank local theta correspondence as a strong Morita equivalence, https://arxiv.org/abs/2207.13484. View this article in WRRO
- 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. View this article in WRRO
- 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.
- On the asymptotic Fermat’s last theorem over number fields. Commentarii Mathematici Helvetici, 93(2), 359-375. View this article in WRRO
- 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