I am interested in the cohomology and K-theory of arithmetic groups, arithmetic of automorphic forms, modularity of abelian varieties and Galois representations. I especially focus on the cases where the underlying arithmetic manifolds have no visible links to algebraic geometry. 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).

Here is my Google Scholar profile.

Here is the Sheffield Number Theory Group.

PhD STUDENTS

Ciaran Schembri (2015-)
Gonca Kızılaslan (Univ. of Kırıkkale) (2015-)

PAPERS and PREPRINTS

  • Hecke operators in KK-theory and the K-homology of Bianchi groups [pdf] 
    with Bram Mesland
    Journal of Noncommutative Geometry (to appear)  (49 pages)
  • Hecke modules for arithmetic groups via bivariant K-theory [pdf] 
    with 
    Bram Mesland
    Annals of K-theory (to appear) (22 pages)
  • Mod p Base Change transfer for GL(2) [pdf] 
    with Andrew Jones
    Journal of the Ramanujan Mathematical Society 33.3 (2018) 
  • On the asymptotic Fermat's Last Theorem over number fields [pdf] 
    with Samir Siksek
    Commentarii Mathematici Helvetici  
    93.2 (2018)  
  • Dimension formulae for spaces of lifted Bianchi modular forms [pdf] 
    with Panagiotis Tsaknias
    (not intended for publication, companion to the paper below.)
  • Torsion homology growth and cycle complexity of arithmetic manifolds [pdf] 
    with Nicolas Bergeron and Akshay Venkatesh
    Duke Math Journal 
    165.9 (2016) 
  • Uniformization of modular elliptic curves via p-adic periods [pdf] 
    with Xevi Guitart and Marc Masdeu
    Journal of Algebra.
     445 (2016) 
  • Darmon points on elliptic curves over number fields of arbitrary signature [pdf] 
    with Xevi Guitart and Marc Masdeu

    Proceedings of the LMS.
     (3) 111.2 (2015) 
  • Theta lifts of Bianchi modular forms and applications to the Paramodularity Conjecture [pdf] 
    with Tobias BergerLassina Dembélé and Ariel Pacetti
    Journal of the LMS.
     (2) 92.2 (2015) 
  • Lower Bounds on the Dimension of the Cohomology of Bianchi Groups via Sczech Cocycles [pdf] 
    with Seyfi Turkelli
    J. Théorie Nombres Bordeaux. 
    28.1 (2016)  
  • Arithmetic aspects of Bianchi groups [pdf] 
    In "Computations with Modular Forms", Eds: G.Boeckle, G.Wiese. 
    Contributions in Mathematical and Computational Sciences, Volume 6, 2014, Springer-Verlag. 
  • On level one cuspidal Bianchi modular forms [pdf] 
    with Alexander Rahm

    LMS Journal of Computation and Mathematics.
     16 (2013) 
  • On the homology of non-arithmetic hyperbolic tetrahedral groups [pdf] 
    International Journal of Number Theory. 8.2 (2012) 
    The DATA discussed in the paper.
  • On the integral cohomology of Bianchi groups [pdf] 
    Experimental Mathematics. 20.4 (2011) 
    The DATA discussed in the paper.
  • Weight reduction for mod ℓ Bianchi modular forms [pdf] 
    with Seyfi Turkelli
    Journal of Number Theory.
     129 (2009)
  • The nonexistence of certain representations of the absolute Galois group of quadratic fields  [pdf]
    Proceedings of the AMS. 137 (2009)