Lecturer in Pure Mathematics

University of Manchester

About me

I am a Lecturer in Pure Mathematics at the University of Manchester. In the past I held positions at City, University of London, the University of Glasgow and at Vrije Universiteit Brussel. I completed my PhD on “Group rings over the p-adic integers” at RWTH Aachen University in 2012. An up-to-date academic CV is available here.

  • Modular representation theory
  • Representations of Artin algebras
  • Integral and p-adic group rings
  • $\tau$-tilting and silting theory
  • Hochschild cohomology
  • Picard groups
  • Unit groups
  • Finite group theory
  • Constructive methods & computer algebra
  • PhD in Mathematics, 2012

    RWTH Aachen University

  • Diplom in Mathematics (minor in Physics), 2008

    RWTH Aachen University


Arbitrarily large Morita Frobenius numbers. Algebra & Number Theory, Vol. 16, No. 8, 1889–1904, 2022.
Bijections of silting complexes and derived Picard groups. J. London Math. Soc., 106: 1008-1060, 2022.
On the geometry of lattices and finiteness of Picard groups. J. Reine Angew. Math. (Crelle’s journal) 782, 219–233, 2021.
The Picard group of an order and Külshammer reduction. Algebr. Represent. Th. 24, pages 505–518, 2020.
On solvability of the first Hochschild cohomology of a finite-dimensional algebra. Trans. Amer. Math. Soc. 373, 7607-7638, 2019.
Donovan's conjecture, blocks with abelian defect groups and discrete valuation rings. Math Z., Vol. 295, Pages 249–264, 2019.
A Counterexample to the First Zassenhaus Conjecture. Adv. Math., Vol. 339, Pages 599-641, 2018.
A reduction theorem for $\tau$-rigid modules. Math Z., Vol. 290, Issue 3–4, Pages 1377–1413, 2018.
On Tate duality and a projective scalar property for symmetric algebras. Pacific J. Math. Vol. 293 (2018), No. 2, 277–300, 2017.
Describing units of integral group rings up to commensurability. J. Pure Appl. Algebra, Volume 219, Issue 7, Pages 2901-2916, 2015.
The $p$-adic group ring of ${\rm SL}_2(p^f)$. J. Algebra, Volume 410, Pages 421-459, 2014.
Basic Orders for Defect Two Blocks of $\mathbb Z_p\Sigma_n$. Comm. Algebra, Volume 42, Issue 7, Pages 2890-2907, 2014.
On the IYB-property in some solvable groups. Arch. Math., Volume 101, Issue 4, Pages 309–318, 2013.
$p$-Adic lifting problems and derived equivalences. J. Algebra, Volume 356, Issue 1, Pages 90-114, 2012.


GAP Code

The “orders” package

This package allows to compute with orders over the $p$-adic integers, such as $\mathbb Z_p G$ for a finite group $G$. Among other things it can compute indecomposable projective lattices and basic algebras. Most of it was written back in 2009 while I was working on my master’s thesis, but I added functionality over the last few years, as needed for my research.