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.

Interests
  • 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
Education

  • PhD in Mathematics, 2012

    RWTH Aachen University

  • Diplom in Mathematics (minor in Physics), 2008

    RWTH Aachen University

Preprints

Florian Eisele. A counterexample to a conjecture on Cartan determinants of monoid algebras. preprint, 2023.
PDF arXiv
Florian Eisele, Leo Margolis. Units in Blocks of Defect 1 and the Zassenhaus Conjecture. preprint, 2022.
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Publications

Florian Eisele, Michael Livesey. Arbitrarily large Morita Frobenius numbers. Algebra & Number Theory, Vol. 16, No. 8, 1889–1904, 2022.
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Florian Eisele. Bijections of silting complexes and derived Picard groups. J. London Math. Soc., 106: 1008-1060, 2022.
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Florian Eisele. On the geometry of lattices and finiteness of Picard groups. J. Reine Angew. Math. (Crelle’s journal) 782, 219–233, 2021.
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Florian Eisele. The Picard group of an order and Külshammer reduction. Algebr. Represent. Th. 24, pages 505–518, 2020.
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Florian Eisele, Theo Raedschelders. On solvability of the first Hochschild cohomology of a finite-dimensional algebra. Trans. Amer. Math. Soc. 373, 7607-7638, 2019.
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Charles W. Eaton, Florian Eisele, Michael Livesey. Donovan's conjecture, blocks with abelian defect groups and discrete valuation rings. Math Z., Vol. 295, Pages 249–264, 2019.
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Florian Eisele, Leo Margolis. A Counterexample to the First Zassenhaus Conjecture. Adv. Math., Vol. 339, Pages 599-641, 2018.
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Florian Eisele, Geoffrey Janssens, Theo Raedschelders. A reduction theorem for $\tau$-rigid modules. Math Z., Vol. 290, Issue 3–4, Pages 1377–1413, 2018.
PDF Code arXiv journal
Florian Eisele, Michael Geline, Radha Kessar, Markus Linckelmann. On Tate duality and a projective scalar property for symmetric algebras. Pacific J. Math. Vol. 293 (2018), No. 2, 277–300, 2017.
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Florian Eisele. Blocks with a generalized quaternion defect group and three simple modules over a 2-adic ring. J. Algebra, Volume 456, Pages 294-322, 2016.
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Florian Eisele, Ann Kiefer, Inneke Van Gelder. Describing units of integral group rings up to commensurability. J. Pure Appl. Algebra, Volume 219, Issue 7, Pages 2901-2916, 2015.
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Florian Eisele. The $p$-adic group ring of ${\rm SL}_2(p^f)$. J. Algebra, Volume 410, Pages 421-459, 2014.
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Florian Eisele. Basic Orders for Defect Two Blocks of $\mathbb Z_p\Sigma_n$. Comm. Algebra, Volume 42, Issue 7, Pages 2890-2907, 2014.
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Florian Eisele. On the IYB-property in some solvable groups. Arch. Math., Volume 101, Issue 4, Pages 309–318, 2013.
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Florian Eisele. $p$-Adic lifting problems and derived equivalences. J. Algebra, Volume 356, Issue 1, Pages 90-114, 2012.
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Miscellaneous

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.

Theses

Contact