About me
I am a mathematician. I am interested in groups, algebras and their representation theory. Recently, I have been thinking about Donovan’s conjecture, profinite groups and pseudocompact algebras.
Education
PhD in Mathematics
2012
RWTH Aachen University
Diplom in Mathematics
2008
RWTH Aachen University
Preprints
(2026).
Finiteness properties of profinite blocks and blocks with defect group $\mathbb Z_p^n$.
preprint.
(2026).
On 2-blocks with quaternion defect groups.
preprint.
Publications
(2025).
Units in group rings and blocks of Klein four or dihedral defect.
Bull. London Math. Soc., Volume 57, Issue 11, 3470-3489.
(2024).
Units in Blocks of Defect 1 and the Zassenhaus Conjecture.
Rev. Mat. Complut., Volume 38, pages 627–664.
(2022).
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.
(2021).
On the geometry of lattices and finiteness of Picard groups.
J. Reine Angew. Math. (Crelle’s journal) 782, 219–233.
(2020).
The Picard group of an order and Külshammer reduction.
Algebr. Represent. Th. 24, pages 505–518.
(2019).
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.
(2018).
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.
(2017).
On Tate duality and a projective scalar property for symmetric algebras.
Pacific J. Math. Vol. 293 (2018), No. 2, 277–300.
(2016).
Blocks with a generalized quaternion defect group and three simple modules over a 2-adic ring.
J. Algebra, Volume 456, Pages 294-322.
(2015).
Describing units of integral group rings up to commensurability.
J. Pure Appl. Algebra, Volume 219, Issue 7, Pages 2901-2916.
(2014).
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.
(2013).
On the IYB-property in some solvable groups.
Arch. Math., Volume 101, Issue 4, Pages 309–318.
(2012).
$p$-Adic lifting problems and derived equivalences.
J. Algebra, Volume 356, Issue 1, Pages 90-114.
Theses & Unpublished Notes
(2023).
A counterexample to a conjecture on Cartan determinants of monoid algebras.
note (not intended for publication).
(2012).
Group rings over the $p$-adic integers.
PhD thesis, RWTH Aachen University.
(2008).
Algorithmische Behandlung $p$-adischer ganzzahliger Gruppenringe.
Diplom thesis (in German), RWTH Aachen University.
Code
The “orders” package
This GAP 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 2008 while I was working on my master’s thesis, but I added functionality over the last few years, as needed for my research.
- Repository: https://github.com/feisele/orders/
- Download: orders-1.03.tar.gz (just unpack this in the
pkg/directory of your GAP installation and useLoadPackage("orders");)
Miscellaneous
- I co-organised the conference Algebra and Number Theory In Conversation (ANTIC) in Manchester, September 2023.
- I co-organised the conference Structure of Group Algebras over Local Rings in Ambleside, August 2022.
Contact
| florian.eisele@manchester.ac.uk | |
|---|---|
| +44 161 275 5838 | |
| Room 2.120, Alan Turing Building, Department of Mathematics, University of Manchester, Oxford Road, Manchester, M13 9PL |