research

Research and publications

My main research area is finite group theory. I am interested in the further development of local techniques and their applications within and outside group theory.
This page will be outdated every once in a while, my German website is usually up to date.

(Diese Seite auf deutsch.)

Publications:

2015:	Primzahltests für Einsteiger, with Lasse Rempe-Gillen, 2nd edition. Springer, 2015. Transitive permutation groups with trivial four point stabilizers, with Kay Magaard. J . Group Theory 18 (2015), no. 5, 687-740. M9-free groups, with Juliane Pölzing. Journal of Group Theory 18 (2015), 155-190. Transitive permutation groups where nontrivial elements have at most two fixed points, with Kay Magaard. Journal of Pure and Applied Algebra 219, Issue 4 (2015), 729-759. Can be found online.
2014:	M9-free groups, with Juliane Pölzing. J. Group Theory 18 (2015), no. 1, 155–190. Transitive permutation groups where nontrivial elements have at most two fixed points, with Kay Magaard. Journal of Pure and Applied Algebra 219, Issue 4 (2015), 729-759. Finite simple 3'-groups are cyclic or Suzuki groups, with Imke Toborg. Archiv der Mathematik 102, No. 4 (2014), 301-312. "Primality testing for beginners", with Lasse Rempe-Gillen. English Version of the book "Primzahltests für Einsteiger", Student Mathematical Library (AMS), appeared 2014.
2013:	Local arguments for Glauberman's Z*-Theorem, habilitation thesis. Isolated involutions in finite groups. Memoirs of the AMS, Volume 226, Number 1061 (2013), available online.
2012:	„Isolierte Involutionen in endlichen Gruppen“, revised version of my PhD thesis, appeared as a book at Südwestdeutscher Verlag für Hochschulschriften (2012). A note on groups in which the centraliser of every element of order 5 is a 5-group (with Sarah Astill, Chris Parker). Sibirsk. Mat. Zh. 53 (2012), no. 5, 967--977; translation in Sib. Math. J. 53 (2012), no. 5, 772–780.
2011:	Contribution to the book Facettenreiche Mathematik (Multifarious mathematics), edited by Katrin Wendland and Annette Werner, Vieweg+Teubner 2011. Special primitive pairs in finite groups , Archiv der Mathematik 97, No. 1 (2011) S. 11-16. There is a short erratum (in Archiv der Mathematik 98 No. 5, 2012), but the version linked here is correct.
2008-2010	„Und was studierst du?“ Beitrag zum Cantor-Heft 2010. Primzahltests für Einsteiger (German), with Lasse Rempe. This book has been published by Vieweg+Teubner in September 2009. Here is a little bit to read from it. „Isolated involutions whose centraliser is soluble “ , J. of Algebra 321 (2009), S.1561–1592. „Soluble Radicals", in Oberwolfach Report No. 20/2008. „A theorem about coprime action", J. of Algebra 320 (2008), S. 2027–2030.

Manuscripts:

New refiners for permutation groups search, with Chris Jefferson and Markus Pfeiffer. In preparation.
Towards the Z*_3-Theorem, with Imke Toborg. In preparation.
Transitive permutation groups with trivial five point stabilizers, with Barbara Baumeister and Kay Magaard. In preparation.
Permutation groups where non-trivial elements have few fixed points, to appear in the Proceedings "Finite Simple Groups: Thirty Years of the Atlas and Beyond", edited by M. Bhargava, R. M. Guralnick, G. Hiss, K. Lux und P. H. Tiep.
Minimal and canonical images, joint with Chris Jefferson, Eliza Jonauskyte and Markus Pfeiffer. In preparation.

Talks (selection):

2016:	"Finding and using symmetry", Mathematics Seminar at the University of Dundee, 8th August. Talk at the conference "Group Theory, Geometry and the Influence of Jacques Tits" in Karlsruhe, 27th May: "Towards a Z*_3-Theorem". NBSAN-Meeting: "Applying permutation group theory" at the University of St Andrews, 18th March.
2015:	CIRCA-Seminar "Fixity and subgroup structure" at the University of St Andrews, 26th August. Lecture Series for the Modern Mathematics International Summer School in Bremen, 4th- 9th July, on Coxeter chamber systems. Inaugural lecture "Was sind und was können Gruppen?" at the Martin-Luther-Universität Halle-Wittenberg, 21st May.
2014:	Talk at the Workshop „Algorithms for Linear Groups” in Banff, 20th November: „Permutation groups where non-trivial elements have few fixed points”. Lecture Series for the Modern Mathematics International Summer School in Lyon, 22nd-29th August, on the topics group theory and primality testing. Talk at the Martin-Luther-Universität Halle-Wittenberg, 24th July, for the application to a professorship: „Permutation groups and Riemann Surfaces". Mathematics Colloquium at the Martin-Luther-Universität Halle-Wittenberg, 3rd July: „Permutation groups working hard".
2013:	Nikolaus-Conference in Aachen, 6th December: "Permutation groups where non-trivial elements have few fixed points". Colloquium on Pure Mathematics at the University of Hamburg, 19th November: "Permutation groups". Talk on the topic "Symmetry" at a spring academy for school students, 28th March. Algebra Seminar at the University of Birmingham, 28th February: "Permutation groups where non-trivial elements have few fixed points". "Women leading in Mathematics" Lecture at the University of Birmingham, 27th February: "Permutation groups".
2012:	„Groups and Geometries“ in Banff, 3rd-7th September: "Special primitive pairs in finite groups". This talk can be watched here. Norddeutsches Gruppentheoriekolloquium at the TU Braunschweig, 29th.-30th. June: „C55-Gruppen“.
2011:	EPFL Lausanne, Group Theory Seminar, 8th November: "The Z-Project". University of Aberdeen, Postgraduate Group Theory Conference, 25th June: "Local arguments for the Z-Theorem". TU Braunschweig, Baer-Colloquium, 28th May: "Das Z_p-Projekt". Research Institute for Mathematical Sciences, Kyoto University, 9th March: "The Z_p-Project". Tokyo University of Science, 6th March: "Local arguments for the Z*-Theorem".
2010:	FU Berlin, 15th September: „Eine neue Sichtweise auf den Z-Satz“. University of Gießen, 9th July, Colloquium for B. Baumann: „Eine neue Sichtweise auf den Z-Satz: der nicht-auflösbare Fall“. University of Birmingham, 23rd. March (Women in Mathematics Seminar): „On Burnside's p^aq^b-Theorem“.
2009:	University of Birmingham, 14th September (Leaving Seminar): „Soluble Radicals“. University of Jena, 20th August: "Sätze vom Z_p-Typ". University of Halle, 29th July: "Auflösbare Radikale". University of Halle, 17th February: "Sätze vom Z_p-Typ".
2008:	Norddeutsches Gruppentheoriekolloquium in Kiel, 18th and 19th July: "Glauberman's Z-Theorem". Groups and Geometries Meeting in Oberwolfach, 20th-26th April: "Soluble Radicals". Group Theory Seminar, University of Kiel, 15th April: "Auflösbare Radikale". George Glauberman Conference in Chicago, 24th-28th March: "A local approach to Glauberman's Z-Theorem". Pure Mathematics Colloquium in Southampton, 22nd February: "Glauberman's Z*-Theorem and the special role of elements of order 2".
2007:	Norddeutsches Gruppentheoriekolloquium in Magdeburg, 9th and 10th November: "Isolierte Involutionen in endlichen Gruppen". Group Theory Seminar, University of Kiel, 6th November: " Quadratisch operierende Elemente der Ordnung p". Algebra Seminar, University of Aberdeen, 25th October: "A local approach to Glauberman's Z*-Theorem". Algebra Seminar, University of Manchester, 15th May: "Isolated involutions in finite groups". Algebra Seminar, TU Kaiserslautern, 24th April: "Isolierte Involutionen in endlichen Gruppen". Algebra Seminar, University of Birmingham, 31st January: "Isolated involutions in finite groups".

Grants:

1998-2003 Grant from the Studienstiftung des deutschen Volkes for undergraduate students.
2002 Grant from the DAAD for a short term visit in Paris.
2003-2006 Grant from the Studienstiftung des deutschen Volkes for postgraduate students.
Conference Grant from the London Mathematical Society.
Mercator-Professorship for Chris Parker (2011), with Gernot Stroth.
Funding for conferences.
DFG grant for 2013.
DFG grant for 2014.
DFG grant for 2016.

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