Rebecca Waldecker - Professor for Algebra
Research

Most of my current research projects stem from applications of group theory. This can be about using symmetry in order to improve algorithms or to solve problems in science outside of mathematics, about the structure of finite groups or specific applications of permutation group theory. I am fascinated by questions from other areas where symmetry plays a role or where a problem can be translated into a group theoretic problem and then solved. Also, I started working in projects about the history of group theory, specifically around the Oberwolfach Institute and the CFSG.


Manuscripts in preparation or in print (accepted):
  • Finite simple permutation groups acting with fixity 4, with Barbara Baumeister, Paula Hähndel, Kay Magaard and Patrick Salfeld. Submitted, in revision. Link to arxiv version.
  • L9-free groups, with Clemens Tietze and Imke Toborg. Submitted. Link to arxiv version.
  • Finite groups of fixity 2 or 3, revisited, with Paula Hähndel, Christoph Möller and Anika Streck. In preparation.
  • Vom Gruppentheoriekolloquium 1954 bis zu "Bären mit Kindern und Kegeln". Eine Einordnung der frühen Gruppentheorietagungen am MFO. (Book chapter, submitted.) Link to arxiv version.
  • Computing canonical images in permutation groups with graph backtracking, with Chris Jefferson and Wilf Wilson. Submitted, in revision. Link to arxiv version.
  • Stories about symmetry. Extended abstract of my talk, to appear in the Humboldt Symposium issue of the Proceedings of the Royal Society of Victoria.


Publications since 2015:
  • Perfect refiners for permutation group backtracking algorithms, with Chris Jefferson and Wilf Wilson. Journal of Symbolic Computation 114 (2023), 18–36. Online version.
  • The occurrence of finite simple permutation groups of fixity 3 as automorphism groups of Riemann surfaces, with Patrick Salfeld. Communications in Algebra 50 (2022), no. 4, 1691–1696. Online version.
  • Textbook Elementare Algebra und Zahlentheorie, with Gernot Stroth. Second edition of his 2012 book. The next edition will appear end of 2023.
  • The occurrence of finite simple permutation groups of fixity 2 as automorphism groups of Riemann surfaces, with Patrick Salfeld, Journal of Algebra 561 (2020), 402–420. Online version.
  • The Sylow structure of transitive permutation groups acting with fixity 4, with Barbara Baumeister und Kay Magaard. Special issue in honor of Kay Magaard, Albanian J. Math. 12 (2018), 137-145. Available online.
  • New refiners for permutation groups search, with Chris Jefferson and Markus Pfeiffer. Journal of Symbolic Computation 92 (2019), 70-92. Online version.
  • Minimal and canonical images, with Chris Jefferson, Eliza Jonauskyte and Markus Pfeiffer. Journal of Algebra 521 (2019), 481-506. Online here.
  • Questions on orbital graphs, with Paula Hähndel. In: Davenport J., Kauers M., Labahn G., Urban J. (eds) Mathematical Software - ICMS 2018. Lecture Notes in Computer Science, vol 10931. Springer, Cham. Here is the online version.
  • Permutation groups where non-trivial elements have few fixed points, in "Finite Simple Groups: Thirty Years of the Atlas and Beyond", herausgegeben von M. Bhargava, R. M. Guralnick, G. Hiss, K. Lux and P. H. Tiep. Contemporary Mathematics 694, AMS (2017), 223-229.
  • Rempe-Gillen, Lasse and Waldecker, Rebecca, Primzahltests für Einsteiger, 2nd edition. Springer, 2015.
  • Magaard, Kay und Waldecker, Rebecca, Transitive permutation groups with trivial four point stabilizers, J. Group Theory 18 (2015), no. 5, 687-740.
  • Pölzing, Juliane and Waldecker, Rebecca, M9-free groups, J. Group Theory 18 (2015), 155-190.
  • Magaard, Kay and Waldecker, Rebecca, Transitive permutation groups where nontrivial elements have at most two fixed points, Journal of Pure and Applied Algebra 219, Issue 4 (2015), 729-759.

Publications before 2015 can be found here.

Funding:
  • PhD position in the DFG Graduate Research School "BEAM", the spokesperson is Dariush Hinderberger.
  • Funding for a workshop at the SwissMAP Research Station, 2022, with Donna Testerman.
  • DFG grant 2020/21 for a project extending the spectrum of search algorithms.
  • Funding from the VolkswagenStiftung (2018-2019) for a summer school on "Constructive Matrix Group Recognition in GAP", with Alice Niemeyer.
  • Grant for a summer school at the Institute Mittag-Leffler (Stockholm) with Cheryl Praeger and Donna Testerman.
  • Project funded by the VolkswagenStiftung (2018-2019) for "Exploring Graph Backtracking".
  • Cheryl Praeger Visiting Research Fellowship 2017 (stay at the UWA).
  • DFG grants 2013, 2014 and 2016.
  • Funding for conferences.
  • Mercator-Professorship for Chris Parker (2011) with Gernot Stroth.
  • 2007 Conference Grant from the London Mathematical Society.
  • 2003-2006 Grant from the Studienstiftung des deutschen Volkes for postgraduate students.
  • 2002 Grant from the DAAD for a short term visit in Paris.
  • 1998-2003 Grant from the Studienstiftung des deutschen Volkes for undergraduate students.



Home