Prof. Dr. Heike Mildenberger
Every year, approximately 50 Fellows are invited to work on their projects at FRIAS for 2 to 12 months in an intellectually stimulating environment. Fellows that have already been at FRIAS before can return to FRIAS for 2 to 6 weeks within the framework of the Alumni Programme, for example in order to finish a project. Furthermore, junior and senior researchers are regularly invited as guest researchers.
Our Research Focus profited enormously from the international team of Fellows and guest researchers at FRIAS.
Prof. Dr. Tobias Schätz, ERC Consolidator Grant 2015, Research Focus Quantum Transport 2014/15
Internal Senior Fellow
October 2013 - July 2014
Mildenberger studied mathematics and physics in the School of Mathematics and Physics of the Albert-Ludwigs-Universität Freiburg. Then she continued in the Section of Mathematical Logic of the Institute of Mathematics, where she finished her doctoral degree. She worked as an assistant at the University of Bonn and was a member of the Logic Group in the Mathematical Institute of the University of Bonn. She completed habilitation in 1998 in Bonn. From January 1995 to December 1996 she worked at the Mathematics Department of the University of Michigan in Ann Arbor, Michigan, supported by a fellowship from the Deutsche Forschungsgemeinschaft. Andreas Blass was her very kind mentor there. From April 1999 to March 2001 she was a Minerva fellow at the Institute of Mathematics of the Hebrew University in Jerusalem working together with Saharon Shelah. From April 2001 to August 2009 she was affiliated with the Kurt Gödel Research Center for Mathematical Logic of the University of Vienna in various positions. From September 2009 until September 2010 she held a Marie Curie Fellowship of the European Union and worked at the Hebrew University in Jerusalem together with Saharon Shelah. From October 2010 onward she has been a professor of mathematics at the University of Freiburg in Germany.
- More canonical forms and dense free subsets, Annals of Pure and Applied Logic 125:75-99 (2004).
- There may be infinitely many near coherence classes under u<d, The Journal of Symbolic Logic 72(4):1228-1238 (2007).
- Joint work Saharon Shelah, The principle of near coherence of filters does not imply the filter dichotomy principle, The Transactions of the American Mathematical Society 361:2305-2317 (2009).
- The club principle and the distributivity number, The Journal of Symbolic Logic 76(1):34-46 (2011).
- Joint with Saharon Shelah The minimal cofinality of an ultrapower of omega and the cofinality of the symmetric group can be larger than b+, The Journal of Symbolic Logic 76(4):1322-1340 (2011).
Few Near-Coherence Classes of Ultrafilter
Mildenberger plans to investigate strengthenings of the semifilter trichotomy and special constellations of near coherence classes of ultrafilters over the set of natural numbers. It is not known whether these properties are consistent relative to ZFC, the Zermelo Fraenkel axioms together with choice. Thus the clarification involves the search for implications in ZFC and at the same time the development and the investigation of forcing partial orders. In particular she will work with Ramsey theoretic properties of ultrafilters built from block sequences.
These ultrafilters over higher spaces shall be used as a reservoir for the second coordinates of conditions in a creature forcing.