Profile
Profile

Prof. Dr. Stefan Geschke

Former Bonn Junior Fellow
Current position: Akademischer Oberrat, University of Hamburg

E-mail: stefan.geschke(at)uni-hamburg.de
Homepage: http://www.math.uni-hamburg.de/home/geschke/
Room: 2.003
Location: Villa Maria
Institute: Mathematical Institute
Research Areas: Research Area KL
Former Research Area L
Date of birth: 14.Nov 1970

Academic Career

1995

Diploma in Mathematics, FU Berlin

1995 - 2001

Assistant, FU Berlin

1998 - 1999

Assistant, Kitami Institute of Technology, Japan

2000 - 2001

Postdoctoral Fellow, Ben Gurion, Israel

2000 - 2006

Assistant Professor, FU Berlin

2006 - 2008

Assistant Professor (tenure track), Boise State University, ID, USA

2009 - 2013

Professor (W2, Bonn Junior Fellow), University of Bonn

Research Profile

My research is centered around applications of combinatorial set theory and forcing to geometry, topology, algebra and analysis. However, I am also interested in finite combinatorics and complexity.

More specifically, I am working on questions concerning the classification of definable graphs on Polish spaces and on problems about automorphisms of the Boolean algebra \mathcal P(\omega)/{\tt fin} and the Calkin algebra.

Research Projects and Activities

DFG project “Continuous Ramsey theory in higher dimensions”
Principal Investigator

NSF standard grant for “Filtrations of Boolean algebras and related structures”

GIF project “New problems in set theory and Boolean algebra”
Principal Investigator

Contribution to Research Areas

Former Research Area L
Some consistent counterexamples to natural conjectures about the structure of the class of infinite compact spaces have been constructed [1].

It was shown that every closed graph on a Polish space either has a perfect clique or in a forcing extension of the set-theoretic universe, the weak Borel chromatic number of the graph is small [2]. This dichotomy fails for graphs of higher complexity.

Together with coauthors, a cardinal invariant that allows a closer analysis of almost disjoint families on the natural numbers has been studied and models of set theory with different behaviours of this new cardinal invariant were constructed [3].

Together with a coauthor, methods from finite and countably infinite Ramsey theory have been used to obtain a dichotomy for the class of continuous n-colorings on Polish spaces, showing that a coloring is complicated in terms of its so called homogeneity number if and only if it contains a copy of one of finitely many complicated colorings [4].

Geschke and a coauthor proved Ramsey theoretic results in the finite and countably infinite that assert the existence of large homogeneous subgraphs whose automorphisms lift to automorphisms of the colored graph [5], starting the field of symmetric Ramsey theory.
Research Area KL

Selected Publications

[3] S. Geschke, S. Fuchino, L. Soukup
How to drive our families mad
Archive for Mathematical Logic
2011
[6] Stefan Geschke
Low-distortion embeddings of infinite metric spaces into the real line
Ann. Pure Appl. Logic
, 157: (2-3): 148--160
2009
[10] Stefan Geschke, Martin Goldstern, Menachem Kojman
Continuous Ramsey theory on Polish spaces and covering the plane by functions
J. Math. Log. , 4: (2): 109--145
2004
[11] Stefan Geschke, Saharon Shelah
The number of openly generated Boolean algebras
J. Symbolic Logic , 73: (1): 151--164
2008
[12] Stefan Geschke, Menachem Kojman
Metric Baumgartner theorems and universality
Math. Res. Lett. , 14: (2): 215--226
2007

Publication List

MathSciNet Publication List (external link)

Editorships

• Set Theory and its Applications, Contemporary Mathematics 533 (2011)

Awards

2002

Best Teaching in Mathematics, FU Berlin

2006

Finalist Kurt Goedel Research Fellowship, Postdoc Category

Selected Invited Lectures

2004

Cardinal Arithmetic at Work, Jerusalem, Israel

2007

ASL Annual Meeting, Gainesville, FL, USA

2010

Logic Colloquium, Section Set Theory, Paris, France

Selected PhD students

Stefanie Frick (2008): “Continuous Ramsey Theory in Higher Dimensions”

Supervised Theses

  • Master theses: 3, currently 2
  • Diplom theses: 11, currently 5
  • PhD theses: 2, currently 1
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