Research
I am mainly interested in the model theoretic study of ordered algebraic structures. This involves the topics of o-minimality, non-archimedean fields, generalised power series, ordered exponential fields (in particular, the real exponential field), integer parts, models of Peano Arithmetic, definable valuations, ordered abelian groups and the surreal numbers. Many of the questions motivating my work originate from Mathematical Logic and have connections to Valuation Theory, Real Algebra, Set Theory, Real Analysis, Group Theory and Recursion Theory.
Projects
Contributions to the Study of Ordered Algebraic Structures (since October 2020)
Habilitation project, University of Konstanz, mentored by
Prof. Salma Kuhlmann
Mathematische Grenzen neuronaler Netze (July 2020 to September 2022)
Wissenschaftspreis 2020 (science prize) of the
Messmer-Stiftung, grant: 10000 EUR
Project video (in German)
Analysis without the Archimedean Property (March 2020 to December 2020)
as
Associated Fellow of the institute for advanced study
Zukunftskolleg, University of Konstanz
supported by an
Independent Research Grant, grant: 2706 EUR
Peer-reviewed publications:
Models of true arithmetic are integer parts of models of real exponentiation (with
Merlin Carl, 2021)
Algebraic and Model Theoretic Properties of O-minimal Exponential Fields (November 2016 to July 2019)
Doctoral scholarship of the
German Academic Scholarship Foundation, grant: 17400 EUR (plus travel expenses)
Peer-reviewed publications:
Value Groups and Residue Fields of Models of Real Exponentiation (2019),
Models of true arithmetic are integer parts of models of real exponentiation (with
Merlin Carl, 2021)
Algebraische und modelltheoretische Eigenschaften O-minimaler Exponentialkörper (July 2016 to June 2018)
Junior researcher funding programme of
Carl-Zeiss-Stiftung, grant: 45600 EUR
Peer-reviewed publications:
Value Groups and Residue Fields of Models of Real Exponentiation (2019)
Algebraic and Model Theoretic Properties of O-minimal Exponential Fields (October 2015 to November 2019)
Doctoral research project, University of Konstanz
Supervisor and first referee
Prof. Salma Kuhlmann, second referee
Prof. Tobias Kaiser (
University of Passau)
Doctoral thesis:
Algebraic and Model Theoretic Properties of O-minimal Exponential Fields (2019)
Unoriented Surfaces, Moebius graphs and outer space (June to August 2014)
Undergraduate Research Bursary of the
London Mathematical Society, grant: 1440 GBP
Supervised by
Prof. Tobias Dyckerhoff,
Mathematical Insitute,
University of Oxford
Research stays*
March 2018
Henri Poincaré Institute, Sorbonne University
Model Theory, Combinatorics and Valued fields, one month
April 2016
Mathematical Institute, University of Münster
Model Theory Month in Münster, two weeks
November 2014 to January 2015
Department of Mathematical Logic, University of Freiburg
guest of
Prof. Heike Mildenberger, eight weeks
September 2014
Working group: Scientific computing in the exascale era, Summer academy Kraków
German Academic Scholarship Foundation, two weeks
*at least two weeks
arXiv public author identifier
http://arxiv.org/a/krapp_l_1.
orcid.org/0000-0003-3102-1923
Last update:
Deutsche Version