## 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

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