Research Interests

Model theory and applications; more specifically, o-minimality (a common model-theoretic generalization of semialgebraic and subanalytic geometries) and its interactions with other areas, including diophantine geometry, real geometry, combinatorics, classical topology, functional analysis, and asymptotic analysis.

  • Diophantine Geometry: The density of algebraic points on definable sets; the Pila−Wilkie Theorem, Wilkie's Conjecture and related questions, and various applications; questions of effectivity.
  • Real Geometry: Smooth parameterization (e.g. $C^r$-parameterization, mild parameterization) in the definable setting of o-minimal structures, such as expansions of the real field by quasianalytic classes (e.g. Denjoy--Carleman classes).
  • Classical Topology: Definable topologies over o-minimal structures, development of the theory of definable topological spaces and their classification; questions of affineness; study of classical notions (e.g. compactness, metrizability, separability, etc.) in the definable context.
  • Functional Analysis: Normed and Banach spaces over o-minimal structures, in particular function spaces; questions of universality and approximation.
  • Combinatorics: Ramsey-type results in the definable setting, e.g. growth rates of Ramsey functions for definable relations.
  • Asymptotic Analysis: QAA (quasianalytic asymptotic) algebras, Hardy fields and their connection to the theory of transseries; interaction between asymptotic and diophantine properties of functions, such as the growth behaviour of integer-valued functions.

Research Grant Funding

Current External Research Grant Funding

NSF Continuing Grant DMS-2154328
Model Theory, Diophantine Geometry and Asymptotic Analysis

2022-2025; held at Purdue University, USA.

For more information see the project entry in the NSF database

Former External Research Grant Funding

DFG Sachbeihilfe Grant (individual multi-year research grant) TH 1781/2-1
Parameterization and Algebraic Points in O-Minimal Structures

Awarded 2012; held 2013-2017 at the University of Konstanz, Germany.

For more information see the project entry in the DFG database

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