Research Interests

Model theory and applications; more specifically, o-minimality and its interactions with other areas, including diophantine geometry, real geometry, combinatorics, topology and functional analysis, and dynamical systems.

In particular:

  • Diophantine Geometry: The density of algebraic points on definable sets; Wilkie's Conjecture, both general results and special cases, and their applications, primarily to obtain transcendence results; questions of effectivity of the Pila−Wilkie Theorem and its applications.
  • Real Geometry: Smooth parameterization in the definable setting of o-minimal structures, including applications of Pila−Wilkie (re)parameterization and questions of effectivity; mild parameterization in o-minimal structures and its applications.
  • Definable topologies over o-minimal structures: Development of the theory of definable topological spaces and their classification; questions of affineness, as well as compactness, metrisability, separability, etc. in the definable context.
  • Functional Analysis over o-minimal structures: 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.
  • Dynamical systems: QAA algebras, Hardy fields and their connection to the theory of transseries.

Funded Research Projects

DFG Research Project (Individual multi-year Research Grant)
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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