(Immanuel Halupczok)

Gebaeude 25.22
Universitaetsstr. 1
40225 Duesseldorf

Phone: +49 211 81-13189


The tree corresponding to the cusp curve
A tree associated to the cusp curve X3 = Y2 in Z3; see Trees of definable sets in Zp for details.

My main research area are geometric and arithmetic questions in henselian valued fields, which I consider using model theoretic methods. Typical examples of henselian valued fields are the p-adic numbers and the field of formal Laurent series with coefficients in some other field. More precisely, I am mainly working on the following two topics:

  • Singularities and stratifications: I proved the existence of a strong notion of stratifications in henselian valued fields. These stratifications in particular induce classical Whitney stratifications over the reals and the complex numbers.
  • Motivic integration and its applications to representation theory of reductive groups over local fields: Motivic integration makes it possible to compute integrals uniformly in all local fields; this can be applied to make representation theory of reductive groups over local fields uniform in the field.

Other topics I worked on:

  • Representation theory (of real reductive groups), symmetric varieties
  • Model theory of pseudo-algebraically closed fields
  • Combinatorics
    • Polyomino achievement games
    • Zero-sum problems in finite abelian groups
    • Covering codes