I'm a french researcher in mathematics.
The mathematics I can understand are limited to what I can picture, so I qualify myself as a geometer.
However, since geometry is about a thousand different things in maths, one geometer is always the non-geometer of another.
Here some mathematical interests of mine:
- Higher category theory, which is both the minimal structure underlying to all mathematical objects, and the "space-time" of mathematics, where all mathematics are done.
- Algebraic geometry, which I understand as the study of spaces by means of different kinds of commutative algebras of functions over them.
- Topos theory, which the kind of algebraic geometry studying those spaces with enough functions int the space of homotopy types.
- Goodwillie calculus, which is differential calculus on topoi.
- Verdier duality, which is measure theory on topoi.
- Symplectic geometry, a.k.a. the geometry of lagrangian correlations, which is arguably the most intriguing hierarchy of geometries in the classification of Lie groups.
- Mathematization of Physics, which is (symplectic) geometry used as a metaphor for natural phenomena.
- Philosophical reflection on mathematics, which I understand as
trying to extract the ideas behind mathematical formalisms
and trying to understand the relationship of maths with other sciences and Nature.