## Section: New Results

### Semicomputable points in Euclidean spaces

Many natural problems/objects from theoretical computer science and logic are not decidable/computable, but semidecidable/semicomputable only: the halting problem, provability, domino problem, attractors of dynamical systems, etc. We pursue our program to study semicomputable objects in a systematic way. In this work, we focus on objects that can be described by finitely many real numbers, in particular polynomials and disks in the plane. Such objects can be identified with points of Euclidean spaces. We therefore introduce and study a notion of semicomputable point in Euclidean spaces, providing a multi-dimensional analog of a well-known unidimensional notion. The study involves ideas from linear algebra, convex analysis and computability. This work was presented at MFCS 2019 [27].