11 problems

Let $G$ be a group acting by type-preserving simplicial isometries on a building $\Delta$. Let $X$ be the Davis realization of $\Delta$, and call the action locally elliptic if every…

Let $K$ be a topological space equipped with maps $K\to\{\bullet\}$ lying in both indicated right-orthogonal classes: the class generated by the finite-space maps…

Holomorphic Lefschetz conjecture for correspondences. The displayed formula holds. This is intended as the correspondence analogue of the holomorphic Lefschetz fixed point formula,…

Let ${\mathcal{N}}$ denote Baire space. A partial ordering $\preceq$ on ${\mathcal{N}}$ is $\Pi^0_1$, every $\preceq$-chain has a least upper bound, and…

Noncommutative Brouwer retract conjecture. There is no $*$-homomorphism

Noncommutative Brouwer fixed-point conjecture. Every continuous map

Let $\mathbb{K}$ be a definably complete expansion of an ordered field, and let $f:[0,1]^2\to[0,1]^2$ be a definable continuous function. Then Brower's fixed-point conjecture. Ther…

Brower and Kakutani fixed point theorem. Brower fixed point theorem. Kakutani fixed point theorem.

Center conjecture. At least one of the following two possibilities holds:

Let $B$ be a spherical building and let $C\subseteq B$ be a closed convex subset. Fixed-point conjecture. Either $C$ is a subbuilding, or the action … has a fixed point. This gener…

Let $B$ be a spherical building and let $K\subseteq B$ be a convex subcomplex. A center is a point fixed by the automorphisms of $B$ preserving $K$. Tits' Center Conjecture. Either…