Mathematics Problem Archive

A scheme is a generalization of a ring, in the same way that a manfold is a generalization of R^n. So maybe there is some kind of model structure on s...

My general theory is that the category of model categories is not itself a model category, but a 2-model category. Weak equivalences of model categori...

The 2-category of simplicial model categories is supposed to be (according to me) 2-Quillen equivalent to the 2-category of model categories. Even wit...

In the appendix to my book on model categories, I said maybe what we are doing in associating to a model category its homotopy category is the wrong t...

Determine the v_1 -exponents for the spheres. Recall that Cohen, Moore, and Neisendorfer showed that the p-torsion in the homotopy of S^2n+1 is all ki...

Suppose X is a simply connected finite complex. Do the Steenrod reduced powers P^t act trivially on the mod p cohomology of the loop space of X when p...

Build MU from the moduli stack of formal groups. This has got to be doable somehow, though it is an old problem (I first heard it in Ravenel's green b...

Classify all possible Bousfield classes of E-infinity ring spectra. I know very little about this problem. Note that the Spanier-Whitehead dual of the...

Is every $n$-dimensional homogeneous absolute neighborhood retract a topological manifold?...

For every fibration $F\to E\to B$ of simply connected spaces whose fiber $F$ is rationally elliptic with nonzero Euler characteristic, does the ration...

For every algebraic variety $X$ defined over $\mathbb{Q}$, does the closure of $X(\mathbb{Q})$ inside the real locus $X(\mathbb{R})$ have only finitel...

Does every wild knot have infinitely many quadrisecants, that is, lines meeting the knot in at least four distinct points?...

Let $M$ be a closed manifold. Is every closed exact Lagrangian submanifold of the cotangent bundle $T^*M$ Hamiltonian isotopic to the zero section?...