17 problems

Let $N\geq 3$ and let $\Omega_N(\mathbb R^D)$ denote the $N$-complex of tensor fields on $\mathbb R^D$ with the generalized differential. For $m\geq N$, consider the construction t…

Let $H$ be an internal symmetry group, let $\mathbb{Z}^d$ act by discrete translations, and let $\mathcal{S}^{d}(H,\mathbb{Z}^d)$ denote the set of $(d+1)$-dimensional gapped short…

Let $\d$ be the spatial dimension, let $H$ be an internal symmetry group, and let $\mathcal{S}^{d}(H)$ denote the set of $(d+1)$-dimensional gapped short-range entangled Hamiltonia…

Consider the invertible phases, including invertible stabilizer phases and quantum cellular automata (QCA), and their classification by a generalized cohomology theory. Kitaev's co…

Let $\mathscr{S}\mathscr{W}$ be the generalized cohomology theory associated to the categorical obstruction, and let $I_\mathbb{Z}M\mathrm{Spin}$ denote the theory classifying 't H…

Let $(\operatorname{QCA}_d)_{d\in\mathbb{Z}}$ and $(\operatorname{inv}_d)_{d\in\mathbb{Z}}$ be the proposed spectra of quantum cellular automata and invertible phases, respectively…

Let $G$ be a discrete group, let $\mathrm{B}G$ be its classifying space, and let $\mathrm{QCA}_{d+1}$ denote the proposed $(d+1)$-dimensional quantum-cellular-automaton spectrum. W…

Let $\mathrm{IP}^d$ be the degree-$d$ cohomology theory associated with the invertible-phase $\Omega$-spectrum, and let … be the top Chern–Dold character. Integral-lift conjecture.…

Segal–Stolz–Teichner conjecture.

Generalized cohomology hypothesis. The group structure of $\operatorname{SPT}^d(G)$ should be obtained by computing

Generalized-cohomology conjecture. The spaces $\Theta_d$ can be chosen to satisfy

Let $\mathsf{G}$ be a finite categorical group, and let $\mathbf{B}\mathsf{G}$ be its classifying space, viewed as a double cover … A Real $n$-class function is the Real analogue o…

Let $M$ be a closed manifold or $Q$-manifold with a fixed metric, let $B$ be a connected, locally connected compact space, and let $\alpha\in h^*(B)$ be nonzero for some generalize…

Let $M$ be a compact manifold or $Q$-manifold with a fixed metric, and let $B$ be a connected, locally connected compact space. A Hurewicz fibration $p:E\to B$ has isometric fibers…

The paper considers $2|1$-dimensional Euclidean field theories, whose partition functions are modular functions, and writes $2|1\text{-}\operatorname{EFT}^n_{loc}[X]$ for the degre…

Let $S$ be the class of morphisms inverted by a generalized cohomology theory, and let a corresponding generalized homology theory be another theory that inverts a class of morphis…

Twisted Morava theory differential conjecture. The cohomology class $W_7+[H_7]$ corresponds to a differential in twisted Morava $K$-theory and twisted Morava $E$-theory, where…