Homology, Homotopy and Applications

$K$-theoretic torsors for infinite dimensional vector bundles of locally compact type

The homotopy types of $U(n)$-gauge groups over $S^4$ and $\mathbb{C}P^2$

On constructing weight structures and extending them to idempotent completions

On a base change conjecture for higher zero-cycles

Golodness and polyhedral products of simplicial complexes with minimal Taylor resolutions

On the Borel transgression in the fibration $G \to G/T$

Relative homological algebra and Waldhausen $K$-theory

Using torsion theory to compute the algebraic structure of Hochschild (co)homology

A homotopy decomposition of the fibre of the squaring map on $\Omega^3 S^{17}$

$E_{\infty}$ obstruction theory

Samelson products in quasi-$p$-regular exceptional Lie groups

Excellent rings in transchromatic homotopy theory

Perfect discrete Morse functions on connected sums

Cyclic vs mixed homology

Tensoring with the Frobenius endomorphism

Intersecting the dimension and slice filtrations for motives

Third cohomology and fusion categories

Small presentations of model categories and Vopěnka’s principle

A comparison of two models of orbispaces

Homotopy theory of symmetric powers