Homotopy theory is a cornerstone of modern algebraic topology, concerned with the study of spaces up to continuous deformations. This approach characterises topological spaces by their intrinsic ...

Type theory and homotopy theory have evolved into profoundly interconnected disciplines. Type theory, with its foundations in logic and computer science, provides a formal language for constructing ...

I am an algebraic topologist and a stable homotopy theorist. I study chromatic homotopy theory and its interactions with equivariant homotopy theory. I also work with condensed matter physicists to ...

Elements λn, n ≥ 0, which generate the homotopy groups of spheres in the category of simplicial Lie algebras are shown to have Hopf invariant one. This fact is shown to have strong implications for ...

$\bullet$ Differential topology, algebraic $K$-and $L$-theory. $\bullet$ Functor Calculus, Homotopy theory.

$\bullet$ Homotopy theory and Higher Algebra. $\bullet$ Algebraic $K$-theory. $\bullet$ Field theories and mathematical Physics. $\bullet$ (topological) Hochschild ...

The telescope conjecture gave mathematicians a handle on ways to map one sphere to another. Now that it has been disproved, the universe of shapes has exploded. In early June, buzz built as ...