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 ...

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 ...

The foundations of equivariant homotopy and cellular theory are examined; an equivariant Whitehead theorem is proved, and the classical results by Milnor about spaces ...

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 ...

Widely influential algebraic topologist and homotopy theorist Jack Morava, professor in the Department of Mathematics at Johns Hopkins University for nearly four decades, died in Boston on Aug. 1 ...

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

The equal sign is the bedrock of mathematics. It seems to make an entirely fundamental and uncontroversial statement: These things are exactly the same. But there is ...

When a legendary mathematician found a mistake in his own work, he embarked on a computer-aided quest to eliminate human error. To succeed, he has to rewrite the ...

The subject matter of topology are discrete invariants of topological spaces (for example smooth manifolds) and maps between them. The simplest such invariant is the winding number of a curve in the ...