Diophantine equations
Equations over integers and rational numbers, from elliptic curves to the limits of decision algorithms.
7 problemsCollections
Selected problems that share a subject or a research tradition. Each leads to its own overview and sources.
Within Algebra and geometry · All collections
Geometric extremes
Packing, covering, distances and other limits set by geometry.
11 problemsFields and rational points
Field symmetries and rational points on curves and higher-dimensional varieties.
7 problemsAlgebras and modules
Representations, extensions and resolutions that reveal algebraic structure.
4 problemsBases and transversals
Rearranging bases, choosing distinct symbols and listing minimal hitting sets.
4 problemsAlgebraic geometry
Polynomial equations define spaces whose shapes, singularities and algebraic cycles pose different open problems.
8 problemsGroups and operators
Structure in groups, representations and infinite-dimensional spaces.
7 problemsKnots and manifolds
Smooth structures, curved spaces and the manifolds produced by knot surgery.
8 problems