In the third century BCE, Apollonius of Perga asked how many circles one could draw that would touch three given circles at exactly one point each. It would take 1,800 years to prove the answer: eight ...

Enumerative geometry and moduli theory address the classification and counting of geometric structures on algebraic varieties and the study of the spaces that parametrise them. Beginning with ...

Algebraic structures—such as groups, rings, modules, Lie algebras and their generalisations—provide a unifying language for diverse areas of mathematics and theoretical physics. Cohomological methods ...