Algebraic structures, encompassing groups, rings, fields and modules, have long formed the backbone of modern mathematics. Category theory, with its focus on objects and morphisms, provides a unifying ...

The human ecosystem is made of open and closed systems. While the earth is a closed system for matter but an open system for energy, the human body is considered an open system. There is a growing ...

On a crisp fall New England day during my junior year of college, I was walking past a subway entrance when a math problem caught my eye. A man was standing near a few brainteasers he had scribbled on ...

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 ...

Transactions of the American Mathematical Society, Vol. 362, No. 7 (JULY 2010), pp. 3499-3533 (35 pages) We introduce a notion of Polish structure and, in doing so, provide a setting which allows the ...

Abstract Let 𝑅 be a commutative Noetherian ring and let 𝒟(𝑅) be its (unbounded) derived category. We show that all compactly generated t-structures in 𝒟(𝑅) associated to a left bounded filtration ...

Katie has a PhD in maths, specializing in the intersection of dynamical systems and number theory. She reports on topics from maths and history to society and animals. Katie has a PhD in maths, ...