Differential geometry is the study of smooth manifolds and the intrinsic properties of spaces that can be described locally by Euclidean geometry. Within this expansive field, singularities represent ...

DIFFERENTIAL geometry is a fascinating subject, because it gives us vivid and picturesque embodiments of theorems obtained by the combination of several branches of pure analysis, such as algebra, ...

Partial differential equations (PDEs) lie at the heart of many different fields of Mathematics and Physics: Complex Analysis, Minimal Surfaces, Kähler and Einstein Geometry, Geometric Flows, ...

When students are genuinely curious about new concepts and ideas, they develop their own study skills, says Professor Pekka Pankka. Geometry, Algebra, and Topology are pure mathematics and essential ...

Distinguished Professor H. Blaine Lawson, Jr., from the College of Arts and Sciences Department of Mathematics, is the recipient of the American Mathematical Society’s (AMS) “2026 Leroy P. Steele ...

The spectrum of the canonical operator in the noncommutative 2-torus Tθ depending on the parameter θ ∈ [0,1] © Douglas Hofstadter's butterfly. Licensed under ...

How can the behavior of elementary particles and the structure of the entire universe be described using the same mathematical concepts? This question is at the heart of recent work by the ...

Luis Caffarelli has won the 2023 Abel prize, unofficially called the Nobel prize for mathematics, for his work on a class of equations that describe many real-world physical systems, from melting ice ...