Mathematicians solve decades-old mystery about the hidden order in high-dimensional randomness

Three mathematicians have laid out proof that solves a long-standing problem in mathematics. Even the mathematician—an Abel ...

AI makes a major breakthrough in a math problem that had stumped experts for decades

For nearly 80 years, mathematicians have struggled to solve a classic geometry puzzle first posed by Paul Erdős in 1946: the ...
Visual Studio Magazine

Spiral Dynamics Optimization with Python

The Data Science Lab Spiral Dynamics Optimization with Python Dr. James McCaffrey of Microsoft Research explains how to implement a geometry-inspired optimization technique called spiral dynamics ...
Nature

Gradient Ricci Solitons in Riemannian Geometry

Gradient Ricci solitons are self-similar solutions to the Ricci flow, characterised by a Riemannian manifold (M,g) endowed with a smooth potential function f satisfying the equation Ric + ∇²f = λg for ...
Nature

Gradient Estimates and Differential Inequalities on Riemannian Manifolds

Gradient estimates and differential inequalities form a cornerstone of modern geometric analysis, providing precise control over the rate of change of solutions to elliptic and parabolic equations on ...
Journal & Courier

When geometry matters: Gradient-wall microresonators enable large-scale optical trapping

GA, UNITED STATES, March 10, 2026 /EINPresswire.com/ — Optical trapping is a powerful tool for manipulating microscopic particles, but conventional approaches often ...
The Desert Sun

When geometry matters: Gradient-wall microresonators enable large-scale optical trapping

The team demonstrates a gradient-thickness-protected microbottle resonator that enables large-scale, stable optical trapping via whispering-gallery modes. By introducing a controlled wall-thickness ...