Tag

Symplectic Geometry

All articles tagged with #symplectic geometry

mathematics1 month ago•21 min saved

A Quiet Genius Reshapes Geometry with the 2026 Fields Medal

John Pardon, renowned for turning hard problems into unifying frameworks, has earned the 2026 Fields Medal for ground‑breaking work in knot theory, topology, and symplectic geometry—ranging from showing arbitrarily large knot distortion to resolving the MNOP conjecture on Calabi–Yau manifolds—and for developing new tools like virtual cycles and what’s now called the Pardon algebra, which are reshaping the foundations of symplectic geometry.

via Quanta Magazine|

#fields-medal #john-pardon #knot-theory

science-and-technology2 years ago•6 min saved

"Advancements in Geometric Engineering for Spacecraft Orbit Control"

Geometers are collaborating with engineers to develop new tools based on symplectic geometry to help understand and predict spacecraft orbits, particularly in complex multi-body systems. These tools include the Conley-Zehnder index to determine orbit families and the Floer number to identify potential new orbit families at bifurcation points. The collaboration aims to provide engineers with tools to test their algorithms and potentially uncover new orbit families, with the hope that symplectic geometry will become a standard part of the space mission toolkit.

via Quanta Magazine|

#engineering #mathematics #science-and-technology