Differential Geometry
Articles tagged with Differential Geometry
Of the geometry of light
Seeking mathematical beauty in imperfect crystals
Researchers from The University of Osaka have devised new mathematical models to describe the mechanics of crystal defects. Using differential geometry, they provided a robust and rigorous framework for understanding these phenomena.
Proof that "one of the parallel worlds cannot be extremely different from the other"
Researchers investigated space B's behavior, proving no blowing up occurs under certain conditions. This achievement provides mathematical proof for one of the previously expected similarities between A-side and B-side.
A simpler path to supercharge robotic systems
Bhattacharya's project uses topological abstraction to reduce complexity in robotic systems, enabling more efficient and accurate motion planning. The approach has potential applications in industries such as transportation, manufacturing, and healthcare.
Bridge built between Kähler-Einstein and Chen-Ning Yang's Equations
Researchers successfully connected two crucial equations, bridging relativity and quantum mechanics. Prof. Chen's work introduces bold ideas to solve previously unsolved equations.
Six years in 120 pages: Researchers shed light on Ricci flows
The study resolves the Hamilton-Tian conjecture, which posits that most space is perfect, while singularities can be restricted to low-dimensional spaces. This breakthrough has far-reaching implications for studies of Ricci flows, thermal expansion, and contraction.
Lobachevsky Medal and prize awarded to Richard Schoen
Richard Schoen was awarded the Lobachevsky Medal for his work on positive energy in general relativity and a complete solution to the Yamabe problem. The prize is part of Kazan Federal University's efforts to revive a tradition from 1895, with an award amount of $75,000 and recognition as a biennial honor.
Leon Simon to receive 2017 AMS Steele Prize for seminal contribution to research
Simon's seminal paper on singularities has had a profound impact on analysis and geometry, with hundreds of papers built upon its insights. His work unifies and generalizes earlier research, providing powerful tools for differential equations and beyond.
Fernando Codá Marques and André Neves to receive the 2016 AMS Oswald Veblen Prize
Fernando Codá Marques and André Neves have made groundbreaking contributions to differential geometry with their proof of the Willmore conjecture. The resolution has far-reaching implications for understanding surfaces and has illuminated new approaches to other significant questions in topology and geometry.
Geometries presented by Chinese scholars for all possible space-time kinematics and their relations
Researchers from Chinese Academy of Sciences and Tsinghua University presented additional, previously unknown geometries corresponding to all possible kinematical algebras. These geometries are classified into three relativistic geometries, absolute-time geometries, and absolute-space geometries, each with unique properties.
Robert McLachlan awarded Germund Dahlquist Prize
Robert McLachlan, a Professor of Applied Mathematics at Massey University in New Zealand, received the Germund Dahlquist Prize for his original contributions to geometric integration. His work has applications in physics, computer science, and engineering, and he has used geometric integration methods to study complex systems.
UC San Diego places in top tier of institutions awarded 2004 Sloan Research Fellowships
Two UCSD professors, Stefan Savage and Henrik Wann Jensen, join a prestigious group of Sloan Fellows with expertise in computer networking and graphics. The fellowships recognize outstanding research in various fields, including the neural control of movement, differential geometry, and level set methods.