symplectic geometry – Quanta Magazine

Geometers Engineer New Tools to Wrangle Spacecraft Orbits

Leila Sloman — Mon, 15 Apr 2024 14:15:34 +0000

In October, a Falcon Heavy rocket is scheduled to launch from Cape Canaveral in Florida, carrying NASA’s Europa Clipper mission. The $5 billion mission is designed to find out if Europa, Jupiter’s fourth-largest moon, can support life. But because Europa is constantly bombarded by intense radiation created by Jupiter’s magnetic field, the Clipper spacecraft can’t orbit the moon itself. Instead...

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The Mathematician Who Sculpted the Shape of Space

Steve Nadis — Mon, 16 Oct 2023 14:03:49 +0000

Eugenio Calabi was known to his colleagues as an inventive mathematician — “transformatively original,” as his former student Xiuxiong Chen put it. In 1953, Calabi began to contemplate a class of shapes that nobody had ever envisioned before. Other mathematicians thought their existence was impossible. But a couple of decades later, these same shapes became extremely important in both math and...

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Emmy Murphy Is a Mathematician Who Finds Beauty in Flexibility

Erica Klarreich — Mon, 27 Mar 2023 14:03:43 +0000

“For me, mathematics exists in the space between us,” Emmy Murphy wrote in accepting the 2020 New Horizons in Mathematics Prize. That space, for her, is a realm of art, perhaps even more than science. And like an artist, she is most fulfilled when exploring the fertile ground where constraint meets creation. The objects she studies are “beautiful to me in the same way that architecture or fashion...

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Mathematicians Discover the Fibonacci Numbers Hiding in Strange Spaces

Leila Sloman — Mon, 17 Oct 2022 13:44:13 +0000

Fourteen years ago, the mathematicians Dusa McDuff and Felix Schlenk stumbled upon a hidden geometric garden that is only now beginning to flower. The pair were interested in a certain kind of oblong shape, one that could be squeezed and folded up in very particular ways and stuffed inside a ball. They wondered: For a certain shape, how big does the ball need to be? As their results began to...

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Mathematicians Transcend Geometric Theory of Motion

Kelsey Houston-Edwards — Thu, 09 Dec 2021 15:23:48 +0000

In a nearly 400-page paper posted in March, the mathematicians Mohammed Abouzaid and Andrew Blumberg of Columbia University have constructed a major extension of one of the biggest advances in geometry in recent decades. The work they built on relates to a well-known conjecture from the 1960s made by Vladimir Arnold. Arnold was studying classical mechanics and wanted to know when the orbits of...

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