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symmetry

number theory

Mathematicians Prove 30-Year-Old André-Oort Conjecture

By Leila Sloman
February 3, 2022
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A team of mathematicians has solved an important question about how solutions to polynomial equations relate to sophisticated geometric objects called Shimura varieties.

A sphere enclosing a space with hyperbolic geometry.
quantum gravity

Symmetries Reveal Clues About the Holographic Universe

By Katie McCormick
January 12, 2022
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Physicists have been busy exploring how our universe might emerge like a hologram out of a two-dimensional sheet. New clues have come from the symmetries found on an infinitely distant “celestial sphere.”

fundamental physics

Gravitational Waves Should Permanently Distort Space-Time

By Katie McCormick
December 8, 2021
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The “gravitational memory effect” predicts that a passing gravitational wave should forever alter the structure of space-time. Physicists have linked the phenomenon to fundamental cosmic symmetries and a potential solution to the black hole information paradox.

Closeup photo of an automated two-wheeled robot on a wooden table
mathematical physics

A New Theory for Systems That Defy Newton’s Third Law

By Stephen Ornes
November 11, 2021
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In nonreciprocal systems, where Newton’s third law falls apart, “exceptional points” are helping researchers understand phase transitions and possibly other phenomena.

topology

How Tadayuki Watanabe Disproved a Major Conjecture About Spheres

By Kevin Hartnett
October 26, 2021
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Watanabe invented a new way of distinguishing shapes on his way to solving the last open case of the Smale conjecture, a central question in topology about symmetries of the sphere.

combinatorics

Mathematician Answers Chess Problem About Attacking Queens

By Leila Sloman
September 21, 2021
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The n-queens problem is about finding how many different ways queens can be placed on a chessboard so that none attack each other. A mathematician has now all but solved it.

Animated illustration showing multiple permutations of colorful letters
group theory

Galois Groups and the Symmetries of Polynomials

By Allison Whitten
August 3, 2021
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By focusing on relationships between solutions to polynomial equations, rather than the exact solutions themselves, Évariste Galois changed the course of modern mathematics.

A pixelated black and white animation of a model of percolation.
mathematical physics

Mathematicians Prove Symmetry of Phase Transitions

By Allison Whitten
July 8, 2021
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A group of mathematicians has shown that at critical moments, a symmetry called rotational invariance is a universal property across many physical systems.

Math Meets QFT

Nathan Seiberg on How Math Might Complete the Ultimate Physics Theory

By Kevin Hartnett
June 24, 2021
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Even in an incomplete state, quantum field theory is the most successful physical theory ever discovered. Nathan Seiberg, one of its leading architects, talks about the gaps in QFT and how mathematicians could fill them.


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