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Terence Tao
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An isometry (from one Hilbert space to another) can be described geometrically as a linear transformation that maps unit vectors to unit vectors. A co-isometry, by definition, is the dual of an isometry, but I only now figured out the geometric interpretation: a co-isometry is a linear transformation that maps the unit ball onto the unit ball! (A good example of a co-isometry to keep in mind is the orthogonal projection map from a Hilbert space H to a closed subspace H'.)

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A few years ago, I posted a puzzle at https://terrytao.wordpress.com/2008/12/09/an-airport-inspired-puzzle/ concerned with, amongst other things, whether one should spend one's energy on sprinting on a moving walkway as opposed to on the stationary ground, when trying to get from one place to another as quickly as possible. It turns out that when there is a lot of congestion on the walkway (or, in this case, an escalator), the answer to this question is quite counterintuitive (at least when viewed as a collective action problem rather than as an individual action problem).

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Nominations for the Breakthrough Prize and New Horizons Prize are now open. 

Timothy Chow proposes a Polymath project to attack Rota's conjecture on bases of finite-dimensional vector spaces.

https://polymathprojects.org/2017/02/23/rotas-basis-conjecture-polymath-12/

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Hopefully...

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Self-explanatory.

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One of the big developments in complexity theory from last year late 2015 is unfortunately slightly less big than first thought, though still significant.

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This would have been a useful video to share with my (recently concluded) graduate complex analysis class.

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Jean Bourgain wins 2017 Breakthrough Prize

Congratulations to Jean Bourgain (Princeton Institute for Advanced Study), who has won the 2017 Breakthrough Prize in mathematics!

https://www.ias.edu/press-releases/2016/bourgain-breakthrough

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Open to students between 13 and 18 in most countries; submission deadline is October 10. First prize is a $250,000 college scholarship, together with an award to a teacher that inspired the student, and funding for a science laboratory at the student's school.
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