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John and Alicia Nash, 1928,1933–2015

May 25, 2015


Our condolences

JohnAliciaNashPrinceton
Awesome Stories source

John Nash and his wife Alicia were killed in a taxi accident on the New Jersey Turnpike Saturday afternoon. They were on their way back from Norway where he and Louis Nirenberg had just accepted the 2015 Abel Prize. Besides meeting the king of Norway, Nash had also expressed a desire to meet world chess champion Magnus Carlsen during remarks at Princeton’s celebration of his Abel Prize in March, and that was also granted this past week.

Today Dick and I join many expressing shock and offering condolences.
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The Shapes of Computations

May 17, 2015


Or rather, what can the shapes of proofs tell us about them?

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April CACM source

Juris Hartmanis did much to lay the landscape of computational complexity beginning in the 1960s. His seminal paper with Richard Stearns, “On the Computational Complexity of Algorithms,” was published 50 years ago this month, as observed by Lance Fortnow in his blog with Bill Gasarch. It is a great achievement to open a new world, but all the more mysterious that after 50 years so much of its landscape remains unknown.

Today we ask what might determine the unseen topography and how much some recent large-data discoveries may help to map it.
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A Tighter Grip on Circuit Depth

May 8, 2015


The polynomial hierarchy is infinite for a random oracle

RossmanServedioTan

Benjamin Rossman, Rocco Servedio, and Li-Yang Tan have made a breakthrough in proving lower bounds on constant-depth circuits. It came from a bi-coastal collaboration of Rossman visiting the Berkeley Simons Institute from Japan and Tan visiting from Berkeley to Servedio at Columbia University in New York. Their new paper solves several 20- and 30-year old open problems.

Today we congratulate them on their achievement and describe part of how their new result works.
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Transcomputational Problems

April 30, 2015


Problems beyond brute force search

Bremermann
Cropped from Wikipedia source

Hans-Joachim Bremermann was a mathematician and biophysicist. He is famous for a limit on computation, Bremermann’s limit, which is the maximum computational speed of a self-contained system in the material universe.

Today Ken and I wish to talk about the limit and why it is not a limit.
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The Anti-Pigeonhole Conjecture

April 26, 2015


A conjecture about faculty behavior

rdkibzwang
“Dr. Kibzwang” source

Colin Potts is Vice Provost for Undergraduate Education at Georgia Tech. His job includes being a member of the President’s Cabinet—our president, not the real one—and he is charged with academic policies and changes to such policies. He is also a College of Computing colleague and fellow chess fan.

Today I want to state a conjecture about the behavior of faculty that arose when Tech tried to change a policy.
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Case Against Cases

April 22, 2015


How to avoid too many cases at least some of the time

Unknown

Theon of Alexandria was history’s main editor of Euclid’s Elements.

Today I want to talk about case analysis proofs.
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Kinds of Continuity

April 15, 2015


Congratulations to John Nash and Louis Nirenberg on the 2015 Abel Prize

NashNirenberg
Combined from src1, src2.

John Nash and Louis Nirenberg have jointly won the 2015 Abel Prize for their work on partial differential equations (PDEs). They did not write any joint papers, but Nirenberg evidently got Nash excited about David Hilbert’s 19th problem during Nash’s frequent visits to New York University’s Courant Institute in the mid-1950s. Nash in return stimulated Nirenberg by his verbal approach of barraging a problem with off-kilter ideas. The Norwegian Academy of Sciences and Letters recognized their ‘great influence on each other’ in its prize announcement.

Today we congratulate both men on their joint achievement.
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