The role of sex?

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Christos Papadimitriou has a joint paper with Adi Livnat, Aviad Rubinstein, Gregory Valiant, and Andrew Wan that will appear soon at FOCS 2014. The conference is October 19–21 in Philadelphia, with workshops and tutorials on the 18th. Here are the accepted papers, several others of which interest me a lot. The last parallel session on Monday afternoon before my own award lecture has three of them in one room, including a paper co-authored by my recent student Danupon Nangonkai, and three on quantum—it would be nice to be in a quantum superposition and attend both sessions.

Today Ken and I want to discuss their paper, which is on complexity-theoretic aspects of evolution.

Congratulating Dick on the 2014 Knuth Prize

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Dick Lipton is of course the founder and driving writer of this weblog. He is also a computer scientist with a great record of pathbreaking research. The latter has just been recognized, I am delighted and proud to say, with the award of the 2014 Knuth Prize. The prize is awarded jointly by the ACM Special Interest Group on Algorithms and Computation Theory and the IEEE Technical Committee on the Mathematical Foundations of Computing, and was instituted in 1996, shortly after the formal retirement of the great—and very much active—Donald Knuth.

Today I am glad to give my congratulations in public, and also my thanks for a wonderful and long association.

Things we did not know

 Ulam holding a strange device

Stanislaw Ulam was a Polish-American mathematician whose work spanned many areas of both continuous and discrete mathematics. He did pioneering research in chaos theory and Monte Carlo algorithms, and also invented the concept of a measurable cardinal in set theory. His essential modification of Edward Teller’s original H-bomb design is used by nearly all the world’s thermonuclear weapons, while he co-originated the Graph Reconstruction conjecture. His name is also associated with the equally notorious 3n+1 conjecture. Thus he was involved in some strange corners of math.

Today Ken and I want to talk about some strange facts observed by Ulam and others that we did not know or fully appreciate.

A reversal question

Freeman Dyson celebrated his ${\text{90}^{th}}$ birthday last December. He is world famous for his work in both physics and mathematics. Dyson has proved, in work that was joint with Andrew Lenard and independent of two others, that the main reason a stack of children’s blocks doesn’t coalesce into pulp is the exclusion principle of quantum mechanics opposing gravity. He shaved a factor of ${\sqrt{2}}$ off the exponent for bounds on rational approximation of algebraic irrationals, before the result was given its best-known form by Klaus Roth. He has received many honors—recently, in 2012, he was awarded the Henri Poincaré Prize at the meeting of the International Mathematical Physics Congress.

Today Ken and I want to talk about one of his relatively recent ideas, which is more mathematics than physics. Perhaps even more theory than mathematics.

See a number, make a set

Henning Bruhn and Oliver Schaudt are mathematicians or computer scientists, or both. They are currently working in Germany, but wrote their survey on the Frankl Conjecture (FC) while working together in Paris. Schaudt is also known as an inventor of successful mathematical games.

Today Ken and I wish to talk about the Frankl conjecture and a principle of mathematics. Read more…

Some algorithmic tricks were first invented in complexity theory

Andrey Kolmogorov, Fred Hennie, Richard Stearns, and Walter Savitch are all famous separately; but they have something in common. Read on, and see.

How exceptions in theorems may affect their complexity

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Manjul Bhargava is a mathematician who just won one of the 2014 Fields Medals. We offer our congratulations on this achievement. He is an expert in number theory, which makes him special to us among Fields medalists. His Fields citation includes his doctoral work on a powerful reformulation and extension of Carl Gauss’s composition law for quadratic forms. He also proved a sense in which 290 is special to us among numbers, since we have been thinking recently about quadratic forms as tools in complexity theory.

Today we talk about his “290 Theorem” with Jonathan Hanke, which is quite accessible, and also raise complexity-related questions about this result. Read more…