### Çetin Kaya Koç

Shared publicly -Time is the indefinite continued progression of existence and events that occur in apparently irreversible succession from the past through the present to the future.

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Start a hangout

Çetin Kaya Koç

Works at University of California Santa Barbara

Lives in Santa Barbara, California

230 followers|36,200 views

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Educate your neighborhood trumpies -- at least try

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Nice!

Here is the kit for my recent graph theory project:

Math for eight-year-olds: graph theory for kids!

http://jdh.hamkins.org/math-for-eight-year-olds/

Print out to double-sided, and then fold each page in half. Place the folded pages one after the other (not nested) inside the cover page.

Math for eight-year-olds: graph theory for kids!

http://jdh.hamkins.org/math-for-eight-year-olds/

Print out to double-sided, and then fold each page in half. Place the folded pages one after the other (not nested) inside the cover page.

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HAYIRRRRRRRRR!!!!!

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In his circles

230 people

Any one knows what is this ?

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This needs to stop. What a waste.

#Bitcoin transactions could consume as much #energy as Denmark by the year 2020 http://boingboing.net/2016/03/31/projection-by-2020-bitcoin-t.html

The numbers in this study are very back-of-the-envelope and assume a worst case: widespread adoption of Bitcoin and not much improvement in Bitcoin mining activity, along with long replacement cycl…

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I'm on the editorial board of Combinatorica. Whether I should be is another matter, since it is a journal owned by Springer, one of the big commercial publishers. But I am, and as a result I have a free subscription to the journal. Today I found the latest issue in my pigeonhole, and the last paper in the issue was a paper by Csaba Tóth, entitled, "The Szemerédi-Trotter theorem in the complex plane."

This paper is remarkable for two reasons. One, which provokes this post, is that at the beginning of the paper it says, "Received December 1999, Revised May 16 2014." So the paper is coming out over 15 years after it was submitted. Doubtless this isn't a record, but it's still a pretty big gap. I noticed it because my first reaction on seeing the title was, "But I thought this had been done a long time ago."

The other reason is the result itself. The Szemerédi-Trotter theorem states that if you have n points and m lines in the plane, then the number of incidences (that is, pairs (P,L) where P is a point in your collection, L is a line in your collection, and P is a point in L) is at most C(n + m + n^{2/3}m^{2/3}). This slightly curious looking bound is best possible up to the constant C and is more natural than it looks.

The known proofs of the theorem relied heavily on the topological properties of the plane, which meant that it was far from straightforward to generalize the result to lines and points in the complex plane (by which I mean C^2 and not C). Indeed, it was an open problem to do so, and that was what Tóth solved.

If you're feeling ambitious, there is also a lovely conjecture in the paper. Define a d-flat in R^{2d} to be an affine subspace of dimension d. Suppose now that you have n points and m d-flats with the property that no two of the d-flats intersect in more than a point. Is it the case that the number of incidences is at most C(n + m + n^{2/3}m^{2/3})? The constant C is allowed to depend on the dimension d but not on anything else. Note that even for d=2 this would be a new result, since Tóth's theorem is the special case where the d-flats are complex lines.

I should say that I haven't checked whether there has been any progress on this conjecture, so I don't guarantee that it is open. If anyone knows about its status, it would be great if you could comment below.

#spnetwork DOI: 10.1007/s00493-014-2686-2

This paper is remarkable for two reasons. One, which provokes this post, is that at the beginning of the paper it says, "Received December 1999, Revised May 16 2014." So the paper is coming out over 15 years after it was submitted. Doubtless this isn't a record, but it's still a pretty big gap. I noticed it because my first reaction on seeing the title was, "But I thought this had been done a long time ago."

The other reason is the result itself. The Szemerédi-Trotter theorem states that if you have n points and m lines in the plane, then the number of incidences (that is, pairs (P,L) where P is a point in your collection, L is a line in your collection, and P is a point in L) is at most C(n + m + n^{2/3}m^{2/3}). This slightly curious looking bound is best possible up to the constant C and is more natural than it looks.

The known proofs of the theorem relied heavily on the topological properties of the plane, which meant that it was far from straightforward to generalize the result to lines and points in the complex plane (by which I mean C^2 and not C). Indeed, it was an open problem to do so, and that was what Tóth solved.

If you're feeling ambitious, there is also a lovely conjecture in the paper. Define a d-flat in R^{2d} to be an affine subspace of dimension d. Suppose now that you have n points and m d-flats with the property that no two of the d-flats intersect in more than a point. Is it the case that the number of incidences is at most C(n + m + n^{2/3}m^{2/3})? The constant C is allowed to depend on the dimension d but not on anything else. Note that even for d=2 this would be a new result, since Tóth's theorem is the special case where the d-flats are complex lines.

I should say that I haven't checked whether there has been any progress on this conjecture, so I don't guarantee that it is open. If anyone knows about its status, it would be great if you could comment below.

#spnetwork DOI: 10.1007/s00493-014-2686-2

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The Riemann Hypothesis is one of the great unsolved problems of mathematics and the reward of $1000000 of Clay Mathematics Institute prize money awaits the person who solves it. But-with or without money-its resolution is crucial for our understanding of the nature of numbers.

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A few hundred meters before the Mount Ararat proper summit ..

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230 people

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Santa Barbara, California

Previously

Istanbul, Turkey

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Professor

Employment

- University of California Santa BarbaraResearch Professor, 2008 - present
- Claveo SoftwareCEO, 2010 - 2013
- CryptocodeCEO, 2003

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Near the Univ of Siena and one of the liveliest Siena streets with restaurants and stores. The host and staff are relaxed and helpful. I stay here every time I come to unisi <3

Public - a week ago

reviewed a week ago

Have ben at Le Logge every time I come to Siena and always the best

Public - 2 weeks ago

reviewed 2 weeks ago