Search Results for: erdos

Mathematics, Science, and Blogs

Michael Nielsen wrote a lovely essay entitled “Doing science online” about  mathematics, science,  and blogs. Michael’s primary example is a post over Terry Tao’s blog about the Navier-Stokes equation and he suggests blogs as a way of scaling up scientific conversation. Michael is writing … Continue reading

Posted in Blogging, What is Mathematics | Tagged , , , , | 5 Comments

Lior, Aryeh, and Michael

Three dear friends, colleagues, and teachers Lior Tzafriri, Aryeh Dvoretzky and Michael Maschler passed away last year. I want to tell you a little about their mathematics.  Lior Tzafriri (  1936-2008  )  Lior Tzafriri worked in functional analysis.

Posted in Obituary | Tagged , , | 8 Comments

Extremal Combinatorics IV: Shifting

  Compression   We describe now a nice proof technique called “shifting” or “compression” and mention a few more problems.   The Sauer-Shelah Lemma: Let . Recall that a family shatters a set if for every there is   such that … Continue reading

Posted in Combinatorics, Open problems | Tagged , | 4 Comments

Extremal Combinatorics III: Some Basic Theorems

. Shattering Let us return to extremal problems for families of sets and describe several basic theorems and basic open problems. In the next part we will discuss a nice proof technique called “shifting” or “compression.” The Sauer-Shelah (-Perles -Vapnik-Chervonenkis) Lemma: (Here we write .) … Continue reading

Posted in Combinatorics, Open problems | Tagged , | 7 Comments

Pushing Behrend Around

Erdos and Turan asked in 1936: What is the largest subset of {1,2,…,n} without a 3-term arithmetic progression? In 1946 Behrend found an example with  Now, sixty years later, Michael Elkin pushed the the factor from the denominator to the enumerator, … Continue reading

Posted in Combinatorics, Updates | Tagged , , | 10 Comments

Extremal Combinatorics I: Extremal Problems on Set Systems

The “basic notion seminar” is an initiative of David Kazhdan who joined HU math department  around 2000. People give series of lectures about basic mathematics (or not so basic at times). Usually, speakers do not talk about their own research and not even … Continue reading

Posted in Open problems | Tagged , , , , , | 10 Comments