Local Events, Turan’s Problem and Limits of Graphs and Hypergraphs

I will write a little about how hectic things are now here at HU, and make two (somewhat related) follow-ups on previous posts: Tell you about Turan’s problem, and about Balázs Szegedi’s lecture from Marburg dealing with limits of graphs and hypergraphs. 

Local Events

The second semester at HU started on Sunday, May 11th and it will run until August. This is due to the 3-months Israeli Professors’ strike at the beginning of the academic year. Issues regarding the strike and Israeli academics are quite interesting and we may come back to them. Let me make just one little remark: There is an initiative to transform Israeli universities to a more “market-based” structure. US universities and the new evaluation system in the UK are mentioned as examples, and the Australian academic reforms are often regarded as an act to follow. I was always quite negative about this initiative and skeptical even about the Australian example, and the following post by Terry Tao is telling regarding the Australian reforms. (See also the new blog mathematics in Australia.)

Thia semester I am teaching the basic course in combinatorics and a seminar in probabilistic combinatorics.

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 always about their field. I gave two lecture series, one about “computational complexity theory” a couple of years ago, and one about extremal combinatorics or Erdös-type combinatorics a few months ago, which later I expanded to a series of five+one talks at Yale. One talk was on  the Borsuk Conjecture,  which I will discuss separately, and five were titled: “Extremal Combinatorics: A working tool in mathematics and computer science.”  Let me try blogging about it. The first talk was devoted to extremal problems concerning systems of sets.

 

 Paul Erdös

 

1. Three warm up problems 

Here is how we move very quickly from very easy problems to very hard problems with a similar flavour.

Problem I: Let  N = {1,2, … , n } . What is the largest size of a family   of subsets of such that every two sets in have non empty intersection? (Such a family is called intersecting.)