Monthly Archives: November 2009

Midrasha Mathematicae: The Mathematics of Oded Schramm

Update: The midrasha is taking place now. After 3 and a half school-days we have a break untill sunday. Clicking on the poster above will lead you the webpage of the event and to  a link to an online broadcast of the lectures.

Our Winter school on Probability and Geometry is approaching. It will take place at the Hebrew University of Jerusalem on December 15-23. The deadline for application is November 25, 2009; by all means, apply! it will be a very nice event. We got additional support from The Clay Mathematics Institute and from Microsoft Research. Financial support (local expences, and, in some cases, partial support for the travel) may be available.

The poster gives the updated list of confirmed speaker. (There may be 1-2 additional speakers that did not confirm yet.)

Here is the link to the site of the school.  I will update this page regarding program and schedule. UPDATE (Preliminary program)

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Math Overflow

So I did try mathoverflow a bit and it is a cool site. Over the few days I spent there I gained 593 reputation points, and no less than 9 bronze badges. The first answer I proposed gave me a badge as “teacher”,  and the first question I asked gave me a badge as “student”. In fact, if I will only reveil my age I would gain also a badge as “autobiographer”.

Indeed, mathoverflow is ran by an energetic and impressive group of very (very very) young people (more precisely, very very young men).  Here is the link to the 35 users with highest reputations.

Update: Well, I got a little addicted and visited quite a bit this nice site.  Among other things, I tried to promote my fundamental examples question. Basic examples can give a quick invitation to wide areas of mathematics. (Maybe to most areas, I find it hard to think about a counterexample.) Overall, there are not that many basic examples and I think there will be a consensus about most of them so lists of different mathematicians will not be so different. More examples of important examples are welcome. 

In my profile you can find there the six questions that I asked and the 10 answers or so that I offered (to other questions).

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Test Your Intuition (10): How Does “Random Noise” Look

This is a bit unusual post in the “test your intuition” corner as the problem is not entirely formal.  

How does random noise in the digital world typically look?

Suppose you have a memory of n bits, or a memory based on a larger r-letters alphabet, and suppose that a “random noise” hits the memory in such a way that the probability of each bit being affected is t.

What will be the typical behavior of such a random digital noise? Part of the question is to define “random noise” in the best way possible, and then answer it for this definition.

In particular, Will the “random noise” typically behave in a way which is close to be independent on the different bits? or will it be highly correlated? or pehaps the answer depends on the size of the alphabet and the value of t?

The source of this question is an easy fact about quantum memory which asserts that if you consider a random noise operation acting on a quantum memory with n qubits, and if the probability that every qubit is damaged is a tiny real number t, then typically the noise  has the following form: with large probability nothing happens and with tiny probability (a constant times t) a large fraction of qubits are harmed.

 I made one try for the digital (binary) question but I am not sure at all that it is the “correct” definition for what “random noise” is.

(Maybe I should try to ask the problem also on “math overflow“. See also here, here and here for what math overflow is.)

Update:  over “mathoverflow” Greg Kuperberg made an appealing argument that for the correct notion of random noise the behavior in the classical case is similar to that of the quantum case.

Test Your Intuition #9 (answer to #9),  #8  (answer),   #7,   #6,  #5,  #4 (answer), #3 (answer), #2#1.

Home

I just came back home after two months in the US, mainly in and around New Haven and also in IPAM (Los Angeles) and Texas A&M. I heard all sort of wonderful things (but some sad news as well). I met a lot of friends and quite a few new people (including quite a few fellow bloggers). I was a bit slow on blogging but I do plan to catch up.

I need help from technically savvy readers for the following Audio project. Continue reading