Jan

27

Ergodic Theory with Benefits

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The Undergraduate Mathematics Society hosts their first talk of the semester this evening. Alex Blumenthal will be speaking about the applications of ergodic theory to additive number theory, plus some cool stuff about primes. Bwog also notes that there will be FREE FOOD from 7  in 508 Math before the talk at 7:30.

Full event details after the jump.

Applications of Ergodic Theory to Additive Number Theory — Alex Blumenthal

Under what conditions will a subset of the integers contain arithmetic progressions of arbitrary length? Szemeredi’s theorem provides a  partial answer to this question. In fact, as of 2004, we know that the  primes are such a subset, due to the theorem of Green and Tao.

In this talk, I will present an ergodic-theoretic proof of Szemeredi’s theorem, which is formally used to prove Green and Tao’s result. The  punchline is that ergodic theory, a field motivated by problems in  statistical mechanics, has something deep to say about number theory.  The talk will emphasize the transition from number theoretical  questions to the theory of dynamical systems. Along the way, I will  discuss several applications of ergodic theory to number theoretic  statements: examples include results from Weyl’s theory of exponential  sums, a simple proof of Van der Waerden’s theorem, and the deep results of Hindeman concerning the existence of IP-systems in subsets  of the integers of upper banach density.

I will assume no background in ergodic theory, but a basic  understanding of [point-set] topology (metrics, compactness) and set theory would be useful.

8 Comments

  1. frustrated  

    i don't understand anything after the jump

  2. Anonymous  

    lol @ humanities major

  3. WOW!  

    Get there early, it's sure to be packed!

  4. frsutrated 2  

    this event is for nErDS!!

  5. hmmm

    I guess the speaker must have some connections to "non-nerds" that previous speakers at the Undergraduate Math Society have lacked. They have these gatherings every week if I'm not mistaken...

  6. OMG  

    Ok, this is going to sound weird, and I'm not one to usually bwog comment but Alex Blumenthal is the absolute hottest math major I've ever met. I ran into him at a Potluck once last semester, and there he was baking cookies AND talking math. Not to give myself away, but as a female math major (we exist!), I swooned.

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