TAU What-Is Seminar

Next lecture's time & location: Wednesday, 10:30 - 13:00 -- Schreiber 210
If you wish to lecture: peleg.michaeli@math.tau.ac.il


Pay attention! The first lecture will be held in Neiman Library, room 107.
Pay attention! The first lecture will be given on Tuesday, 13:10-14:30.


When Who Theme Abstract
29/11/11 Dror Speiser What are Elliptic Curves? It started with trying to calculate arc lengths on ellipses. These calculations introduced integrals never seen before -- the elliptic integrals. They had the disturbing knack to be impossibly reducible to known integrals. But these integrals also had a geometric interpretation. This geometry, not as simple as that of an ellipse, but not as complex as that of a 10-dimensional lie group underlying our universe, was quickly recognized as fundamental.
Over two hundred years later, these so-called elliptic curves, have justly made a name for them, most famously in the solution of Fermat's last theorem, and most currently in modern day cryptography.
The lecture will touch on the calculus, geometry, arithmetic, and computability of elliptic curves.
15/12/11 Yaniv Ganor What is the Borsuk-Ulam Theorem? The Borsuk-Ulam Theorem states that every continuous map S^n -> R^n maps some pair of antipodal points to the same point. It is a theorem similar in spirit to the Brouwer fixed point theorem, and in fact implies it.
In this lecture we will see a relatively elementary proof, and corollaries such as the Ham Sandwich theorem, as well as some applications to combinatorics.
19/1/12 Nattalie Tamam What are Sieve Methods? Sieve methods are a set of techniques meant to measure the size of "sieved" sequences, that is, sequences from which a subsequence has been removed. These are common methods for finding upper bounds on the sizes of certain sets.
In this talk we will present two methods: Erastosthenes' method, which is basic, and Selberg's method, which is an improvement of Erastosthenes'. We will also discuss some applications, such as bounds on the amount of primes and on the amount of twin primes up to a given natural number n.
20/3/12 Dudu Lagziel What is Regret-Free Decision Making? The term regret has a simple interpretation, both in real life and in game theory: it is the amount of dissatisfaction a person might have about his past acts and behavior. Regret-free or having no-regret means that the decision maker (DM) did the best he could, in the sense that his past performance is not bluntly inferior to the performance of some pre-specified alternative strategies. This assessment in retrospect is especially significant when the decision problem is repeated over and over again.
Is it even possible to reach this state? If so, under which conditions? What is the significance of information being delayed in terms of having no-regret? In this talk we will discuss these issues through a very unrealistic betting game in a much non existent casino.
18/4/12 Uri Grupel What is Measure Concentration? In this talk I will present some phenomena occuring in high dimension, namely, in R^n when n tends to infinity. We will talk briefly about measure concentration in general and focus on two of its beautiful manifestations. The first is Sudakov's theorem, which gives us a new criterion for a random vector to have Gaussian marginals (namely, that for a random vector X and a unit vector \theta, the scalar product <X,θ> is "almost" Gaussian). The second is the Central Limit Theorem for convex sets (following B. Klartag's proof), which states that a random vector X distributed uniformly on a convex set K has "almost" Gaussian marginals. The proof relies on Sudakov's theorem.
We will see a sketch of the proofs of both theorems. No prior knowledge is needed (though some steps will be left without proof).
2/5/12 Nadav Yesha What is Uniform Distribution Modulo 1? For an irrational alpha, what can we say about the sequence of the fractional parts {n*alpha} ? Is it dense in the interval [0,1)? How is it distributed there? And what about the sequence {n^2*alpha} ? The theory of uniform distribution modulo 1 addresses such questions. We will define what it means to be uniformly distributed mod 1, and explain Weyl's criterion, discrepancy, the Erdős-Turan inequality and some examples.
16/5/12 Konstantin Kliakhandler TBA TBA.