The EMS lecturer 2013, Tamar Ziegler (Technion), will give a series of 3 lectures at the congress. Prof. Ziegler is a specialist in ergodic theory and in number theory. She has collaborated with, amongst others, Vitaly Bergelson, Ben Green and Terence Tao.

**Dynamics and prime solutions to linear equations**

In the first two talks I will describe some of the ideas behind the recent developments in additive number theory and ergodic theory leading to the proof of Hardy-Littlewood type estimates for the number of prime solutions to systems of linear equations of finite complexity.

**On the Mobius randomness principle**

The Mobius function is one of the most important arithmetic functions. There is a vague yet well known principle regarding its randomness properties called the "Mobius randomness law", stating that the Mobius function should be orthogonal to any "structured" sequence. A few years ago P. Sarnak suggested a far reaching conjecture as a possible formalization of this principle. Sarnak conjectured that "structured sequences" should correspond to sequences arising from deterministic dynamical systems. We will discuss this conjecture as well as some recent progress establishing several special cases.

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Last update: 2019-10-17

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