### [RG # 137] Arithmetic & Dynamics

##### Sept. 15, 2013 - February 15, 2014

Organizers:

Peter Sarnak (Princeton University)

Shahar Mozes (The Hebrew University)

Elon Lindenstrauss (The Hebrew University)

Arithmetic has its roots in antiquity, in the attempts of ancient civilizations to understand interger numbers, and in particular integer (and rational) solutions of equations. Dynamics is a younger mathematical discipline, though still with substantial historical roots, one of them being Poincare's attempt to understand celestial mechanics - the motion of planets, and even of the earth-moon-sun trio, where a closed-form solution cannot be written down.

One particular type of question regarding integer and rational points is regarding the distribution of these points e.g. in the space of all solutions by real numbers. When these equations have a large group of symmetries, a strong bond between the arithmetic and a special kind of dynamics (known as homogenous dynamics) ensues.