Friday August 22. Room 311. Starting time 16:00. Speaker: Oleg Karpenkov (Moscow--Leiden). Title: Lattice trigonometry. Abstract: In this talk we introduce a notion of lattice trigonometric functions of lattice angles in lattice geometry and study their basic properties. We show a necessary and sufficient condition for three angles to be the angles of some lattice triangle in terms of lattice tangents. This condition is a version of the Euclidean condition: three angles are the angles of some triangle iff their sum equals Pi. The condition for lattice angles implies a global condition for a complex projective toric surfaces --- http://pdmi.ras.ru/~lowdimma