**Course 1:** *“The Geometry of Fractal Sets from the Perspective of Fourier Analysis and Projection Theory”,* Krystal TAYLOR (Ohio State University, USA)
**Course 2:** *“Applications of Spectral Graph Theory to problems in Combinatorics and Number Theory”*, Jonathan PAKIANATHAN (University of Rochester, USA)
**Course 3:** *“Lozenge tilings via algebraic combinatorics”*, Greta PANOVA (University of Pennsylvania, USA)
**Course 4:** *“Determinantal point processes”*, Alexander BUFETOV (Aix Marseille, France)
**Course 5:** *“Geometric Configurations and Sets of Positive Upper Density”*, Neil LYALL (University of Georgia, USA)
**Course 6:** *“An interplay between Fuglede Conjecture, tiling and Gabor analysis”*, Azita MAYELI (City University of New York, USA)
**Course 7:** *“Finite point configuration and discrete Painlevé Equations”*, Anton Dzhamay (University of Northern Colorado)
**Abstract:** The aim of this course is to give an introduction into the geometric approach to the theory of discrete Painlevé equations, following the approach of Japanese school of M. Noumi, H. Sakai, Y. Yamada, and the others. Discrete Painlevé equations are certain non-linear non-autonomous second-order recurrence relations that originally appeared as discrete analogues of differential Painlevé equations. Such recurrences occur in many important problems in Mathematics and Mathematical Physics, in particular in questions related to the theory of discrete orthogonal polynomials and to computation of gap probabilities in Random Matrix Theory. Geometrically, each family of discrete Painlevé equations correspond to a particular configuration type of eight points on a complex projective plane; such configurations are described by affine Dynkin diagrams. Associated to this data is a (family of) rational algebraic surfaces and a birational representation of an affine Weyl symmetry group acting on this family; discrete Painlevé equation corresponds to translational elements of this group. We give an introduction to this geometric approach and explain how it can be used to study various applied problems.