The first purpose of our school is to introduce young researchers to the geometric Langlands program in its most recent categorical version. The latter was formulated in the paper by Arinkin, Gaitsgory, "Singular support of coherent sheaves and the geometric Langlands conjecture". It provides a deep interrelation between derived algebraic geometry, geometric representation theory, theory of automorphic forms, and representation theory of p-adic groups. To this end, there will be 3 mini-courses by B. Toen, D. Arinkin, D. Ben-Zvi oriented to young researchers. Besides, there will be research talks on the recent advances in the geometric Langlands program by leading specialits in the field.

Geometric Langlands is a very active area of research in mathematics and physics. Important breakthrough developments have occurred recently in this field, in particular, B-C. Ngo's proof of the fundamental lemma (which was one of the central problems in the classical Langlands program) via geometric methods. Another major development was a deep interconnection established between the geometric Langlands program and four-dimensional gauge theory due to Witten, Kapustin and others. (Conformal field theories, the AdS/CFT correspondence, and integrability are some of the most active areas in modern theoretical physics). There are also continously developing interactions with other areas of representation theory, number theory and algebraic geometry, such as affine and double affine Hecke algebras and their relations to integrable models, geometry of various homogeneous spaces, Knizhnik-Zamolodchikov equations, Verlinde algebras, Gromov-Witten invariants of flag varieties, categorification and canonical bases in representation theory, quantization of certain algebraic varieties, vertex algebras, etc. We think that this unifying structure of the geometric Langlands program would be a motivation to learn it for young researchers.

Geometric Langlands is a very active area of research in mathematics and physics. Important breakthrough developments have occurred recently in this field, in particular, B-C. Ngo's proof of the fundamental lemma (which was one of the central problems in the classical Langlands program) via geometric methods. Another major development was a deep interconnection established between the geometric Langlands program and four-dimensional gauge theory due to Witten, Kapustin and others. (Conformal field theories, the AdS/CFT correspondence, and integrability are some of the most active areas in modern theoretical physics). There are also continously developing interactions with other areas of representation theory, number theory and algebraic geometry, such as affine and double affine Hecke algebras and their relations to integrable models, geometry of various homogeneous spaces, Knizhnik-Zamolodchikov equations, Verlinde algebras, Gromov-Witten invariants of flag varieties, categorification and canonical bases in representation theory, quantization of certain algebraic varieties, vertex algebras, etc. We think that this unifying structure of the geometric Langlands program would be a motivation to learn it for young researchers.