The geometric Langlands conjecture

In the first meeting of this reading group, I will begin with an overview of the statement of the geometric Langlands conjecture. Then, following Arinkin and Gaitsgory, I will outline a strategy of the proof in the case of GL_n. Some ingredients of the proof are direct translations of number theoretic constructions, while others are specific to the geometric situation. No prior familiarity with the subject is assumed. However, a number of technical tools is necessary for both the statement and the proof; in this talk I intend to list these tools (to be explained in future talks) and motivate why they are essential.