About the lecturer: Dennis Gaitsgory is among the leading mathematicians of today, whose work centers around the geometric Langlands program. In 1968 Langlands formulated a series of conjectures connecting number theory, modular functions and representation theory. Advanced methods coming from algebraic geometry have allowed for the recent breakthroughs in the geometric version of Lang-lands conjectures, which also has deep connections with quantum field theory. The beginning phase in the study of geometric Langlands correspondence was aimed at proving a specific construction of automorphic forms, culminating in a paper by E. Frenkel, D. Gaitsgory and K. Vilonen, published in the Journal of American Mathematical Society in 2002, and a separate 2004 paper published in the Annals of Mathematics. In the second phase the emphasis shifted to-wards proving a conjecture of Beilinson and Drinfeld regarding the complete equivalence of data coming from arithmetic and automorphic sides. This was finally achieved twenty years later by a group of young mathematicians led by Gaitsgory (Arinkin, Beraldo, Campbell, Chen, Faergeman, Lin, Raskin and Rozenblyum). Gaitsgory received his doctorate from Tel Aviv University (Israel), where he studied under Joseph Bernstein. Prior to his current position as a director at the Max Planck Institute for Mathematics in Bonn, he was a professor at Harvard University and Israel Gelfand Chair at IHES. He has been awarded the prize of the European Mathematical Society and the Chevalley prize in Lie theory for his work. He is a member of the National Academy of Sciences and has mentored 12 PhD students. As a part of his ongoing efforts in bringing more visibility to the geometric Langlands program, he coauthored a 1425-page book together with J. Lurie and N. Rozenblyum.