On the work of Akshay Venkatesh

Number theory while one of the oldest subjects in mathematics, continues to be one of the most active areas of research. One reason for this is that it borrows from and contributes to many other fields, sometimes quite unexpectedly. Uncovering deeper number theoretic truths often involves advancing techniques across these disciplines resulting in new avenues of research and theories. Venkatesh's work fits squarely into this mold. His resolution and advancement of a number of long standing problems start with fundamental new insights connecting theories and have led to active research areas. He is both a problem solver and a theory builder of the highest caliber. Due to space limitation and the nature of this report, I have chosen to describe three examples of Venkatesh's works and end by simply listing a number of his other striking results. Also, in this brief description of some of the results I have omitted some technicalities and the reader should go to the references for precise statements.