The PI together with the team assembled for the project, consisting of three postdoctoral researchers and 1 PhD student, have obtained results on the topics outlined in the proposal. These results are documented in 9 mathematical articles, out of which 3 are already published in peer-reviewed international journal and 6 are submitted for publication. Team members have travelled to conferences and seminars around the world to collaborate and to disseminate the results of the project; invited expert guest to visit the Host Institution, collaborate and present talks on their results; co-organized two international workshops at the host institution
The most significant results of the project to date is a series of results showing that Aut(F_n), the automorphism group of the free group on n generators, has Kazhdan's property (T) for n from 5 to infinity. This has been a long-standing open question. Our methods make use of convex optimization through a recently invented method of establishing property (T).