Conference: Manifolds and Groups: Towers of Covers; September 7th ‐ September 12th, 2015, Ventotene, Italy

Overview of the conference The scope of the conference is to strengthen the already existing knowledge of the relationship between 3-manifold theory, topology, probability theory, and analytic group theory, while expanding it in directly related areas of research that recently came to the forefront of the worldwide mathematical scenery. We intend to reinforce the importance of the scienti�c cooperation between USA, Italy, Switzerland and Israel. To make this point, there is nothing as good as a high quality conference organized in full cooperation between these countries, where the scienti�c goals prevail over all political and economic considerations. We plan to have the following structure of the conference. It is our experience that conferences with some instructional component attract a much wider audience. In this spirit we chose to have part of the conference devoted to three mini-courses, taught by experts known also for their ability to give enlightening talks and for being very approachable. In parallel to the minicourses, there will be research talks. The speakers however will be prompted by the organizers to aim their talks at a knowledgeable but not necessarily specialized audience. The choice of the topics of the minicourses was made in the spirit of the conference, namely by building on existing knowledge and branching into new and important directions. The focus of this years minicourses is on Towers of covers and applications. The young participants, such as graduate students and postdocs, will be supported. We aim to encourage female participants and minorities. Intelectual Merit A central impact of this proposal is through its educational goals. The aim of the conference is to bring experts in the group theory and geometry together. Several mini courses will be given. The conference is aimed to bring experts and young participants together, give an opportunity for discussions on the modern state of �eld and set up collaborations. Broader Impacts As one of the broader impacts of the conference is to build up a strong international collaboration between several participating countries. There are several grant agencies involved in the organization of the conference, Israel, Switzerland, Italy, and hopefully USA. The support will allow to bring young participants and postdocs to the conference. The interaction of students with experts during the conference will be encouraged at many levels. During the conference we also to increase participation of female students and experts. The large amount of participants (which we saw on the previous conference) will allow us to support the diversity in more flexible way.