Bernoulli convolutions are a family of natural self-similar measures on the real line. Their study was pioneered by a young Paul Erd%C3%B6s in 1939, and many challenging problems remain to this day. The course will introduce the main properties of Bernoulli convolutions, especially in regards to their absolute continuity, following the historic development from Erd%C3%B6s to very recent results of the lecturer (and collaborators). Along the way we will introduce relevant fractal-geometric concepts, and briefly survey the connection of Bernoulli convolutions to other areas of mathematics, and beyond.

Course leader
Lecturer: Prof. Pablo Shmerkin (Torcuato Di Tella University, Buenos Aires, Argentina) Coordinator: Dr. Antti Kenmki (University of Jyvskyl, Finland)

Target group
The course is aimed at graduate students, but strong advanced undergraduate students with the appropriate background might find it suitable. The main prerequisite is measure theory. Knowledge of Hausdorff dimension and Fourier transform will be useful but will not be assumed. The Summer School annually offers courses for advanced master's students, graduate students, and post-docs in the various fields of science and information technology.

Course aim
The most important aims of the Summer School are to develop post-graduates scientific readiness and to offer students the possibility to study in a modern, scientific environment and to create connections to the international science community.

Credits info
2 ECTS Passing: Obligatory attendance at lectures, and completing the exercises.Grading: Pass/fail

Fee info
EUR 0: Participating the Summer School is free of charge, but student have to cover the costs of own travel, accommodation and meals at Jyvskyl.

Scholarships
The 25th Jyvskyl Summer School is not able to grant any Summer School students financial support. In order to ensure your participation, we recommend that you take steps to secure your own funding, for example, by turning first to your home institution

University of Jyv%C3%A4skyl%C3%A4
Address: Faculty of Mathematics and Science and Faculty of Information Technology, Jyv%C3%A4skyl%C3%A4 Summer School, Faculty of Mathematics and Science P.O.Box 35 (YK312), FIN-40014 University of Jyv%C3%A4skyl%C3%A4, Finland
Postal code: FIN-40014
City: Jyv%C3%A4skyl%C3%A4
Country: Finland
Website: http://www.jyu.fi/summerschool
E-mail: jss@jyu.fi
Phone: +358505818351