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MATS531 MA2: Bernoulli Convolutions (JSS25), 2 ECTS [home page]

Department of Mathematics and Statistics

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You cannot register for the course because the course has expired.
The registration deadline for this course passed 30.4.15 at 23:59.

General information

Home page: http://www.jyu.fi/summerschool
Begins - ends: 10.8.15 - 14.8.15
Registration period: 1.2.15 at 0:00 - 30.4.15 at 23:59
The registration may be cancelled before 25.6.2015 at 00:00.
Instructor(s): Antti Käenmäki
Credits: 2 ECTS cr.
Languages: language(s) of instruction: English; completion language(s): English
Registered: 31
Organisations:Department of Mathematics and Statistics (MATHS), Faculty of Mathematics and Science (SCI), Jyväskylä Summer School (JSS), Mathematics (MAT)
Current events:
  • Lecturer: Prof. Pablo Shmerkin (Torcuato Di Tella University, Buenos Aires, Argentina) 
  • The course is a part of the 25th international Jyväskylä Summer School programme.

Bernoulli convolutions are a family of natural self-similar measures on the real line. Their study was pioneered by a young Paul Erdös 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 Erdös 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.


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.

Modes of study:

Obligatory attendance at lectures, and completing the exercises.

Completion mode:


Course workload:

10 h lectures (2 x 45 min/day, and consultation/day)

[Limit information on study groups]

Lecture [group details and registration]

Lecture [group details and registration]; registered 31, maximum 200
reg.time: 1.2.2015 00:00 - 30.4.2015 23:59
 LocationWeekDayDateAtSupervisorFurther informationURITapahtuman tiedot
1MaD 20233Mo10.8.201510:00-12:00KäenmäkiTapahtuman tiedot
2MaD 20233Tu11.8.201510:00-12:00KäenmäkiTapahtuman tiedot
3MaD 20233Wed12.8.201510:00-12:00KäenmäkiTapahtuman tiedot
4MaD 20233Th13.8.201510:00-12:00KäenmäkiTapahtuman tiedot
5MaD 20233Fr14.8.201510:00-12:00KäenmäkiTapahtuman tiedot