We will study geometric properties of fractal sets and measures in Euclidean spaces. Topics include:
- Hausdorff measures and dimension
- Frostman's lemma, Riesz energies and capacities
- Fourier transforms of measures
- Marstrand's projection theorem
- Dimension estimates for distance sets
- Kakeya sets and estimates for their dimension
- Rectifiable and unrectifiable sets
- Besicovitch's projection theorem
- Marstrand's slice theorem
- Self-similar sets

Lectures on Mondays and Wednesdays. Return exercises in writing to Giovanni Canarecci.

News: Change of time/class in the second period: On Mondays, lectures will be 10.15-12.00 in class C220.

Enrol
13.8.2018 at 09:00 - 13.12.2018 at 23:59

Messages

Eino Rossi

Published, 30.10.2018 at 12:02

GMT kurssin keskiviikon 31.10 luennot on myös peruttu (samasta syystä kun maanantain 29.10 luennot).

Timetable

Here is the course’s teaching schedule. Check the description for possible other schedules.

DateTimeLocation
Mon 3.9.2018
12:00 - 14:00
Wed 5.9.2018
10:00 - 12:00
Thu 6.9.2018
12:00 - 14:00
Mon 10.9.2018
12:00 - 14:00
Wed 12.9.2018
10:00 - 12:00
Thu 13.9.2018
12:00 - 14:00
Mon 17.9.2018
12:00 - 14:00
Wed 19.9.2018
10:00 - 12:00
Thu 20.9.2018
12:00 - 14:00
Mon 24.9.2018
12:00 - 14:00
Wed 26.9.2018
10:00 - 12:00
Thu 27.9.2018
12:00 - 14:00
Mon 1.10.2018
12:00 - 14:00
Wed 3.10.2018
10:00 - 12:00
Thu 4.10.2018
12:00 - 14:00
Mon 8.10.2018
12:00 - 14:00
Wed 10.10.2018
10:00 - 12:00
Thu 11.10.2018
12:00 - 14:00
Mon 15.10.2018
12:00 - 14:00
Wed 17.10.2018
10:00 - 12:00
Thu 18.10.2018
12:00 - 14:00
Mon 29.10.2018
10:00 - 12:00
Wed 31.10.2018
10:00 - 12:00
Thu 1.11.2018
12:00 - 14:00
Mon 5.11.2018
10:00 - 12:00
Wed 7.11.2018
10:00 - 12:00
Thu 8.11.2018
12:00 - 14:00
Mon 12.11.2018
10:00 - 12:00
Wed 14.11.2018
10:00 - 12:00
Thu 15.11.2018
12:00 - 14:00
Mon 19.11.2018
10:00 - 12:00
Wed 21.11.2018
10:00 - 12:00
Thu 22.11.2018
12:00 - 14:00
Mon 26.11.2018
10:00 - 12:00
Wed 28.11.2018
10:00 - 12:00
Thu 29.11.2018
12:00 - 14:00
Wed 5.12.2018
10:00 - 12:00
Mon 10.12.2018
10:00 - 12:00
Wed 12.12.2018
10:00 - 12:00
Thu 13.12.2018
12:00 - 14:00

Material

Description

Optional course.

Master's Programme in Mathematics and Statistics is responsible for the course.

Belongs to the Mathematics and Applied mathematics module.

The course is available to students from other degree programmes.

Measure and integral, Real analysis I

Deep knowledge on measure theory

Recommended time/stage of studies for completion: 3rd, 4th or 5th year

Term/teaching period when the course will be offered: varying

The actual content may vary, e.g. fractals, rectifiability, tangent spaces and measures. More detailed info on the course page.

Recommended: Mattila: Geometry of sets and measures in Euclidean spaces. Fractals and rectifiability

Lectures and exercise classes

Exam and excercises, Course will be graded with grades 1-5

Exam, other methods will be described later