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.

Ilmoittaudu
13.8.2018 klo 09:00 - 13.12.2018 klo 23:59

Viestit

Eino Rossi

Julkaistu, 30.10.2018 klo 12:02

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

Aikataulu

Tästä osiosta löydät kurssin opetusaikataulun. Tarkista mahdolliset muut aikataulut kuvauksesta.

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

Materiaalit

Kuvaus

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