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.

Anmäl dig
13.8.2018 kl. 09:00 - 13.12.2018 kl. 23:59

Meddelande

Eino Rossi

Publicerad, 30.10.2018 kl. 12:02

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

Tidsschema

I den här delen hittar du kursens tidsschema. Kontrollera eventuella andra tider i beskrivning.

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

Material

Beskrivning

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