Classical analysis and its applications 7,5 credit

Last day for handing in HW is Jan 15, 2018.

Last day for finalizing the course is January 21, 2018.

At this day we need report from each participants for their final grading of handin HW from others.

Course starts in Fall 2017,

Mondays 13:15--15:00

First meeting day:

Monday Sept. 4, 13:15--15:00

Lecture room Lindstedtsv. 22, room F11

Course leaders:

Danijela Damianovic (KTH)

Henrik Shahgholian (KTH)

Course format: Lectures

Examination:

1) Homework

2)presentation 2h of a topic suggested by course leaders. For PhD students the topic should not be close to their research area.

Literature:

1)Functional Analysis:

2)Geom. measure theory:

Pertti Mattila: Geometry of sets and measures in Euclidean spaces.

3)Ergodic Theory:

Peter Walters: An introduction to Ergodic theory

4)Probabilistic Techniques:

5)Harmonic Analysis on Groups:

Katznelson: An introduction to Harmonic Analysis.

Folland: A course in abstract harmonic analysis

6)Sobolev Spaces:
A.Bressan: Lecture Notes on Sobolev Spaces

R. Adams, J.F. Fournier: Sobolev Spaces

Classical analysis and its applications 7,5 credit

The course is intended for all PhD students, and will encompass many areas in mathematics at a reasonable level.

The core idea is to see how Analysis can be applied in different branches of mathematics.

Topics to be covered include:

1)Functional Analysis: Notes

2) Geometric Measure Theory: Notes

3)Ergodic Theory: Notes

4) Probabilistic Techniques: Notes

5) Harmonic Analysis on Groups: Notes

6)Sobolev Spaces: Notes

Presentations:

2 presentation at each occasion, 80 minutes each, with 10 min break

* = Confirmed

Nov. 13

* Julian Mauersberger

C* algebras, Gelfand theory,Spectral measures

* Sergi Arias

Distributions and elliptic operators

Nov. 20

Johan Ericsson

Ergodic theory with applications to additive combinatorics

* Samuel Fromm

Schrödinger Equation/ Selfadjoint Operators/ Semigroups/ Functional Calculus.

Nov. 27

* Boris Petkovic

Nilpotent group representations

* Jeroen Hekking

Haar measure

Dec. 4

* Phillipe Moreillon

Not decided

* Tomas Berggren

stochastic diff. eq.

Dec. 11

* Scott Mason

Representation theory for the Lie algebra sl(2,C), sl(3,C)

* Oliver Gäfvert

SL(2, R) representations