Functional Analysis Seminar
Spring 2023

Harmonic Analysis


Organisers
Marcel de Jeu (mdejeu@math.leidenuniv.nl)
Bram Mesland (b.mesland@math.leidenuniv.nl)
Onno van Gaans (vangaans@math.leidenuniv.nl)

Contact
If you are interested, please contact Marcel de Jeu, Bram Mesland, or Onno van Gaans.

Topic
"Harmonic analysis" is generally used to denote a wide range of subjects that are all related to function spaces on groups or representations of groups. It goes back to Fourier, who introduced the series that carry his name, but it has evolved since then into an active and broad research area that connects to many other fields in mathematics. In this seminar, we aim to cover topics such as the Haar measure, the Fourier transform for locally compact abelian groups, the structure of such groups, representations of locally compact groups and their naturally associated algebras, the representation theory of compact groups, direct integrals, the Selberg trace formula, the Heisenberg group, and SL2(R). If time permits, we shall also venture into wavelets and p-adic numbers and adeles.

Intended for
Advanced MSc students, PhD students, postdocs, and faculty.

Prerequisites
Proficiency in the functional analytic language at the level corresponding to a solid `pass' for the national functional analysis course in the Mastermath programme. Although there are happy exceptions, an introductory course in functional analysis is usually not sufficient.

Literature
Anton Deitmar and Siegfried Echterhoff: Principles of Harmonic Analysis (2nd ed.), Springer, 2014.
Please note:
- the second edition that we use is really different from the first one;
- participants from institutes with the appropriate subscription to SpringerLink have free access to the PDF of the book, and can use the MyCopy option to purchase a softcover copy with a discount.

Venue
Room DM 0.13 in the Gorlaeus Building, commonly known as `the new building'. Entering the Gorlaeus Building goes via the entrance of the Huygens/Oort Building, after which an unexpected route via the LMUY Building has to be taken to reach the Gorlaeus Building itself. See the Science Campus map for more details. If you are not from Leiden (and perhaps also if you are), then this can be a challenge. At least for the first meeting on 10 February, we shall, therefore, leave as a group from office 218 in the Mathematical Institute in the Snellius Building. Please note that free parking is not possible on the premises, but that 600-700m further down Endegeesterstraatweg there are usuall some public spots available, free of charge.

The meetings are from 14.15-17.00 (at the latest) on the following Friday afternoons:
10 February
17 February
24 February
03 March
10 March
17 March
24 March
14 April
21 April
28 April
02 June
09 June
16 June

EC
6 EC for participation and taking care of one of the afternoons by delivering a lecture.

Grade
It is enevitable that some topics are more suitable for an attractive presentation than others, so, as in previous years, there will be no grades but simply a `pass'.

Please note
If you are a student, but not from Leiden, contact your study advisor or exam committee beforehand about the eligibility of this seminar for your own programme, in order to prevent unwanted surprises. If your institute should require this, then, although this is not the preferred method, a grade could be supplied instead of a `pass'.

Programme

TO BE ANNOUNCED.