## Public defence in Mathematics, M.Sc. (Tech) Kim MyyrylÃ¤inen June 6, 2024

28. May 2024

Functions of bounded mean oscillation (BMO) and Muckenhoupt weights are essential concepts in modern harmonic analysis. They are used to measure the oscillation of a function at respective scales and to distribute mass to the underlying space. The theory of BMO and Muckenhoupt weights is comprehensive and has many applications also in other fields of mathematics such as partial differential equations.

This thesis studies parabolic bounded mean oscillation and Muckenhoupt weights that are generalizations of the classical time-independent concepts. The objective of the study is to extend the classical theory of BMO and Muckenhoupt weights to the time-dependent parabolic setting. Parabolic BMO and Muckenhoupt weights arise from parabolic partial differential equations, in particular, a doubly nonlinear equation that models nonlinear diffusion. The doubly nonlinear equation is a generalization of the classical heat equation modelling heat conduction.

The results obtained in the thesis include various decay estimates for the oscillation of a function. We show weighted norm inequalities for a parabolic maximal function and obtain a complete theory for the limiting parabolic Muckenhoupt class including characterization and factorization results. The theory for the other endpoint class is also developed and several new characterizations and self-improving phenomena are discovered. The proofs of our results apply covering, chaining and decomposition techniques adapted to the parabolic geometry. In addition to the parabolic framework, other forms of oscillation are considered in the general context of metric measure spaces.

Thesis available for public display 10 days prior to the defence at: https://aaltodoc.aalto.fi/doc_public/eonly/riiputus/

Contact information: kim.myyrylainen@aalto.fi

## Camilla Hollanti elected as a member of Finnish Academy of Science and Letters

26. April 2024

The Finnish Academy of Science and Letters invites academics and scientists who have distinguished themselves in their own fields to become members. Membership of the Finnish Academy of Science and Letters, in common with membership of any other academy of science, is looked on as a considerable achievement in a person’s academic career.

One of the new members is professor of mathematics Camilla Hollanti. Hollanti leads a prominent research group on applications of algebra and number theory. The central topic of her research is to apply the methods of algebra and number theory to problems encountered in communication systems. Applications include wireless security and secure distributed computation.

The academy was founded in 1908 with the aims of promoting scientific research and acting as a bond between those engaged in advanced research.

It arranges meetings, discussions and educational events, in addition to producing scientific publications and issuing comments on topical issues pertaining research and researchers. The Academy of Science and Letters also distributes grants chiefly to young researchers.

## New hourly paid teachers of mathematics and systems analysis for fall 2024

8. April 2024

The Department of Mathematics and Systems Analysis is seeking

**New hourly-paid teachers in Mathematics and Systems Analysis for fall term 2024.**

Your tasks include teaching in exercise groups and grading exercises and exams.

Regarding teaching in mathematics, we expect the applicants to have completed at least 20 credits of mathematical studies at university level with good grades. Regarding teaching in systems analysis (courses MS-C/E2xxx), we expect the applicants to have completed the course they would like to teach. If you have previous experience in teaching, it is considered as an advantage, but is not necessary. This is a part-time job (2-4 hours/week). The salary is 30-40 euros/teaching hour based on your education level.

Grading exercises and exams will be (typically) compensated separately (300-400 euros depending on your education and the course level).

**Read carefully!** If you are *not working for Aalto* at the moment you apply, fill in the application form here. If you *are working for Aalto* at the moment you apply, you have to apply as an internal candidate via Workday, see instructions Sisäisen työpaikan hakeminen | Aalto-yliopisto.

Attach an open motivation letter, a cv and a transcript of records as one PDF file.

Deadline for the applications is **Monday 6 May 2024**.

Based on the applications, we will invite some of the applicants for a web interview.

More information: johanna.glader@aalto.fi

Note: if you have previously worked as an hourly-based teacher at the MS Department, you have received a separate link from johanna.glader(at)aalto.fi.

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