The Domast student seminar is an informal seminar for doctoral students of mathematics and statistics, as well as (advanced) Master’s degree level students interested in research. The aim is to give students an opportunity to develop science communication and presentation skills and to get a peek into other fields than their own. Students of Domast may obtain study credits for presenting in or organising the seminar. After every speaker there will be a relaxed discussion as well as a feedback session, so be prepared to take part in these if you attend. The seminar was organised for the first time in Autumn 2020.
Everyone is welcome and we hope to have speakers from all Domast fields!
In Spring 2023 the seminar is organized by Susanna Heikkilä (susanna.a.heikkila
) and Petri Laarne (@helsinki.fi
). If you are interested in giving a talk in the autumn series or still this spring, please get in touch with us.
The seminar is held biweekly on Fridays at 14–16, in Exactum D123 (unless otherwise mentioned).
Spring 2023 
Speaker 
20 January 2023 
Jonathan Pim
Evading Epsilons with Ultrafilters
Ultrafilters and ultralimits provide a generalized and convenient (though nonconstructive) theory of convergence and other related topological notions such as compactness that avoids many of the technicalities of managing epsilons and taking subsequences of subsequences. I will discuss some of the basic definitions and results related to ultrafilters such as the fact that every bounded sequence of real numbers has an ultralimit.
Expected time: 20 or maybe 30 minutes.
Goal: Practise giving a talk and explain the basics of ultrafilters.
Target audience: Regular DOMAST seminar attendees.
Presentation slides

3 February 2023 
Davide Quadrellaro
Szemeredi’s Regularity via Counting Measures
In this talk I plan to sketch a proof of Szemerédi’s graph regularity lemma which uses tools from pseudofinite model theory. I will review the basic ultraproduct construction and I explain how one can extend measures over a class of finite structures to their ultraproduct. Finally, if time permits, I will briefly describe the strengthenings of Szemeredi’s regularity that follow once we consider graphs with nice model theoretic properties.
Expected length: 45 minutes.
Goal: Show an application of ultrafilters and model theory to graph theory.
Target audience: Regular DOMAST seminar attendees.
Presentation slides

17 February 2023 
Heli Virtanen (double talk)
High school students and vectors: What kind of misconceptions arise?
The study is based on the Spring 2020 Advanced mathematics matriculation examination, question 2, with over 13,000 students taking the exam. Most of the students do very well. However, there are some widespread errors. We will briefly present the format of the Finnish electronic matriculation examination and then go further in to the found misconceptions the students had.
Expected length: 20 min.
Goal: Introduce the Finnish matriculation examination and to present the findings from our research on the found misconceptions.
Target audience: Fellow PhD students, but also master students, especially in the teacher program.
Presentation slides
Summamutikka: Mathematics science class
Do you know what all the mathematics science class, Summamutikka, a part of the department and of LUMAcenter Finland does? How could you take part in it?
Expected length: 20 min.
Goal: Introduce Summamutikka, show some of our recent material and tell about possible collaborations.
Target audience: PhD students, but also anyone in the department or a student of the programs.

3 March 2023 
Ensio Suonperä
Bilevel optimization with singlestep inner method
We propose a new approach to solving bilevel optimization problems. Main motivation for developing new approach is that some problems are computationally demanding with the previous approaches. The overall idea is to solve the fullsystem optimality conditions, but to precondition them to alternate between taking steps of simple conventional methods for the inner problem, the adjoint equation, and the outer problem. While the inner objective has to be smooth, the outer objective may be nonsmooth. We demonstrate good performance on learning the regularization parameter and the convolution kernel for image deconvolution with anisotropic total variation regularization. This talk also introduces ideas providing linear convergence proof for the approach.
Expected length: 20 minutes (or little more)
Goal: Develop my conference presentation of optimization topic better suited for audience whose main field is not optimization. Audience might be focused on some field that use optimization methods as a tool in their research.
Target audience: PhD students or more experienced scientists.
Presentation slides

17 March 2023
Exceptionally in room Exactum B120.

(We unfortunately had to reschedule Tapio Saarinen’s talk – a new date will be posted later.)
Siiri Kivimäki
The notion of a logic, topologically
There is way to associate a topological space to each abstract logic, in such a manner that important properties of the logic reflect as topological properties of the space. For instance, a logic is compact if and only if its corresponding space is compact.
In this talk, I will discuss the notion of a logic, define its associated topological space, and sketch ways to obtain information of the logic by studying its corresponding space. The ultimate motivation comes from the fact that in firstorder model theory, the most important tool is a topological one: the socalled space of types. I will try to start from the beginning and motivate everything through a lot of examples.
Expected length: about 30 minutes
Goal: Practice giving a presentation at short notice
Target audience: PhD and MSc students

31 March 2023 
Joni Puljujärvi
TBA
TBA

21 April 2023 
Julia Sanders
TBA
TBA

5 May 2023 
Aapo Laukkarinen
TBA
TBA
