The Domast student seminar is an informal seminar for doctoral students of mathematics and statistics. The aim is to give students an opportunity to develop science communication and presentation skills and to get a peak into other fields than their own. Students of Domast may get 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 is organised for the first time in Fall 2020 and will be developed along the way.
Everyone is welcome and we hope to have speakers from all Domast fields!
If you wish to present in the seminar or have other questions, contact the seminar organisers Tuomas Oikari (firstname.lastname@example.org) or Antti Mikkonen (email@example.com). If you wish to be one of the seminar organisers in Spring 2022, contact the current organisers.
The seminar is held bi-weekly on Fridays at 14-16, currently on Zoom.
Meeting ID: 652 8387 0579
The seminar schedule for the current semester is found below.
|3 September 2021||
Quasiconformality, distortion and regularity: an introduction
The notion of quasiconformality is nearly a century old yet still provides some interesting research questions. We first discuss the concept of quasiconformal mappings and more general mappings of finite distortion. Then we study both old and new regularity results in this setting. Both geometric and analytic regularity are considered, with the aim of presenting the research to broader audience.
|17 September 2021||Saara Sarsa
Insights into the regularity theory of elliptic partial differential equations: from Hilbert’s 19th problem to the 21st century
In 1900, in the International Congress of Mathematics, David Hilbert presented his famous collection of problems. The problems of Hilbert have inspired mathematicians throughout 20th century, and up to today.
Hilbert’s 19th problem is: Are the solutions of regular problems in the calculus of variations always necessarily analytic?
In my talk, I will
(a) explain the Hilbert’s 19th problem,
(b) present the way it was solved, focusing on ideas rather than rigorous proofs; and
(c) discuss my own research on the regularity theory of elliptic partial differential equations, and how it connects to the Hilbert’s 19th problem.
The goal of my talk is to provide historical perspective to the modern research of regularity theory of elliptic partial differential equations. The talk is aimed at a broad audience. No deep understanding of the topic is expected and all Domast students from any subfields of mathematics are warmly welcome.
|1 October 2021||Tommi Heikkilä
4D Dual-tree complex wavelet transform for time dependent data
Regularization is the key to solving ill-posed inverse problems, such as computing tomographic reconstructions from noisy and limited data, and sparsifying representation systems such as wavelets are a common and reliable choice. If we consider repeated cone-beam measurements of a dynamic object of interest, the regularized object is 4-dimensional (3D + time)! Motivated by this challenge we extend the dual-tree complex wavelet transform to 4D and apply it to sparse dynamic tomography regularization.
The aim is to give a rough idea on the construction of the 4D dual-tree complex wavelets, how the implementation can be made relatively simple and briefly illustrate what are the advantages of using complex valued wavelets over traditional real valued ones. Finally we compate both in 4D sparse dynamic tomography setting.
|15 October 2021||Riku Laine
Evaluating Decision Makers over Selectively Labelled Data: A Causal Modelling Approach
We present a Bayesian approach to evaluate AI decision systems using data from past decisions. Our approach addresses two challenges that are typically encountered in such settings and prevent a direct evaluation. First, the data may not have included all factors that affected past decisions. And second, past decisions may have led to unobserved outcomes. This is the case, for example, when a bank decides whether a customer should be granted a loan, and the outcome of interest is whether the customer will repay the loan. In this case, the data includes the outcome (if loan was repaid or not) only for customers who were granted the loan, but not for those who were not. To address these challenges, we formalize the decision making process with a causal model, considering also unobserved features. Based on this model, we compute counterfactuals to impute missing outcomes, which in turn allows us to produce accurate evaluations. As we demonstrate over real and synthetic data, our approach estimates the quality of decisions more accurately and robustly compared to previous methods.
|29 October 2021||TBA|
|12 November||Emil Airta
|26 November||Aleksis Vuoksenmaa