Domast PhD seminar

 

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 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 Saara Sarsa or Anna Suomenrinne-Nordvik (firstname.lastname@helsinki.fi).

 

The seminar is held bi-weekly on Fridays at 15-17, currently on Zoom.

Fall 2020 Speaker
4 September 2020 Eugenia Franco
One dimensional reduction of a Renewal Equation with a continuum of states at birth

Structured population models aim at studying phenomena at the population level, starting from mechanisms at the individual level. Individuals are characterized by their state (age, size, immunity level, …) and appear (for example through birth) in the population with a certain state, which is called state at birth.
If the set of the states at birth is finite it is possible to formulate the model as a Renewal Equation; the asymptotic behviour of its solution can be studied with the Renewal Theorem.
When, instead, we deal with a continuum of states at birth we can still easily formulate the model as a Renewal Equation, but its analysis will typically be difficult.
The focus of this talk is on the second case and on linear Renewal Equations.
Since a Renewal Equation is an integral equation it is chracterized by an integral kernel, which is the bridge between the mathematical formalization and the biological interpretation.
In the first part of the talk I will focus on the modelling aspect, presenting also some examples.
In the second part of the talk I will explain how, under a factorization assumption on this kernel, it is possible to deduce the asymptotic behviour of the solution of the Renewal Equation.
18 September 2020 Akseli Haarala
On the electrostatic Born-Infeld equations and the Lorentz mean curvature operator

In 1930’s Born and Infeld proposed a new model of nonlinear electrodynamics. In the electrostatic case the Born-Infeld equations lead to the study of a certain quasilinear, non-uniformly elliptic operator that comes with a natural gradient constraint. The same operator appears also as the mean curvature operator of spacelike surfaces in the Lorentz-Minkowski space, the setting of special relativity. We will explain both of these contexts to motivate the mathematical study of said operator.Our main focus will be on the regularity of the solutions of the electrostatic Born-Infeld equations. We will talk about some now classical results as well as some recent developments. We hope to give some ideas on the problems and methods involved without going into details.

2 October 2020 Tommi Heikkilä
TBA
16 October 2020
30 October 2020
13 November 2020 Emil Airta
TBA
27 November 2020 Stefanos Lappas
TBA
11 December 2020