The seminar takes place at room MaD355 at 12:15–13:15, unless otherwise stated. Everyone is welcome.

If you are willing to give a talk or have any questions you can contact Timo Schultz or Ville Kivioja. See math department personnel for contact information.

Back to seminar 2022.

Milica Lučić (University of Novi Sad, Serbia)

This talk is dedicated to the study of locally convex topologies on a vector space. We will introduce one such topology, called $\sigma$-topology, and discuss more in detail a special type of it - - namely, the strong topology. We will show that, on a normed vector space, the strong topology and the topology induced by the norm do not necessarily coincide, and provide a necessary and sufficient condition for having the equality between the two. Time permitting, a couple of words will be said about the motivation for the study of the strong topology.

Sebastiano Don

The Lusin's Theorem states that a measurable function on a set of finite measure is continuous outside a set of small volume. In general, finding Lipschitz approximations for functions with low regularity has many application for example in the Calculus of Variations and in the Regularity Theory. We present a proof of Lusin's Theorem and present its improvements on more regular functions. In particular, we describe its version about Sobolev functions due to Liu, its quantitative version for Sobolev functions due to Acerbi and Fusco and finally, the very recent quantitative result about BV functions due to Breit, Diening and Gmeineder.

Janne Nurminen

This talk is about an inverse problem that is called the Calderón problem. This is connected to electrical impedance tomography which will be briefly discussed: If we have some object, it has some conductivity inside and on the boundary. If we measure current (induced by voltage on the boundary) coming out of the object we get the so called Dirichlet to Neumann map. Main theorem of the talk is that from electrical measurements on the boundary, we can determine the conductivity on the boundary.

Tapio Kurkinen

Normalized p-parabolic equation is a parabolic partial differential equation arising from stochastic game theory. In this talk, we will look at the connection between viscosity solutions of this equation and weak solutions of a modified heat equation we get by introducing a fictitious dimension in the radial case. I intend to show the connection between the equations themselves and give an idea on how to prove the equivalence of the solutions.