The seminar takes place at room MaD380 at 14:15–15:15, 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.
Back to seminar 2022.
Ville Kivioja
I will consider the Citti--Sarti--Petitot model for the image completion in the primary visual cortex of humans. This model, based on subRiemannian geometry of the rototranslation group, explains in particular quantitatively the appearences of illusonary contours in, for example, the Kanizsa Triangle. I will show how, and I will introduce the necessary concepts of biology and subRiemannian geometry along the way.
Timo Schultz
I will prove that the subgroups of a free group are free. This is done using the fundamental group, theory of covering spaces and graph theory.
Shirsho Mukherjee
The topics that shall be discussed, will mainly involve the notion of non-linear eigenvalues and ways of generating such eigenvalues under invariance with respect to compact symmetry groups, acting on Finsler manifolds.
Atte Lohvansuu
I will present some interesting facts about the topology of orientable compact connected 3-manifolds: the existence of a Heegaard splitting and the Lickorish-Wallace theorem, which states that any such manifold can be obtained by performing surgeries on the 3-dimensional sphere.
Debanjan Nandi
We will discuss Interpolation (real) in Banach spaces of functions and consider some examples.
Toni Ikonen
I will introduce a Uniformization Theorem for general Riemann surfaces and some of its corollaries. The proof uses some algebraic topology and the Uniformization Theorem for simply-connected Riemann surfaces.
Zheng Zhu
According to several results of Shvartsman, Koskela, Rajala and Zhang, we can obtain that the inward cusp domain in plane is $W{1,1}$-extension. Also we find that both outward and inward cusp domains do not satisfies the sufficient condition for the extension of $W{1,p}$ for $p>1$. Then the interesting problem is that what is the optimal Sobolev-extension results for these two kinds of cusp domains, than means, if we extend $W{1,p}$ outside to get a function belonging to $W{1,q}(\mathbb{R}{2})$, what is the optimal upper bound for $q$? Obviously, we have $q < p$.
Joonas Heino
In this talk, I will introduce option pricing in the context of a two-player zero-sum stochastic differential game in a multi-dimensional financial market. In the original Black-Scholes model, the arbitrage free price of an option is the unique solution to the Cauchy problem for a linear second order uniformly parabolic equation (heat equation). However, in this new game context, the underlying PDE is much more involved due to the presence of the nonlinear and degenerate infinity Laplace operator.
Martti Rasimus
I will discuss standard regularity results for (quasi-)minimizers of the p-Dirichlet energy in the non-standard setting of general metric measure spaces.
Zhuang Wang
In the talk, I will introduce some classical results about the trace spaces of some function spaces, like Sobolev space, Besov space. I will also give a proof of the trace result of Sobolev space.
Erika Pirnes
Let R be a Noetherian ring (every ideal is finitely generated). Consider the polynomial ring over R with n variables. Let J be an ideal in this polynomial ring generated by some set of polynomials. The goal of my master's thesis is to find (or at least estimate) the minimal number of polynomials needed to generate J.