Mathematicians, statisticians, students, researchers - Everyone is welcome.

If you are willing to give a talk or have any questions you can contact

Antti Kykkänen (antti.k.kykkanen[at]jyu.fi) or

Janne Nurminen (janne.s.nurminen[at]jyu.fi).

What is the seminar about? Get to know each other. Coffee, tea and something sweet provided!

**Abstract:** In this talk, I will introduce the game called Hex and show that it is linked to an important result named after L. E. J. Brouwer. That is, I will discuss the equivalence of Brouwer's fixed point theorem and the fact that a game if Hex can never end in a draw.

**Abstract:** I will introduce metric spaces with geometric boundaries and an extension of Gromov-Hausdorff distance for such spaces. I will discuss some basic results and give an application to inverse problems on metric spaces.

**Abstract:** In this talk, I will present our current research for the reconstruction of the nonlinearity term in a certain kind of nonlinear Schrödinger equations from the DtN map. We derived a reconstruction formula using superpositions of multiple detections by combinatorics. Numerical tests show the validity for the reconstruction scheme. Besides, I'd like to further discuss some possible extensions of our current research.

**Abstract:** In this talk we consider the eigenvalue problem for a weighted spectral fractional second order elliptic operator in a bounded domain. We show that any eigenvalue is strictly monotone with respect to the weight function if the corresponding eigenfunction satisfies the unique continuation property from a measurable set of positive Lebesgue measure. This talk is based on one of my previous note.

**Abstract:** Is it possible to find five 5-letter words that repeat no letters between them? We dip into combinatorics, graph theory, and some algorithms and see how many ways there are to solve the same problem and try to understand why some methods are faster than others computationally.

**Abstract:** I will prove a classical existence and uniqueness result for mean field stochastic differential equations that states that if the coefficient functions are Lipschitz continuous and satisfy a linear growth condition in the space and measure components, then there exists a unique strong solution.

**Abstract:**

**Abstract:** Since kindergarten we know what a fractal is. This lecture will explore several peculiar places where we can find them, be it geometry, blood transfusions, or nature. Fractals are everywhere!

**Abstract:** In this talk, I will introduce one of the key points to get the second-order two-sided estimates in a kind of p-Laplace type equation. By using the transformation, the boundary term can be simplified under the boundary conditions. This talk is based on the paper “Second-Order Two-Sided Estimates in Nonlinear Elliptic Problems” by A. Cianchi and V.G. Maz’ya.

**Abstract:** I will talk about solutions to an elliptic PDE and how the boundary condition to this PDE can be used to control critical points (points, where the gradient of the solution vanishes) in the interior of the domain. In this context I will mention the weak maximum principle and Sobolev spaces (the natural space for the solutions). Furthermore, I will elaborate what happens, when the boundary condition is a discontinuous function so that the solution is not in the natural Sobolev space anymore. I will highlight how these insights can be used for an inverse problem of recovering the electrical condutivity from interior measurements of the domain.

**Abstract:**

**Abstract:** I will talk about extension domains in general metric measure spaces. First I will introduce some of the classical Euclidean results for W^{1,1}, BV and perimeter extension domains and then define these objects in general metric measure spaces. Furthermore in the metric setting I will introduce several implications between the different extension properties and give examples for the implications that fail.

**Abstract:** This is the first out of a three part talk on algebraic geometry. In this talk, we will look at affine geometry and affine varieties (geometric objects that are cut out by polynomial equations). We will look at how (commutative) algebra is used in order to describe geometric objects and present the algebra-geometric language, i. e. we will see that radical ideals are in bijection with varieties, prime ideals are in bijection with irreducible varieties, and that maximal ideals correspond one-to-one with (closed) points. For simplicity and intuition, we confine ourselves to an algebraically closed field.

The webpage for spring 2020 seminar can be found here.

The webpage for autumn 2019 seminar can be found here.

The webpage for autumn 2018 seminar can be found here.

The webpage for autumn 2017 seminar can be found here.

The webpage for spring 2014 seminar can be found here.