Seminar for Young Researchers

The seminar takes place in the room MaD245 on Wednesdays at 10:15–11:15, unless otherwise stated.

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

In the spring we will award the best speaker with the traditional Truly Awesome Robust Honorary Award. The T.A.R.H.A. prize is awarded for the fifth time. The awarded person is chosen by a public vote.

If you are willing to give a talk or have any questions you can contact
Onni Hinkkanen (onni.u.i.hinkkanen[at]jyu.fi),
Miro Arvila (miro.t.arvila[at]jyu.fi), or
Riku Anttila (riku.t.anttila[at]jyu.fi) (until Friday 24.1.).

Talks in Spring 2025

12.2. Pieti Kirkkopelto: The Onsager and Kolmogorov theories of turbulence and the Duchon-Robert measure as a link between them

Abstract: If we model a flow of water or gas with the incompressible Navier-Stokes equations, assuming smooth solutions leads to the prediction that the energy dissipation rate should vanish in the inviscid limit. If we then try to verify this experimentally, we see that the prediction is false and instead the energy dissipation rate seems to converge to a strictly positive constant, contradicting the theory.

Kolmogorov's idea was to model turbulent flows by taking the anomalous dissipation of energy as a postulate and try to make predictions about the statistical properties of turbulent flows via so called structure functions. Onsager on the other hand looked at the possibility that weak solutions of the incompressible Euler equations could demonstrate anomalous dissipation of energy, if irregular enough. Since the Euler equations are the inviscid limit of the Navier-Stokes equations, it is natural to wonder whether there would be a connection between the Onsager and the Kolmogorov theories.

The answer is yes and our goal is to introduce the two theories and use the Duchon-Robert measure to draw the connection between them.

19.2. Miika Manu: The light ray transform

Abstract: Let $f$ be a function on a Lorentzian manifold. The light ray transform $Lf$ encodes the integrals of $f$ over all light-like geodesics. On a Riemannian manifold, the geodesic X-ray transform encodes the integrals over all maximal geodesics.

In this talk, I will show that the light ray transform is injective on the Lorentzian manifold $[0,T]\times M$, where $M$ is a Riemannian manifold, if the geodesic X-ray transform is injective on $M$. Moreover, I will discuss when the assumption of the injectivity of the geodesic X-ray transform holds.

5.3. Guangzheng Yi: A weighted incidence estimate via high-low method

Abstract: In this talk, we review a weighted incidence estimate. Let $\mathcal{P}$ be a set of distinct $\delta$-balls in $[0,1]^2$ with weight function $w:\mathcal{P}\to (0,+\infty)$ and let $\mathcal{T}$ be a set of distinct $\delta$-tubes. If $\delta^{-\epsilon/100}\leq S\leq \delta^{-1}$, then $$\mathcal{I}_w(\mathcal{P},\mathcal{T})\lesssim_\epsilon \left(S\delta^{-1}|\mathcal{T}|\sum_{p\in\mathcal{P}}w(p)^2\right)^{1/2}+S^{-1+\epsilon}\mathcal{I}_w(\mathcal{P},\mathcal{T}^{S\delta}),$$ where $\mathcal{T}^{S\delta}:=\{T^{S\delta}: T\in\mathcal{T}\}$. The proof uses the high-low method which was due to Guth-Solomon-Wang. This incidence estimate has been applied in recent solution of Furstenberg sets problem in $\mathbb{R}^2$.

19.3. Miro Arvila: Introduction to ICA

Abstract: In this talk I will give short introduction to independent component analysis (ICA). I will give some basic properties about the model, needed assumptions for identifiability and examples using R software.

26.3. Joonas Vaakanainen: Theorem of Cartan and Hadamard

Abstract: In this talk we will state the Cartan Hadamard theorem; given a complete and connected Riemannian manifold $M$ with non-positive sectional curvature $K$, then for every point $p\in M$ the exponential map $exp_p:T_pM$ is a covering map. In other words we can derive global properties of the manifold from local information.

We shall also give some preliminary definitions from Riemannian geometry.

2.4. Eetu Satukangas: Geodesics in gas giant geometry

Abstract: Gas giant geometry is a special type of a Riemannian manifold where the metric tensor has a conformal blow up similar to asymptotically hyperbolic geometry. The blow up is small enough that for example geodesics have finite length. Gas giant geometry is used to model the acoustic wave propagation inside gas giant planets. We wish to study inverse problems in such geometry e.g. travel time tomography via injectivity of the geodesic X-ray transform. In this presentation I will show what types of results and ideas can be obtained and used for geodesics of gas giants.

9.4. Janne Taipalus: TBA

Abstract: TBA

23.4. Tuomas Niemi: TBA

Abstract: TBA

30.4. Shubham Jaiswal: TBA

Abstract: TBA

7.5. TBA: TBA

Abstract: TBA

14.5. Awarding of the Truly Awesome Robust Honorary Award

Abstract: We will award the fifth edition of T.A.R.H.A. to the most popular speaker of the spring chosen by a public vote.

Previous organizers

Antti Kykkänen
Janne Nurminen
Tapio Kurkinen
Timo Schultz
Ville Kivioja

Previous T.A.R.H.A award winners

Veikko Vuolasto (Autumn 2024)
Damian Dabrowski (Spring 2024)
Tapio Kurkinen (Autumn 2023)
Henri Hänninen (Spring 2023)

Previous seminars

Fall 2024

Spring 2024

Fall 2023

Spring 2023

Fall 2022

Spring 2020

Autumn 2019

Autumn 2018

Autumn 2017

Spring 2014