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 sixth 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
Riku Anttila (riku.t.anttila[at]jyu.fi),
Janne Taipalus (janne.m.m.taipalus[at]jyu.fi), or
Onni Hinkkanen (onni.u.i.hinkkanen[at]jyu.fi).
Abstract: I will introduce an "elementary" problem concerning the simple question of which (bounded) planar sets look finite if one squints their eyes, or alternatively, simply has bad eyesight. Since all people have bad eyesight (one cannot zoom infinitely), this is a very inclusive topic. The problem gets a bit more technical once one attempts to make rigorous observations as this leads to the study of measures, curves and Lipschitz maps. I will introduce all of the necessary tools in their simplest form and answer the question from the title. I will also demo some 3Blue1Brown-style animations I have been working on.
Abstract: Liquids in containers have a tendency to slosh around when subjected to outside perturbations. In worst-case scenarios, this sloshing can cause the liquid to spill. In this talk, I'll attempt to calculate the normal modes of sloshing for a cylindrical tank with a linearized free-surface condition, which models my coffee mug. Hopefully, this better understanding of the sloshing frequencies will help us all avoid spilling our coffee.
Abstract: In this talk we study the geodesic X-ray transform \(If\), which encodes the integrals of \(f\) over all maximal geodesics, on Riemannian manifolds with low regularity metrics. When metric is smooth, it is known that normal operator \(N=I^*I\), where \(I^*\) is a formal adjoint of \(I\), is an elliptic pseudodifferential operator. Hence there exists an approximative inverse operator \(Q\) such that \[QNf(x)=f(x)+Rf(x),\] where \(R\) is smoothing operator. Now \(If=0\) implies \(f=-Rf\) i.e functions \(f\) in the kernel of \(I\) are smoother than assumed a priori. In order to prove injectivity of the geodesic X-ray transform, one needs to prove injectivity only for smooth functions.
In non-smooth case we use similar approach. We decompose normal operator \[N=P+R,\] where \(P\) is pseudodifferential operator in suitable non-smooth calculus and \(R\) is smoothing operator. Moreover, we use symbol smoothing arguments to reduce matters to an elliptic operator in the smooth calculus. This talk is based on joint work with Pieti Kirkkopelto and Mikko Salo.
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Abstract: The prime number theorem is the result about asymptotic distribution of prime numbers. It was originally stated by Legendre in 1808 and proved independently by Jacques Hadamard and Charles Jean de la Vallée Poussin in 1896 by using the Riemann zeta function. Somewhat surprisingly this simple number theoretic result can be proven by Fourier analysis which is has nothing to do with number theory at least in principle. This is one instance that shows how powerful tool the Fourier analysis and can be applied to wide variety of mathematics. I try to go through the proof but in somewhat backwards direction since machinery gets deeper that way. In the end I will also mention the connection to the (well known) Riemann hypothesis, which gives another surprising connection between number theory and complex analysis.
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Abstract: We will award the sixth edition of T.A.R.H.A. to the most popular speaker of the spring chosen by a public vote.
Miro Arvila
Antti Kykkänen
Janne Nurminen
Tapio Kurkinen
Timo Schultz
Ville Kivioja
Tuomas Niemi (Spring 2025)
Veikko Vuolasto (Autumn 2024)
Damian Dabrowski (Spring 2024)
Tapio Kurkinen (Autumn 2023)
Henri Hänninen (Spring 2023)
Fall 2022
Spring 2020
Autumn 2019
Autumn 2018
Autumn 2017
Spring 2014