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 third 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

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

Tapio Kurkinen (tapio.j.kurkinen[at]jyu.fi).

**Abstract:** In this talk I will go over the mathematics of describing the probabilistic time development of a fluctuating dynamical system. The approach that I will use is due to Itô's description of stochastic differential equation (SDE) on a Riemannian manifold in pre-point sense, and Graham's path integral description of the time development of the probability law of Itô's SDE. The probabilistic part of Itô's SDE is w.r.t. the Wiener process so the probability law is given by the Fokker-Planck heat equation, and the focus will be on a geometrically invariant description of the Brownian motion on a Riemannian manifold. While path integrals are infamous for having non-unique and non-rigorous constructions and results, Graham's path integral is proven to converge to the correct probability law in a paper by Anderson and Driver. At the end of the talk, I will go over some results and open questions regarding path integrals on Riemannian manifolds.

**Abstract:**
In this talk I will discuss basic concepts and techniques regarding viscosity solutions of partial differential equations. I will demonstrate methods for proving existence and uniqueness of a viscosity solution, given some reasonable boundary condition. Additionally, I will present some connections to classical- and weak solutions of PDEs.

**Abstract:** In this talk I give some intuition why one would look at inverse problems for the minimal surface equation (MSE). I will start with the Calderón problem and try to motivate from that perspective why we study inverse problems for the MSE and also try to give some motivation arising from physics.

**Abstract:**
In this talk, we are concerned with game-theoretic approaches to several types of PDEs. Probabilistic methodology has been used as a powerful tool to study PDEs in recent decades. It not only provides a different perspective to comprehend PDEs but also contributes to leading to new mathematical discoveries. It is well-known about the association between the Laplacian and random walk processes. In this discussion, the mean value property of harmonic functions is a key property. We can also consider similar approaches to more general equations. For nonlinear cases, 'tug-of-war' is a representative example in this respect, which is a discretized scheme for the normalized p-Laplace operator. Recently, game theoretic approaches have been actively studied for other nonlinear PDEs.

**Abstract:**
Rescheduled due to difficulties with public transit.

**Abstract:**
In the classical secretary problem a company is interviewing candidates for a given position. It is assumed that the applicants can be ranked from worst to best unambiguously. The company wants to find the best candidate, and everything else is considered a failure. Candidates are interviewed one by one, and after each interview the company has to decide whether to accept or reject the applicant. Once a candidate is rejected, they cannot be recalled. The challenge comes from the fact that the company does not know the absolute ranks of the applicants, only the relative ranks, that is, how they compare to the previously interviewed people, and the hiring strategy must be based on this information only.

**Abstract:**
In this talk, I will discuss homogeneous and non-homogeneous Sobolev (p,q) extension domain and some of the results on bounded homogeneous (p,q) extension domain, more precisely the existence of a particular non-homogeneous Sobolev extension domain which is not a homogeneous Sobolev extension domain under some given conditions on p and q.

**Abstract:**
In machine learning - and more specifically in supervised learning - the goal is to train a model from a given labeled data (also known as the training set) that can be used for labeling unseen data points. For instance, one might be interested in training a model that labels pictures based on whether or not the picture contains a dog. A conventional wisdom in classical machine learning is that if the trained model is too big, it will most likely "overfit" on the training data: while its performance on the training set is good, it performs badly on unseen examples. In other words, bigger models do not generalize as well as smaller models. Recently this wisdom has been challenged by the modern deep learning paradigm, as empirical results indicate that bigger models perform better than smaller models on unseen examples. These models are "overparameterized" in the sense that they are large enough to label their training sets in an arbitrary way. In this talk I will try to point out possible explanations for this puzzling situation.

**Abstract:** The classical inverse problem of reconstructing an electrical conductivity from voltage to current measurements at the boundary is very difficult in practical settings. In order to tackle this issue, a class of problems called “hybrid inverse problems” were developed that combine two imaging modalities to obtain interior measurements (instead of just exterior measurements as for the voltage to current map). I will give an introduction to 5 of such hybrid inverse problems and highlight how the procedure of reconstructing the electrical conductivity from the corresponding interior measurements is more feasible than in the classical case.

**Abstract:**
In this talk I will go though some basic properties of extended metric-topological measure spaces. These are spaces that have an extended metric so we can for example talk about Lipschitz functions, but the topology on these spaces is not necessarily induced by the extended metric. I will also talk about a way of compactifying these spaces.

**Abstract:**
In this talk we will discuss about the existence and uniqueness of limits along different kind of curves for functions in homogeneous fractional Sobolev spaces defined on Euclidean space. These limits turns out to be unique in every direction. We shall discuss the range of exponents s, p, n for which limit will exists.

**Abstract:**
Mathematicians over the years have come up with different notations and uncomputable functions to represent absurdly large natural numbers and given two of these, it is suddenly surprisingly hard to know which is larger. I will give a quick glimpse into the field of Googology and talk about some of my favorite ridiculously big numbers, how they are defined, and which one is the biggest.

**Abstract:**
This talk will be a gentle introduction to the classical Buffon’s needle problem, which can be stated as follows: can you measure the length of a set by randomly tossing a needle on top of it? Time permitting, we will also discuss some modern incarnations of this question. The talk may involve throwing pens around the room, proceed with caution.

**Abstract:**
In this talk I introduce the very basics of the finite element method and then show how to use the finite element method in Python with the library FEniCS. I start with the simplest case, the Poisson equation with Dirichlet boundary. I then show how to modify this to solve more interesting problems, such as systems of PDEs with mixed boundary conditions.

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

Fall 2022

Spring 2020

Autumn 2019

Autumn 2018

Autumn 2017

Spring 2014