Room: NU-09A46 (next to the common area)
Organisers: Michael Jung
Upcoming talks:
Previous talks:
- 31.5.2023, 15:00: Marc Corstanje – Statistics for continuous-time stochastic processes in a nutshell.
A continuous-time stochastic process can be thought of as a collection of random variables { X(t), t > 0 }. Such processes are widely used for modelling phenomena that evolve over time. For instance, one can think of modelling a population size, where at certain random times, an individual might die or a new individual is born, but there are many more examples, such as solutions to SDEs or chemical reaction processes. As is usually the case in mathematical models, there are almost always some underlying parameters governing the dynamics of the process, which are of interest. In the talk, I’ll introduce some notions from the field of stochastic processes and then I’ll discuss the statistical problem of estimating such parameters based on a discrete set of observations { X(t_k), k = 1, … n }. If time permits, I’ll demonstrate a method proposed in our latest article in which we propose a simulation method for the so-called bridge process between the observations.
Reference:
Corstanje, Marc, van der Meulen, Frank, & Schauer, Moritz. 2022. Conditioning continuous-time Markov processes by guiding. To appear in Stochastics, https://doi.org/10.1080/17442508.2022.2150081.
- 8.5.2023, 16:00: Lindsey van der Aalst – The suspension bridge equation in a nutshell.
The one-dimensional suspension bridge equation has been well studied in literature: traveling waves of various types have been proven to exist. Far less is known about the two-dimensional case. We use computer-assisted proof methods to find and prove periodic traveling waves in two spatial dimensions.
- 7.12.2022, 16:00: Mark van den Bergh – Variants of combinatorial games
In the field of combinatorial games, we study two-player games with perfect information and no chance. Examples include chess, go and tic-tac-toe. For this class of games, a beautiful mathematical theory exists, providing a lot of structure and solution methods. We wonder what remains of this framework if we drop one of the requirements, in particular the one of perfect information. During the talk, we will discuss the basics of combinatorial games and provide some results for imperfect information variants for some of these games.
- 2.12.2022, 16:00: Erik Sandin Vidal – Existence of invariant tori in skew-product systems: A Computer-Assisted approach
Skew-product dynamical systems are a certain type of dynamical systems that have a fiber bundle as a base space. The main theoretical result of this work is a validation theorem that ensures the existence of an invariant torus in a skew-product dynamical system should certain conditions be fulfilled. We will validate the torus computationally using computer assisted proofs that will help us check such conditions. Fourier transforms and Fourier series will become the pillar over which the validation algorithm is sustained as well as some interval arithmetics packages for the programming tasks.
- 11.11.2022, 15:30: Francesca Cavallini – Modeling and quantifying uncertainty in the brain using Neural Field equations
Transcranial Magnetic Stimulation (TMS) is a promising therapy for several neurological and psychological disorders. However, it is not well understood why it seems to induce a positive response only in 30-50% of clinical cases. This has to do with the little knowledge we have of the brain: its state when the stimulus is applied, its connections within different areas and other quantities that are only partially known by scientists. In this talk, I will introduce Neural Field equations to model the neural activity in the cortex (the part of the brain involved in TMS), and explain how we include this uncertainty in the model. I will also talk about a numerical method we are studying in order to estimate quantities of interest for this problem, such as the neural activity at a certain time-space coordinate.
- 01.06.2022, 16:00: Pepijn Hooefgeest – Introduction to Persistent Homology
In this talk, I will give an introduction to persistent homology, motivated by some concrete examples. We will then look at some practical applications, as well as interactions with various fields of pure mathematics.
- 13.04.2022, 17:00: Marina Dietrich – Wild Bootstrap for Counting Process-Based Statistics with Application to Fine-Gray Models
- 23.03.2022: Alexandra Vegelien – Relapse prediction for acute myeloid leukemia patients
"Survival analysis is a branch of statistics for analyzing the expected duration of time until one event occurs, such as death in biological organisms and failure in mechanical systems".
I will give an introduction and discuss an application of this to modeling the probability of relapse for Leukemia patients and how mathematics can be used to improve patients' treatment.
- 17.12.2021: Ronen Brilleslijper – The geometry behind classical physics
In this talk I will explain the geometry that comes into play when we want to formalize Newtons laws. There are multiple ways of extending this formalism to the more modern physical theory of classical field theory. I will explain the difference and talk about their pros and cons.
- 3.12.2021: Davide Sclosa – Why trees synchronize, but rings don’t
Phase oscillator networks are widespread in neuroscience, chemistry and power networks theory. They provide a natural framework for studying synchronization and pattern formation. At the same time, they constitute an active field of mathematical research, which combines dynamics, combinatorics, geometry, and abstract algebra. Despite this, synchronization of particular networks can be understood by elementary tools. We will see why trees synchronize, while rings may not.
- 12.11.2021: Dennis Nieman – Estimation of the input to a Lévy-fed queue from observations of its workload.
We discuss the notion of a Lévy process and the construction of the workload process of a queue which has a Lévy process as input. Then we consider the problem of estimating the input process of such a queue from discrete observations of its workload process.
- 05.11.2021: Casper Putz – A method for solving generalized Fermat equations
In this talk I will introduce generalized Fermat equations and (parts of) a method to solve them. I will discuss this in the light of a specific Diophantine equation which serves as the main focus of my research.
- 22.10.2021: Michalis Tsironis – A small introduction to cluster algebras
In this talk we will discuss the concept of cluster algebras. We will focus on cluster algebras coming from surfaces and see how a geometric model can be used for the understanding of such algebras. If time allows it, we will also briefly mention some connections of this model to Category Theory.
- 01.10.2021: Michael Jung – Manifolds and characteristic classes in SageMath
In this talk, we recall some basic definitions for manifolds and introduce the software Sage and its link to geometry.
The second part of this talk is devoted to my main contribution in Sage. That includes vector bundles, bundle connections and characteristic classes.
- 17.09.2021: Fabio Buccoliero – Introduction to knots and spatial graphs
In this talk, we introduce knots and their generalization: spatial graphs. The main goal of Knot Theory is to determine if a knot is trivial; in order to determine this, invariants play a major role in the theory. The same happens for spatial graphs.
The easiest spatial graph invariant consists of the knots contained in a spatial graph. There is though a family of spatial graphs which is resistant to this invariant...