Title: Analyzing Point Processes Using Ripley’s K-function

Abstract: Point processes are models for random point patterns used for modelling spatial data such as plant growth locations, disease outbreaks or physical particle distributions. One of the goals in spatial statistics is to try to capture geometric information about the point process such as clustering and repulsion.

This talk will give an introduction to one of the most popular tools in this context, Ripley’s K-function, along with some rigorous asymptotic distributional result.

This is joint work with C. Biscio.

Title: Conditional Tail Moment and Reinsurance Premium Estimation Under Random Right Censoring

Abstract: We propose an estimator of the conditional tail moment (CTM) when the data are subject to random censorship. The variable of main interest and the censoring variable both follow a Pareto-type distribution. We establish the asymptotic properties of our estimator and discuss bias-reduction. Then, the CTM is used to estimate, in case of censorship, the premium principle for excess-of-loss reinsurance.

The finite sample properties of the proposed estimators are investigated with a simulation study and we illustrate their practical applicability on a dataset of motor third party liability insurance.

This is a joint work with Yuri Goegebeur and Jing Qin from SDU.

Title: Almost Global Stability of Switched Systems with Stable and Unstable Modes

Abstract:  In this talk, I will provide brief summaries and motivations for switched systems, multiple Lyapunov density and almost global stability initially. After I will mention about a certification method for almost global stability of nonlinear switched systems consisting of both stable and unstable subsystems using  multiple Lyapunov densities.

Moreover, I will mention that by using slow switching for stable subsystems and fast switching for unstable subsystems lower and upper bounds for mode-dependent average dwell times will be calculated to ensure stability.

In addition to that, by allowing each subsystem to perform slow switching and using some restrictions on total operation time of unstable subsystems and stable subsystems, a lower bound for an average dwell time will be provided.

Abstract:  According to the World Health Organization, hepatitis C virus (HCV) infection should be under control by 2030.

This talk presents an estimation approach based on removal sampling from binomial distributions which we applied in a recent article to estimate the size of the hidden (undiagnosed) population with chronic HCV infection in Denmark and Sweden born before 1965. Data specific challenges and bootstrap confidence intervals will be discussed.

Reference: Christensen Peer Brehm, Debrabant Birgit, Cowan Susan, Debrabant Kristian, Øvrehus Anne, Duberg Ann-Sofi. Hepatitis C time trends in reported cases and estimates of the hidden population born before 1965, Denmark and Sweden, 1990 to 2020.
Euro Surveill. 2022;27(50):pii=2200243.

Title: Important Female Researchers in Mathematics Education

Abstract: The presentation focus on how specific female researcher in mathematics education has had important research contributions over time and how to use these perspectives in research and teaching.

I will end with a description of how I have used an Anthropological theory of didactic approach to understand the role of mathematics in integrated STEM-teaching. This with specific focus on inquiry-based teaching in mathematics. 

Title: The Philosophy of Mathematical Practice – a brief introduction

Abstract: I introduce some motivations for and themes from what is referred to as the philosophy of mathematical practice.

The philosophy of mathematical practice started out as a reaction to the previous one-sided focus on discussions on the foundations of mathematics and its ontology. In the talk I present some examples of contributions within this field and indicate what is meant by ‘practice’ in these cases.

I give examples of studies on the foundations of mathematics from a practice point of view as well as some of my own recent considerations on various characterisations on understanding and explanations in mathematics. 

Title: From Equivariant Stable Homotopy Theory to Data Science via Parallel Computing; in 30 Years

Abstract: Algebraic Topology is being applied in data science. In Topological Data Analysis, questions and problems are often both theoretical and very much “inside” mathematics and practical – what is needed for a given application.

In parallel computing, there are models which use tools built from or inspired by standard tools in Algebraic Topology. Work within these boundary areas is on the one hand very inspiring and on the other hand challenging:

   • How much does one need to understand of an application to give sensible math answers to the questions arising?

   • Does a mathematician entering an applied field stop being a mathematician at some point?

Such questions will be asked with the speakers own balancing act through a long life in and with mathematics as a point of departure.

Also, there will be examples of the mathematics encountered and in some cases conquered on that journey.

Title: The Role of Symmetry in Mathematics – Motivations and Historical Considerations

Abstract: What is symmetry in mathematics? Scholarship of the last two centuries suggests that group theory provides a mathematical language for describing symmetry in a formal way. But when the notion of symmetry is used in mathematical practice, are mathematicians always referring to group theory?

I suggest that they are not and give some examples of how the concept of symmetry is used in practice. Furthermore, when investigating symmetry, one must be aware of how this notion has developed over the course of history. In particular, the term was introduced in Greek antiquity long before the formulation of group theory. 

Title: Nonparametric Modeling of Event Processes with Applications to Causal Discovery

Abstract: In the context of disease progression analysis, estimating the causal effect of a time-continuous treatment assigned to a given population is an important problem. This is particularly relevant for understanding (the causal) underlying phenomena in many applications gathering massive high-dimensional and time-dependent data structures, ranging from biomedicine to financial markets. In practice, existing learning algorithms inferring the underlying causal graph consider the progression of the recorded markers as time-continuous event processes, for which it is required to specify a model.

We propose, in this work, a nonparametric model for testing if a process directly influences another when conditioned on the history of others, also known as the (asymmetric) conditional local independence test. Finite-sample concentration bounds for the estimation and prediction errors are derived, yielding data-driven optimal sparse expansion of the statistical test.

This is a joint work with Professor Niels Richard Hansen at Department of Mathematical Sciences, University of Copenhagen.

Title: Quantum Computing and its Applications in the NISQ Era

Abstract: The field of quantum computing has rapidly evolved in recent years, with exciting developments in hardware, software, and algorithms. In particular, the Noisy Intermediate-Scale Quantum (NISQ) era has opened up new possibilities for practical applications of quantum computing.

In this talk, we will explore the landscape of quantum computing, with a particular focus on the NISQ era and its applications.

We will start by introducing the basic concepts of quantum computing, followed by an overview of the state-of-the-art hardware platforms and software tools.

Finally, we will showcase some of the recent applications of quantum computing, with focus on the continuous variable paradigm.

Title: Quantum Spaces and Graph Algebras

Abstract: In noncommutative geometry we investigate objects for which the classical multiplication rule ab=ba is violated. The main object of study is a so-called C*-algebra which heuristically can be viewed as a noncommutative analogue of a function algebra on a non-existing, virtual, space. Various classical spaces have been given such a noncommutative analogue, called a quantum space, which are the main objects of interest in my studies.

In this talk I will present examples of quantum spaces studied in my projects. These quantum spaces fall into a certain class of C*-algebras called graph C*-algebras. Graph C*-algebras are particularly nice objects since we can obtain a lot of useful information on the structure of the underlying C*-algebra simply by looking at the corresponding directed graph.

Title: Uncertainty Quantification of Inclusion Boundaries

Abstract: In this talk, we will describe a Bayesian framework for reconstructing the boundaries of piecewise constant regions in the X-ray computed tomography (CT) problem in an infinite-dimensional setting. In addition to the reconstruction, we are also able to quantify the uncertainty of the predicted boundaries.

Our approach is goal oriented, meaning that we directly detect the discontinuities from the data, instead of reconstructing the entire image. This drastically reduces the dimension of the problem, which makes the application of Markov Chain Monte Carlo (MCMC) methods feasible.

We will show that the new method provides an excellent platform for challenging X-ray CT scenarios (e.g., in case of noisy data, limited angle, or sparse angle imaging).