# List of Lecturers

**Titel:** *Mean Geometry of 2D Random Fields*

**Abstract: **"In these lectures I will mainly present joint works with Ag-

nès Desolneux (CNRS, ENS Paris Saclay) in which we consider three

geometric characteristics of stationary 2D random field excursion sets,

called Lipschitz-Killing curvatures, which are linked to the area, perime-

ter and Euler characteristic of these sets. By adopting a weak functional

framework we obtain explicit formulas for their mean values which make

it possible to extend known results in the context of smooth Gaussian

surfaces to non-Gaussian shot-noise fields. In particular this framework

allows to recover results from stochastic geometry on boolean models

and to shed new lights on the so-called Gaussian kinematic formula of

Robert Adler and Jonathan Taylor."

University of Tours

Tours, France

**Titel:** *Stationary random fields appearing in number theory*

**Abstract:**

Institut für Mathematische Stochastik

University of Münster

Münster, Germany

**Titel:** *Markov Chain Monte Carlo.*

**Abstract**: "In my presentation, I'll start with a brief overview of Markov

chains, highlighting their mathematical foundations, coupling mechanisms,

and some results on convergence. Following this, I'll explore Markov Chain

Monte Carlo methods, covering essential algorithms. Lastly, I'll briefly

discuss some recent progress in the area of non-reversible chains."

The Institute of Statistical Mathematics

ISM

Tokyo, Japan

**Titel: ***Hyperuniformity: a hidden long-range order in random geometric systems*

**Abstract**: "A random geometric system can be both locally similar to

complete spatial randomness and globally homogeneous like a lattice.

Such an anomalous suppression of large-scale density fluctuations is

known as hyperuniformity, and it has profound implications for the

mathematical and physical properties of the system. In these two lectures,

we will take a closer look at the definitions and properties of hyperuniform

random geometric systems, highlighting some of the subtleties of this

fascinating field of research. We will discuss prominent examples as well

as physical implications and relations to different fields of mathematics.

Moreover, we will touch upon the connections to other types of novel

short- and long-range order, like rigidity or quasicrystal symmetries."

Deutsches Zentrum für Luft- und Raumfahrt e.V. (DLR)

Institute for AI-Safety and Security

Ulm, Germany

**Titel: ***Fourier analysis of surface time series*

**Abstract:** "Fourier analysis has been successfully applied in time series analysis with

popular tools of discrete Fourier transform, periodogram, spectral density

function that led to fruitful theoretical and empirical applications in non-

parametric or parametric inference. We have interests in extending Fourier

analysis of time series to that of spatial/spatio-temporal data, or surface

time series in recent terminology. We extend a discrete Fourier transform

and periodogram of time series to those for spatial data and examine

conditions under which they have good asymptotic properties held in time

series cases, i.e. asymptotic independence. As an application of them, we

show theories and practices of spatial CARMA model estimation by Whittle

likelihood. Finally, we extend Fourier analysis of spatial data to that of surface

time series as the goal of this talk. We will introduce functional principal

component analysis as a good alternative to Fourier analysis of surface

time series, by which we can clarify interesting features regarded as advan-

tages and disadvantages of Fourier analysis. Specifically, we will discuss

the extensions of Fourier analysis from time series to surface time series

in the following schedule:

- Review of Fourier analysis of time series
- Spatial Continuous Autoregressive and Moving Average (CARMA) models
- Fourier analysis of spatial data with applications to CARMA model estimation
- Fourier analysis of surface time series
- Functional principal component analysis (fPCA) to surface time series
- Empirical applications"

Tohoku University

Sendai, Japan

**Titel: ***New issues in extremes: imperfect extremes, extremal clustering in high dimension, causality and privacy in extreme value analysis*

**Abstract**: "Modern applications of extreme value analysis require going

beyond analyzing extremes of an i.i.d. sequence or extremes of a weakly

dependent stationary process or a random field in 2 or 3 dimensions.

The extremes may be truncated and some of them may be simply missing.

We will learn that, in some cases, one can still obtain useful information

about the extremes. A particularly difficult case of the curse of dimensionality

occurs when one needs to analyze extremes in a high dimension. This often

requires estimation of a measure on a high-dimensional sphere, and this must

be done based on a relatively small number of imperfect extremes. Finding

low-dimensional structures in the support of this measure is crucial, and we

will learn some techniques for doing so, including the spectral clustering of the

extremes and the kernel PCA approach. In many cases statistical analysis of

non-public data requires public results of the analysis to be privatized in the

sense on revealing certain personal information contained in the data.

The usual approaches for achieving that appear to be unsuitable in the extreme

value analysis. We will learn what techniques can be used to achieve privacy when

working with extremes. Causal statistics aims to detect causal relations between

different random objects. Doing so in extreme value analysis is both important and

difficult. We will learn some new techniques for causal extreme value analysis."

*Cornell University*

*Ithaca, New York, USA*