Fall School Lecturers

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


Theme to be announced

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

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