List of Plenary Speakers
Titel: From Generative Models to Hyperuniformity Estimation for Point Processes
Abstract: A single realization of a spatial process may, in principle, encode its full distri-
bution through ergodicity—but how can this information be extracted from finite data?
I will present recent work on learning and generating point processes from a single sample
using particle-based gradient descent and multiscale descriptors, and on estimating
hyperuniformity through wavelet and spectral methods. These approaches emphasize the
role of multiscale geometry in connecting stochastic modeling, statistical inference, and
topological data analysis.
Titel: Order k: Delaunay and Brillouin
Abstract: The k-th Brillouin zone of a point A in a locally finite set consists of the locations
at which A is the k-nearest point in the set. The first Brillouin zone is also
known as the Voronoi domain of A. In the relatively straightforward case of a
lattice, all Brillouin zones have the same volume, and their regions can be used
to tile one another.
This talk is an attempt to review related solved and unsolved questions in
discrete geometry, with an eye on what happens when the points are not quite
as regularly spaced as in a lattice.
Titel: Strongly correlated particle systems: a toolbox for machine intelligence
Abstract: The classical paradigm of randomness in the sciences is that of i.i.d. random
variables, and going beyond i.i.d. is often considered a difficulty and a challenge
to be overcome. In this talk, we will explore a new perspective, wherein strongly
constrained random systems in fact help to understand fundamental problems
in machine learning. In particular, we will discuss strongly correlated particle
systems that are well-motivated from statistical and quantum physics, including
determinantal probability measures. These will be used to shed important light
on questions of fundamental interest in learning theory, focusing on applications
to novel sampling techniques and advances in stochastic gradient descent.
The talk is based in part on work on Gaussian determinantal processes, negatively
dependent coresets, determinantal minibatch sampling for stochastic gradient
descent, and negative dependence as a toolbox for machine learning.
Titel: Persistence of asymptotic variance under transport
Abstract: We consider invariant transports of stationary random measures on Euclidean
space. Under natural mixing criteria, based on two-point Palm probabilities, we
show that the asymptotic variance does not change. The mixing assumptions can
be checked, for instance, by combining factorial moment expansion and stopping
set techniques. In the second part of the lecture we will focus on hyperuniformity,
that is, on a vanishing asymptotic variance. By constructing suitable transports
from a hyperuniform source we are able to rigorously establish hyperuniformity
for many point processes and random measures. In particular, we define a
hyperuniformer that turns any ergodic point process with finite intensity into
a hyperuniform process by randomizing each point within its cell of a fair
partition. The lecture is based on joint work with Michael Klatt, Luca Lotz and D.
Yogeshwaran.
Titel: Characterizing Distributions of Local Structures in Hyperuniform Patterns via Persistent Homology
Abstract: Hyperuniformity refers to the suppression of density fluctuations at large scales.
Its classical definition uses information at the largest accessible scales, such as
the scaling of the number variance with large sampling window sizes or the
structure factor at small wave numbers. At the same time, hyperuniform (HU)
patterns exhibit distinctive local arrangements that are not captured by these
global measures. This presentation illustrates how local features in HU point
clouds and fields can be characterized using persistent homology, along with
key implications and applications.
Geometric and topological features across scales are encoded in persistence
diagrams, and their similarities are quantified using Wasserstein distances.
We find that varying HU characteristics leads to patterns with systematically
different topological signatures. These features are preserved in subsets of
such patterns, establishing a direct link between idealized infinite systems and
experimentally or numerically accessible configurations. We further apply this
framework to numerical solutions of the Cahn–Hilliard equation, a canonical
model for generating HU scalar fields, discussing the characterization of self-
similarity and scaling properties of its solutions at finite interface thicknesses.
Finally, concepts for the detection and inverse design of HU patterns leveraging
persistent homology are outlined, showing that global HU properties can be
inferred from distributions of local topological features in both point clouds and
fields. The conclusions will highlight current challenges and perspectives, as
well as potential further applications
Titel: Recent results on Anderson localization and photonic band gap properties in stealthy hyperuniform media
Abstract: Anderson localization in one dimension is the phenomenon where waves propa-
gating through a disordered medium become exponentially localized in space,
suppressing transport and turning the system into an effective insulator for that
wave type, with the remarkable feature this occurs regardless of how weak the
disorder is. This talk will describe how this textbook view must be modified for
disordered stealthy hyperuniform one-dimensional media due to their possessing
correlated disorder. We will also comment on gyromorphs, a recently proposed
disordered medium in two and higher dimensions which has been proposed as
an alternative to hyperuniformity with superior wave propagation properties.
Titel: Disordered Ultradense Stealthy Hyperuniform Packings as a SAT–UNSAT Transition
Abstract: Stealthy hyperuniform point processes are those whose structure factor S(k)
vanishes over a finite exclusion region about the origin in reciprocal space
(i.e., S(k) = 0 for 0 < k < K) and therefore represent a strong form of
hyperuniformity in which density fluctuations are anomalously suppressed
from intermediate to infinite wavelengths [1]. The disordered variants have
been shown to be the ground states of long-ranged pair potentials for the
“stealthiness” parameter χ between zero and 1/2. Sphere packings derived from
disordered stealthy hyperuniform point configurations generated from numerical
simulations have novel physical properties with advantages over their crystalline
counterparts. However, the success rate to find allowable packing configurations
with even moderate values of the packing fraction ϕ falls off rapidly with the
number of particles within the fundamental cell.
Disordered ultradense stealthy packings are a recently introduced subclass of
stealthy systems in which particles are subject to both the standard long-range
constraints on density fluctuations and a short-range soft-core interparticle
repulsive interaction [2]. At fixed χ, ϕ can be increased to its maximum value,
ϕmax, beyond which the ground state ceases to exist, which can be viewed as a
satisfiable–unsatisfiable (SAT–UNSAT) transition [3]. I will discuss these recent
developments.
References. [1] S. Torquato, G. Zhang, and F. H. Stillinger, Physical Review X
5, 021020 (2015). [2] J. Kim and S. Torquato, The Journal of Chemical Physics
163, 024902 (2025). [3] S. Torquato and J. Kim, Soft Matter 21, 4898–4907
(2025).