2nd Annual Conference of
Random Geometric Systems

The conference will start in the afternoon of Monday 27 March and will end on Thursday 30 March after lunch. All lectures will take place at the DLR premises in Cologne-Porz. The programme is available below.

Invited speakers

Wilfrid Kendall

Wilfrid Kendall

University of Warwick,
United Kingdom

Emeritus professor
Department of Statistics

Joseph Brader

Joseph Brader

University of Fribourg,

Department of Physics

Salvatore Torquato

Salvatore Torquato

Princeton University,
United States of America

Department of Chemistry, Department of Physics
Princeton Materials Institute and Program in Applied and Computational Mathematics


Invited talks

Scale-invariant Spatial Random Networks everywhere?

Wilfrid Kendall

Scale-invariant random spatial networks (SIRSN) are remarkable random structures providing patterns of random routes that satisfy some very plausible axioms (see Aldous and Ganesan 2013, Aldous 2014) including scale-invariance, as found empirically in online maps. It is not a priori apparent that such networks can exist at all! Nevertheless Aldous (2014) constructed a SIRSN based on a dense dyadic mesh, and WSK and Kahn showed how to build a SIRSN from a dense Poisson line process. But both these constructions involve infinitely long linear paths, and in particular do not easily admit local influences. Can one do better? I shall discuss recent work showing that SIRSN can arise under far less stringent conditions, based on line segments or even stiff fibres.

Superadiabatic Dynamical Density Functional Theory for interacting Brownian systems

Joseph Brader

When a system of interacting particles is subjected to an external field, then their average one-body density becomes spatially varying. The primary tool for describing equilibrium states is the density functional theory (DFT), a well-established approach in the field of statistical mechanics. If the particles undergo Brownian dynamics, then the response of the one-body density to a time dependent external field is commonly treated using a simple dynamical extension of the equilibrium theory - the classical dynamical density functional theory (DDFT). Although widely used, this approach can often provide only a qualitative description and even fails completely in many situations of interest. However, improving the theory has turned out to be very difficult.
In this talk I will introduce and discuss a recently developed 'superadiabatic-DDFT' which identifies clearly and intuitively how to go beyond standard DDFT and which promises to become an essential method in future liquid-state theories.

Hyperuniformity of Point Processes and Its Generalizations

Salvatore Torquato (online)

The study of hyperuniform states of matter is an emerging multidisciplinary field, influencing and linking developments across the physical sciences, mathematics and biology. A hyperuniform point process in d-dimensional Euclidean space is characterized by an anomalous suppression of large-scale density fluctuations relative to those in typical disordered systems, such as liquids and amorphous solids. As such, the hyperuniformity concept generalizes the traditional notion of long-range order to include not only all perfect crystals and quasicrystals, but also exotic disordered states of matter, thus providing a unified framework to quantitatively categorize such phases of matter. Disordered hyperuniform states have attracted great attention across many fields over the last two decades because they have the character of crystals on large length scales but are isotropic like liquids. I will review briefly the hyperuniformity concept, including generalizations to two-phase media (random sets), scalar fields and vector fields. Then I will give an overview of how hyperuniformity is linked to the Epstein zeta function of number theory, sphere packing problems, eigenvalues of random matrices, nontrivial zeros of the Riemann zeta function, spatial distribution of the prime numbers, free fermions, Laughlin's incompressible quantum states, and photoreceptor mosaics in avian retina. Finally, I will show how to generate disordered hyperuniform two-phase media that are rigorously disordered and hyperuniform.


Click here to download this schedule as a PDF file.

Monday (27/03) Tuesday (28/03) Wednesday (29/03) Thursday (30/03)
09:00–09:30 Registration
09:30–10:00 P17: Michael Andreas Klatt
When can we uniquely map a classical density to a time-dependent potential?
P11: Daniel Hug, Dominik Pabst
Integral geometry in spaces of constant curvature and applications to stochastic geometry
P21: Matthias Sperl
Minimal models for glassy dynamics and jammed packings
10:30–11:00 Coffee break Coffee break Coffee break
11:00–11:30 Invited talk: Joseph Brader, Salomée Tschopp
Superadiabatic dynamical density functional theory for interacting Brownian systems
Invited talk: Wilfrid Kendall
Scale-invariant spatial random networks everywhere?
P19: Céline Kerriou, Peter Mörters
Large deviations for the edge count in scale-free geometric graphs
11:30–12:00 P25: Marco Seiler
Contact processes on evolving graphs
12:00–12:30 Lunch Lunch break Lunch break P07: Pia Steinmeyer
Dynamics of contact processes on simplicial complexes
12:30–13:00 Lunch
13:30–14:00 Registration P10: Martin Huesmann, Francesco Mattesini
Optimal transport and balancing allocations
P18: Christian Mönch
Inhomogeneous long range models: an overview
14:00–14:30 Welcome address
14:30–15:00 P05: Bingxiao Liu
Random polynomials and random Kähler geometry
P06: Jonas Jalowy, Bastian Müller
Optimal transport for stationary point processes
P09: Alejandro Caicedo
Critical behaviour of the weight-dependent random connection model
15:30–16:00 Coffee break Coffee break Coffee break
16:00–16:30 Invited talk: Salvatore Torquato (Online)
Hyperuniformity of point processes and its generalizations
P23: Anna Gusakova, Christoph Thäle
Concentration and cumulants for stabilizing functionals on point processes
P12: Karin Jacobs, Jens Uwe Neurohr
Morphometric roughness of nanostructured surfaces
17:00–17:15 Coffee break Coffee break Coffee break
17:15–17:45 P16: Günter Last
A genuine test for hyperuniformity
P15: Lorenzo Dello Schiavo, Eva Kopfer
Random Riemannian geometry
P04: Alexander Drewitz, Karl Olof Hallqvist Elias, Benedikt Jahnel, Wolfgang König, Alexander Zass
The statistical mechanics of the interlacement point process
17:45–18:15 Guest: Steffen Winter
Ballistic aggregation
18:15–open Conference dinner at Jaumann's hotel



The conference will take place at the DLR site in Cologne-Porz.


The organisers have reserved hotel rooms at Jaumann's Hotel. The conference dinner is held at Jaumann's hotel.


  • Birkner, Matthias (Universität Mainz)
  • Brader, Joseph (University of Fribourg)
  • Caicedo, Alejandro (LMU München)
  • Dello Schiavo, Lorenzo (Institute of Science and Technology Austria)
  • Disertori, Margherita (Universität Bonn)
  • Drewitz, Alexander (Universität Köln)
  • Düsterbeck, Marilyn (Universität Köln)
  • Erbar, Matthias (Universität Bielefeld)
  • Ganguly, Saswati (DLR MP)
  • Gracar, Peter (University of Cologne)
  • Gusakova, Anna (Universität Münster)
  • Hafer, Bernhard (Universität Osnabrück)
  • Hallqvist Elias, Karl Olof (Universität Köln)
  • Huesmann, Martin (Universität Münster)
  • Hug, Daniel (Karlsruhe Institute of Technology)
  • Jacobs, Karin [Online] (Saarland University)
  • Jahnel, Benedikt (TU Braunschweig/ WIAS Berlin)
  • Jalowy, Jonas (Universität Münster)
  • Jhawar, Sanjoy Kumar (WIAS Berlin)
  • de Jonge, Lianne (Universität Osnabrück)
  • Kendall, Wilfrid (University of Warwik)
  • Kerriou, Céline (Universität zu Köln)
  • Klass, Paul (University of Cologne)
  • Klatt, Michael (HHU Düsseldorf)
  • Klymovskiy, Anton (Universität Würzburg)
  • König, Wolfgang (WIAS Berlin)
  • Kopfer, Eva (Universität Bonn)
  • Kranz, Till (Uni Köln)
  • Last, Günter (Karlsruhe Institute of Technology)
  • Liu, Bingxiao (Universität Köln)
  • Löwen, Hartmut (HHU Düsseldorf)
  • Magnanini, Elena (WIAS Berlin)
  • Mattesini, Francesco (WWU Münster)
  • Mecke, Klaus (FAU Erlangen-Nürnberg)
  • Merkl, Franz (LMU München)
  • Mönch, Christian (JGU Mainz/ Universität Augsburg)
  • Mörters, Peter (Uni Köln)
  • Mu, Yingxin (Universität Leipzig)
  • Müller, Bastian (Universität Münster)
  • Neumann, Jan Philipp (LMU München)
  • Neurohr, Jens Uwe (Universität Saarland)
  • Pabst, Dominik (Karlsruhe Institute of Technology)
  • Reitzner, Matthias (Universität Osnabrück)
  • Robinson, Joshua (Universität Mainz)
  • Rolles, Silke (Technische Universität München)
  • Sapozhnikov, Artem (Universität Leipzig)
  • Seiler, Marco (Frankfurt Institute for Advanced Studies)
  • Sperl, Matthias (DLR MP)
  • Steinmeyer, Pia (Technische Universität München)
  • Strotmann, Anna (Universität Osnabrück)
  • Thäle, Christoph (RUB)
  • Torquato, Salvatore [Online] (Princeton University)
  • Tschopp, Salomée (University of Fribourg)
  • van Belle, Thomas (Universität Duisburg-Essen)
  • Wagner, Stefan (LMU München)
  • Winter, Steffen (Karlsruhe Institute of Technology)
  • Zakhar, Kabluchko (Universität Münster)
  • Zass, Alexander (WIAS Berlin)


If you have any questions, please do not hesitate to send us an email at contact@random-geometric-systems-cologne.de.

Local organisers

  • Dr. Michael Klatt
  • Dr. Till Kranz
  • Prof. Dr. Matthias Sperl