Random Geometric Systems

The schedule is available below. You can also download it as a .pdf here.

The conference will start on the afternoon of Monday, April 11, and end after lunch on Thursday, April 14. The programme will include:

• Two guest talks on Tuesday and Wednesday morning
• 14 project talks
• A special session on Tuesday afternoon

All lectures will take place in the Hahn hall, the open problem session in the Goethe hall, and all coffee breaks in the Meitner hall.
The conference dinner will take place at the conference venue on Tuesday evening.

Guest speakers

Pierre Calka

Raphaël Salem Mathematics Laboratory, University of Rouen

Maximal fluctuations of random convex hulls (Click for abstract)

This talk deals with the random polytope constructed as the convex hull of a random point set constituted with independent and uniformly distributed points in a smooth convex body of the d-dimensional Euclidean space. In particular, we are interested in its asymptotic behavior when the size of the random input goes to infinity. We show that the rescaled Hausdorff distance between the random polytope and the initial convex body and rescaled maximal facet area follow asymptotically a Gumbel extreme value distribution. These two quantities make explicit the maximal fluctuations of the boundary of the random polytope in the radial and longitudinal directions. Surprisingly, these fluctuations are similar to those observed for a large variety of random interfaces in probability theory (subcritical random cluster model, oriented random walks...).
We start with a basic overview on random polytopes and we then intend to describe the main tools for proving our results, including the introduction of a so-called typical facet, the use of integral geometry formulas or the blocking method in extreme value theory. We will in particular emphasize the structural differences between the two convergences.
This is joint work with J. E. Yukich (Lehigh University, USA).

Jean-Baptiste Gouéré

Denis Poisson Institute, University of Tours

Percolation threshold in the Poisson-Boolean model (Click for abstract)

Let K be a convex, compact and symmetric subset of the Euclidean d-dimension space. Let ρ be a positive random variable. We consider percolation in the Poisson-Boolean model where the grains are independent copies of ρK. The percolation threshold depends on d, K and on the distribution of ρ. We will present some conjectures on this dependence and give some results on the behavior of the threshold when the dimension d tends to infinity.
This is joint work with F. Labéy.

Aim of the conference

Project talks

There will be 14 project presentations, of 45 (or 60) minutes each.
These must take into account the highly heterogeneous nature of the SPP and try to overcome the "language barriers".
In particular, each talk should give an extensive overview of the background, motivation, possible connections and goals of the project. The talk may, for example, be divided into a survey by a PI and a result presentation of a young researcher.

Special session

On Tuesday afternoon, there are going to be 2 parallel sessions:

• Young researchers will be able to attend a series of crash courses, where postdocs will present fundamental topics of the SPP.
• In problem sessions, more experienced researchers will discuss open research questions coming, for example, from modern physics.

Monday

13:00-14:00 Registration
14:00-14:30 Welcome address
14:30-15:30 P. Mörters and C. Kerriou (P19)
Condensation in random geometric graphs. Localisation and delocalisation in a geometric random graph with excess edges
15:30-16:30 Coffee break
16:30-17:15 S. Jansen (P13)
Towards renormalization for Gibbs point processes
17:15-18:00 A. Klimovsky and T. van Belle (P08)
Information exchange on evolving networks

Tuesday

8:00-9:00 Registration
9:00-10:30 Pierre Calka

10:30-11:00 Coffee break
11:00-11:45 C. Kühn (P07)
Dynamics of contact processes on simplicial complexes
11:45-12:30 K.-T. Sturm (P15)
Conformally invariant random fields, quantum Liouville measures, and random Paneitz operators on Riemannian manifolds of even dimension
12:30-14:00 Lunch break
14:00-16:00 Special Sessions
16:00-16:30 Coffee break
16:30-18:00 Special Sessions
18:00-20:00 Conference dinner

Wednesday

9:00-10:30 Jean-Baptiste Gouéré

10:30-11:00 Coffee break
11:00-12:00 L. Andreis, W. König and T. Iyer (P01)
Spatial coagulation and gelation
12:00-13:00 N. Gantert and A. Callegaro (P02)
Branching random walks: some recent results and open questions

13:00-14:30 Lunch break
14:30-15:15 F. Merkl and S. Rolles (P03)
Emergence of macroscopic phenomena in the non-linear hyperbolic supersymmetric sigma model
15:15-16:00 G. Last (P16)
Hyperuniform point processes
16:00-16:30 Coffee break
16:30-17:15 A. Sapozhnikov (P20)
Connectivity properties of Brownian interlacements and its vacant set

Thursday

09:00-09:45 Z. Kabluchko (P14)
Angles of random simplices
09:45-10:30 C. Pokalyuk (P25)
Pathogens spreading on random networks
10:30-11:00 Coffee break
11:00-12:00 L. Taggi and A. Quitmann (P22)
Macroscopic loops in the Bose gas and related models
12:00-13:00 A. Winter and O. Angtuncio-Hernández (P24)
The uniform tree and the uniform spanning tree on the high-dimensional torus

13:00-14:00 Lunch snack
End of the conference

The problem sessions will include the following topics:

• Continuum statistical mechanics (S. Jansen)
• Random geometric structures generated by tumor growth (C. Pokalyuk)
• Self-Interacting random walks (P. Tarrès)
• Nonreciprocal interactions (H. Löwen)

The schedule for the crash courses is as follows:
14:00-14:45 Continuum Percolation (P. Gracar)
14:45-15:30 Co-polyharmonic Gaussian fields and Liouville Gravity Quantum measures (L. Dello Schiavo, R. Herry, E. Kopfer)
15:30-16:00 "Where there is matter, there is geometry" (M. Klatt)
16:30-17:15 Marked Gibbs point processes (A. Zass)
17:15-18:00 Phase transitions and the reflection positivity method (L. Taggi)