Registration open until May 31th.

- 2 Minicourses on Thursday and Friday morning:
- Aernout van Enter, University of Groningen
- Wolfgang König, TU Berlin & Weierstrass Institute Berlin
- Scientific Talks:
- David Dereudre, Université de Lille
- Michael Klatt, Heinrich-Heine-Universität Düsseldorf
- Christof Külske, Ruhr-Universität Bochum
- Günter Last, Karlsruhe Institute of Technology
- James Lutsko, Universite Libre de Bruxelles
- Wioletta Ruszel, Utrecht University
- Alexander Zass, WIAS Berlin

The Conference Dinner will take place on Thursday evening.

Bernoulli Institute for Mathematics, Computer Science and Artificial Intelligence, University of Groningen

Wednesday

13:00-13:30 Registration

13:30-13:45 Welcome Address

13:45-14:45 Scientific Talk: David Dereudre

14:45-15:45 Scientific Talk: Michael Klatt

15:45-16:15 Coffee Break

16:15-17:15 Scientific Talk: Christof Külske

17:15-18:15 Scientific Talk: Günter Last

Thursday

9:00-10:30 Minicourse I: Wolfgang König

10:30-11:00 Coffee Break

11:00-12:30 Minicourse II: Aernout van Enter

12:30-13:30 Lunch Break

13:30-14:30 Scientific Talk: James Lutsko

14:30-15:30 Scientific Talk: Wioletta Ruszel

15:30-16:00 Coffee Break

16:00-17:00 Scientific Talk: Alexander Zass

17:00-18:00 Discussion on Math-Phys Notions

18:30-20:30 Conference Dinner

Friday

9:00-10:30 Minicourse I: Wolfgang König

10:30-11:00 Coffee Break

11:00-12:30 Minicourse II: Aernout van Enter

12:30-13:30 Lunch Snack

The workshop is designed as an inperson meeting without additional streaming. There is an upper bound of 30 participants and preference will be given to members of the SPP2265.

- Luisa Andreis
- Irene Ayuso Ventura
- Friedemann Brockmeyer
- Matteo D'Achille
- David Dereudre
- Matthias Eckardt
- Tejas Iyer
- Benedikt Jahnel
- Jonas Jalowy
- Sanjoy Kumar Jhawar
- Michael Klatt
- Wolfgang König
- Christof Külske
- Vaios Laschos
- Günter Last
- James Lutsko
- Hartmut Löwen
- Robert Patterson
- Wioletta Ruszel
- Cédric Schoonen
- Thais Silva
- András Tóbiás
- Anh Duc Vu
- Marwan Wehaiba El Khazen
- Wei Xu
- Alexander Zass
- Aernout van Enter
- Mandala von Westenholz

Conference Dinner

- Aernout van Enter: Gibbs measures on lattice systems, discreteness and continuity.

I will discuss Gibbs measures and various discrete vs continuous aspects of them. Among other things, I will mention some examples how the study of lattice models can inform that of continuum models. We will discuss various classes of examples of measures where the characterisation of measures as Gibbs measures in terms of continuity properties can be checked and has been the subject of recent studies. In particular we will explore the distinction between Gibbs and g-measures, and the related issue of local and global Markov properties. I will describe how the implementation of the Renormalisation Group, coarse-graining. thinning and decimation transformations on Gibbs measures has led to various obstructions. I will also discuss stochastic evolutions and how modelling `'heating" (raising the temperature) can lead to measures where the notion of temperature becomes ill-defined. - Wolfgang König: Many-body systems and the interacting Bose gas

In the first part, we consider a many-body system with pair interaction of Lennard-Jones type and discuss it from the viewpoint of large-deviations theory for point processes. In a particular regime with high diluteness at low temperature, we are able to derive an explicit picture of the particle configuration. In the second part, we start from the Hamilton operator of the interacting Bose gas and derive a representation in terms of a marked point process. We analyse the free energy with the help of large-deviation theory for marked point processes and discuss the possible appearance of macroscopic structures. - David Dereudre: Number-rigidity and beta-circular Riesz gas

For an inverse temperature beta>0, we define the beta-circular Riesz gas on Rd as any microscopic thermodynamic limit of Gibbs particle systems on the torus interacting via the Riesz potential g(x) = 1/|x|^s. We focus on the non integrable case d-1~~0, the existence of a beta-circular Riesz gas which is NOT number-rigid. Recall that a point process is said number rigid if the number of points in a bounded Borel set Delta is a function of the point configuration outside Delta. It is the first time that the non number-rigidity is proved for a Gibbs point process interacting via a non integrable potential. We follow a statistical physics approach based on the canonical DLR equations.~~ - Michael Klatt: Hyperuniformity in physics and mathematics

What do the eyes of chicken, Coulomb gases, and the prime numbers have in common? In all of these systems, an anomalous suppression of large-scale density fluctuations has been found, known as disordered hyperuniformity. This talk will take a look at this rapidly growing research topic from both the point of view of mathematics and physics. First, this will include a brief overview, from basic definitions to recent progress. Then, as a specific example, the talk will show how a stable matching between perfect order (represented by a lattice) and complete spatial randomness (i.e., the Poisson point process) results in a hyperuniform point process [1]. The talk will also touch upon the relation to rigidity phenomena [2] and higher-order moments of the so-called number distribution [3]. [1] Klatt, Last, Yogeshwaran. Random Struct. Algor. 57, 439 (2020); [2] Klatt, Last. arXiv:2008.10907 (2020); [3] Torquato, Kim, Klatt. Phys. Rev. X 11, 021028 (2021) - Christof Külske: Hidden phase transitions in thinned point clouds

Thinning transformations play an important role in the study of point particles in continuous space. We consider a discrete analogue of such a setup, namely the independent Bernoulli lattice field under projection to isolated sites. This transformation comes with a natural companion, namely the projection to non-isolated sites. We describe recent results on the regularity/irregularity of such maps on the level of infinite-volume measures, and how they are linked to absence/presence of internal phase transitions. Joint work with Nils Engler and Benedikt Jahnel. - Günter Last: Disagreement coupling of finite Gibbs processes

We will present a general version of the so-called disagreement coupling of finite Gibbs processes based on a (non-dynamical) Poisson embedding. The thinning version of this coupling was introduced in a seminal paper by van den Berg and Maes (1994) in a discrete setting and was then extended to the continuum by Hofer-Temmel (2019). Assuming the underlying Poisson process to be subcritical in a suitable sense, we will provide two applications to repulsive Gibbs processes. The first is exponential decorrelation and the second are new uniqueness citeria for Gibbs distributions based on a non-negative pair potential. The talk is based on joint work with Steffen Betsch and Moritz Otto. - James Lutsko: Understanding crystallization using density functional theory and fluctuating hydrodynamics

The theoretical description of any first order phase transition requires an understanding of both thermodynamics and dynamics. Crystallization is particularly challenging due to the inhomogeneous nature of the crystalline state. I will discuss the use of classical Density Functional Theory, which gives a realistic ab initio description of the thermodynamics of solids, in combination with fluctuating hydrodynamics to give a fully nonequilibrium description of crystal nucleation. It will be shown how Classical Nucleation Theory can be recovered from this framework as a natural approximation. Application of the full theory to crystallization of particles interacting via the Lennard-Jones potential leads to several non-classical effects including long-wavelength, low-amplitude density fluctuations as nucleation precursors and a complex, multistep nucleation pathway leading to the solid state. - Wioletta Ruszel: Random field induced order in 2d

In this talk we will discuss random field induced ordering. In particular we shall prove that a classical O(2) model subjected to a weak i.i.d. Gaussian field pointing in a fixed direction exhibits residual magnetic order on the square lattice Z^2 and moreover aligns perpendicular to the random field direction. This type of transition is also referred to as of spin-flop type. Our approach is based on a multi-scale Peierls contour argument developed. This is joint work with N.Crawford (Technion, Israel). - Alexander Zass: Interacting diffusions as marked Gibbs point processes

The motivation for this talk comes from seeing a class of infinite-dimensional diffusions in interaction as marked point configurations: the starting points belong to R^d, the marks are the paths of Langevin diffusions, and the interaction between two diffusions is given by the integration of a pair potential along their paths. In the first part of the talk, we use the entropy method to show the existence of an infinite-volume Gibbs point process for a general mark space and a general interaction with unbounded range. This result can be applied not only to the path-space pair-potential setting, but also to stochastic-geometry multi-body examples, like the area-interaction process. In the second part of the talk, we present a uniqueness result in the general pair-potential setting, obtained by using cluster expansion techniques.

The venue of the Workshop is the Harnack-Haus at Ihnestraße 16-20, 14195 Berlin-Dahlem.

Most of the event will take place in the Meitner-Hörsaal.

The hygiene concept of the venue is available here. The organisers have the right to take additional measures.

The venue is close to the U-Bahn station Freie Universität (Thielplatz), on the U3 line.

To reach it from the Zoologischer Garten train station, you can take the U9 towards Rathaus Steglitz and change at Spichernstrasse.

If you have any questions, please do not hesitate to

at Benedikt.Jahnel@wias-berlin.de.

Homepage of the SPP2265.