## About

**A sound theory for analysing the complex behaviour of dynamic networks**

The aim of the EU-funded DYNASNET project is to engage leading experts in network science and graph theory to build a mathematically sound theory of dynamic networks.

## News

### Report on the Focused Workshop on Combinatorics of Integer Programming

The Focused Workshop on Combinatorics of Integer Programming took place at the Erdős Center in the period from August 14 to 25 in association with the Dynasnet 8100115 Project

### Report on Focused Workshop on Networks and Their Limits

### László Lovász receives the Prima Primissima Award

## Latest Publications

### Problems and results on 1-cross-intersecting set pair systems

### Random interlacement is a factor of i.i.d.

The random interlacement point process (introduced in [47], generalized in [ 50 ]) is a Poisson point process on the space of labeled doubly infinite nearest neighbour trajectories modulo time-shift on a transient graph G. We show that the random interlacement point process on any transient transitive graph G is a factor of i.i.d., i.e., it can be constructed from a family of i.i.d. random variables indexed by vertices of the graph via an equivariant measurable map.

### State-controlled epidemic in a game against a novel pathogen

The pandemic reminded us that the pathogen evolution still has a serious effect on human societies. States, however, can prepare themselves for the emergence of a novel pathogen with unknown characteristics by analysing potential scenarios. Game theory offers such an appropriate tool.

## Researchers

Samuel Braunfeld is a postdoctoral researcher at Charles University, working on model theory and combinatorics. He studies the model-theoretic complexity of infinite structures, such as graphs, and how that is reflected in the complexity of large finite structures. Additionally, he works on Fraisse theory and structural Ramsey theory.

I work on graph limits of sequences of intermediate density

In spring 2022, I was helping to run the summer school Mathematics of Large Networks, organised by Márton Karsai, János Kertész, László Lovász, and Balázs Rath, as well as the summer school Graphs, Groups, Stochastic Processes that both took place in the Erdős Center within the semester of Large Networks and their Limits.

I am studying optimal transport related geometric properties of Markov processes with a particular emphasis on the Ollivier-Ricci curvature of graph limits.

## Events

There will be a Dynasnet Retreat in Visegrád in February, 2024.