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Can spatial fungal networks be informative for both ecology and network science?

Filamentous organisms grow as adaptive biological spatial networks. These networks are in a continuous balance of two main forces: exploration of the habitat to acquire scarce resources, and the transport of those resources within the developing network. In addition, the construction of the network has to be kept a low cost while taking into account the risk of damage by predation. Such network optimization is not unique to biological systems, but is relevant to transport networks across many domains. Thus, this collaborative project between FU-Berlin and University of Oxford represents the beginning of a research program that aims at: First, setting up protocols for the use of network analysis to characterize spatial networks formed by both macroscopic and microscopic filamentous organisms (e.g. Fungi), and determining the fitness and ecological consequences of different structure of the networks. Second, extracting biologically-inspired algorithms that lead to optimized network formation in fungi and discuss their utility in other network domains. This information is critical to demonstrate that we have a viable and scalable pipeline for the measurement of such properties as well provide preliminary evidence of the usefulness of studying network properties of fungi.

Given a number field K, it is natural to ask whether it has a finite extension with ideal class number one. This question can be translated into a fundamental question in class field theory, namely the class field tower problem. In this talk, we are going to discuss this problem as well as its solution due to Golod and Shafarevich using methods of group cohomology.
 

Gromov hyperbolicity is a property to metric spaces that generalises the notion of negative curvature for manifolds.
After an introduction about these spaces, we will explain the construction of horocyclic products related to lamplighter groups, Baumslag solitar groups and the Sol geometry.
We will describe the shape of geodesics in them, and present rigidity results on their quasi-isometries due to Farb, Mosher, Eskin, Fisher and Whyte.

Right-angled Artin groups (RAAGs) were first introduced in the 70s by Baudisch and further developed in the 80s by Droms.
They have attracted much attention in Geometric Group Theory. One of the many reasons is that it has been shown that all hyperbolic 3-manifold groups are virtually finitely presented subgroups of RAAGs.
In the first part of the talk, I will discuss some of their interesting properties. I will explain some of their relations with manifold groups and their importance in finiteness conditions for groups.
In the second part, I will focus on my PhD project concerning subgroups of direct products of RAAGs.

The automorphism group of a d-regular tree is a topological group with many interesting features. A nice thing about this group is that while some of its features are highly non-trivial (e.g., the existence of infinitely many pairwise non-conjugate simple subgroups), often the ideas involved in the proofs are fairly intuitive and geometric. 
I will present a proof for the fact that the outer automorphism group of (Aut(T)) is trivial. This is original joint work with Gil Goffer, but as is often the case in this area, was already proven by Bass-Lubotzky 20 years ago. I will mainly use this talk to hint at how algebra, topology and geometry all play a role when working with Aut(T).
 

Whitehead published two papers in 1936 on free groups. Both concerned decision problems for equivalence of (sets of) elements under automorphisms. The first focused on primitive elements (those that appear in some basis), the second looked at arbitrary sets of elements. While both of the resulting algorithms are combinatorial, Whitehead's proofs that these algorithms actually work involve some nice manipulation of surfaces in 3-manifolds. We will have a look at how this works for primitive elements. I'll outline some generalizations due to Culler-Vogtmann, Gertsen, and Stallings, and if we have time talk about how it fits in with some of my current work.

We will be discussing a Fourier-analytic approach
to optimal matching between independent samples, with
an elementary proof of the Ajtai-Komlos-Tusnady theorem.
The talk is based on a joint work with Michel Ledoux.

The notion of emergence is at the core of many of the most challenging open scientific questions, being so much a cause of wonder as a perennial source of philosophical headaches. Two classes of emergent phenomena are usually distinguished: strong emergence, which corresponds to supervenient properties with irreducible causal power; and weak emergence, which are properties generated by the lower levels in such "complicated" ways that they can only be derived by exhaustive simulation. While weak emergence is generally accepted, a large portion of the scientific community considers causal emergence to be either impossible, logically inconsistent, or scientifically irrelevant.

In this talk we present a novel, quantitative framework that assesses emergence by studying the high-order interactions of the system's dynamics. By leveraging the Integrated Information Decomposition (ΦID) framework [1], our approach distinguishes two types of emergent phenomena: downward causation, where macroscopic variables determine the future of microscopic degrees of freedom; and causal decoupling, where macroscopic variables influence other macroscopic variables without affecting their corresponding microscopic constituents. Our framework also provides practical tools that are applicable on a range of scenarios of practical interest, enabling to test -- and possibly reject -- hypotheses about emergence in a data-driven fashion. We illustrate our findings by discussing minimal examples of emergent behaviour, and present a few case studies of systems with emergent dynamics, including Conway’s Game of Life, neural population coding, and flocking models.
[1] Mediano, Pedro AM, Fernando Rosas, Robin L. Carhart-Harris, Anil K. Seth, and Adam B. Barrett. "Beyond integrated information: A taxonomy of information dynamics phenomena." arXiv preprint arXiv:1909.02297 (2019).