Get to know Base4NFDI, a framework that develops, integrates, and sustains basic services for research data management across all domains and disciplines. The Base4NFDI portfolio currently includes eight essential services:

IAM4NFDI – Identity and Access Management PID4NFDI – Persistent Identifier Service TS4NFDI – Terminology Services Jupyter4NFDI – Central JupyterHub service DMP4NFDI – Data (and Software) Management Plans KGI4NFDI – Knowledge Graph Infrastructure nfdi.software – Research Software registry/catalog RDMTraining4NFDI – Training and education service for RDM

This talk will explore how these services can support your research by aligning workflows with the FAIR principles. You’ll also learn about the Base4NFDI service lifecycle - from initialization to ramp-up - and how your community’s needs and contributions can help shape the next generation of basic services.

Lean is a proof assistant which has a large mathematical library containing results from most areas of mathematics. It contains a good foundation to verify current research problems in various areas of mathematics, and enables new collaborative projects. In this talk, I will give an overview of Lean and its mathematical library Mathlib, and describe some of the exciting formalization projects in this area. In particular, I will describe a recently finished project formalizing a generalization of Carleson's 1966 theorem in harmonic analysis, about the pointwise convergence of Fourier series. This is a major result in harmonic analysis with a difficult proof, and this result has been fully verified in Lean.

The formalization was a large collaborative project with 13 main contributors.

I will present recent advances in applying AI-based methods to interpret genetic sequences, with a particular focus on identifying disease-causing mutations. In addition, I will share insights from establishing GHGA—the German Human Genome-Phenome Archive—an NFDI initiative dedicated to the secure sharing of human genomic data for secondary research.

In this talk we are going to compare two approaches (quenched and annealed) for obtaining invariant measures in open random dynamical systems. The quenched approach employs thermodynamic formalism techniques applied to a weighted transfer operator, constructing conditionally invariant measures for each fiber of the system and deriving a corresponding fiberwise limit invariant measure. On the other hand, the annealed approach relies on spectral analysis of the stochastic Koopman operator to derive a state-space invariant measure for the open system. We focus on establishing a correspondence theorem linking the results of both methods and introducing an annealed framework for a weighted transfer operator on the state space through which one can obtain an invariant measure that is absolutely continuous with respect to the conformal measure of the open system. We lastly discuss large deviation principles for the empirical measures of the killed process under both the annealed Koopman and weighted transfer operators, highlighting the role of spectral gaps in determining fluctuation behavior.

Nonlinear acoustic phenomena are highly relevant in many applications, from medical imaging to industrial cleaning. This talk first provides an overview of how the modeling equations arise from fundamental physical principles, such as the Navier–Stokes equations, and how standard models can be extended, for example, by incorporating fractional damping due to viscoelasticity. Then, while second-order wave equations are standard, we focus on a first-order-in-time formulation and highlight key aspects of a proof of existence and uniqueness of solutions in suitable Sobolev spaces.

Higher-order networks have become a popular tool in the network science community to model dynamics such as synchronization and diffusion. The linearized system often depends on a Laplacian operator and its spectral properties. We introduce a Laplacian operator for uniform hypergraphs and study the limiting operator for an increasing sequence of dense uniform hypergraphs using the theory of graph limits. Although a theory of dense hypergraph limits has been developed by Elek and Szegedy, and independently Zhao, not much of its implications to spectral properties is known. We show that a weaker notion of convergence for the sequence of hypergraphs is sufficient to obtain pointwise convergence of the spectrum of the Laplacians.

TBA

A central issue in modern Galois theory is the profinite inverse Galois problem, which asks how to characterize absolute Galois groups of fields among all profinite groups. While an answer to this question is unknown, even conjecturally, several necessary conditions for a profinite group to qualify as an absolute Galois group have been established. The most classical result in this direction is due to Artin and Schreier, who proved that every non-trivial finite subgroup of an absolute Galois group is cyclic of order 2. A much deeper necessary condition is the Bloch-Kato conjecture, now a theorem due to Voevodsky and Rost, which in particular implies that the mod p cohomology ring of an absolute Galois group of a field containing a primitive p-th root of unity is generated in degree 1 with relations in degree 2. In the lecture, we will discuss restrictions to the profinite inverse Galois problem coming from the embedding problem with abelian kernel. This is a joint work with Federico Scavia.

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Invited by Prof. Nikita Geldhauser