A growing and impactful area of computational mathematics and numerical analysis is the solution of PDEs modeled from underlying geometric principles. This field covers a broad range of PDE problems, including geometric ...

The workshop "Model Theory and Arithmetic'' brought together communities working in model theory (a subfield of mathematical logic) and in number theory, in particular arithmetic geometry. There has been a flurry of new ...

Combinatorics is a thriving branch of Mathematics with strong links to other areas of Mathematics and the sciences. Many of the modern techniques employed in Combinatorics draw on diverse ideas from Probability, Analysis, ...

Many fundamental mathematical structures, such as the rationals or the random graph, are homogeneous, meaning that local isomorphisms extend to global automorphisms. Such structures arise as limits of classes of finite ...

The approximation of unknown functions from scattered, possibly high-dimensional data is central to many scientific applications. Advances in data acquisition have driven the need for flexible nonlinear models, including ...

Functional inequalities form a unifying theme across a wide spectrum of modern analysis, geometry, and probability. They encode deep geometric and analytic information - for instance through Poincaré, log-Sobolev, ...

The workshop focused on various directions of arithmetic statistics in algebra and number theory. These include statistical problems for random polynomials and varieties, probabilistic Galois theory, and counting and ...

Artificial neural networks (ANNs) have emerged as a powerful tool in modern machine learning, yet their mathematical foundations remain only partially understood. A key challenge is the inherently stochastic nature of ANN ...

The resurgent analysis of asymptotic series has found diverse applications and led to profound insights into our understanding of enumerative geometry, difference equations, and quantum modular forms. Consequently, ...

This Oberwolfach Arbeitsgemeinschaft focuses on the mathematical analysis of quantum many-body systems. Of particular interest is the ground state energy of dilute quantum gases, either fermions or bosons, and its low-density ...