The logarithmic Brunn-Minkowski conjecture is a fascinating open problem on the borderline of convex geometry, differential geometry and non-linear PDE's.

The aim of this workshop is to discuss and make progress on open problems related to properties and applications of asymptotic tensor parameters.

Jointly organized with the RTG Berlin-Hannover "From geometry to numbers: Moduli, Hodge theory, rational points" financed by the DFG. Part of the thematic semester Algebraic Geometry (August-December 2026) hosted by the Erdős Center.

The Workshop will highlight the enumerative and birational geometry of the moduli spaces of curves, abelian varieties and K3 surfaces, etc.

The 4 lecture series of the School will focus on modern techniques in the classification theory of higher dimensional algebraic varieties, highlighting connections to K-stability and singularity theory. Part of the thematic semester Algebraic Geometry (August-December 2026) hosted by the Erdős Center.

The Workshop will focus on modern techniques in the classification theory of higher dimensional algebraic varieties, highlighting connections to K-stability and singularity theory. Part of the thematic semester Algebraic Geometry (August-December 2026) hosted by the Erdős Center.

This workshop will showcase some classical as well as emerging areas of combinatorial algebraic geometry, alongside applications to other areas of science outside of core mathematics, including theoretical physics and systems biology.

Ordered structures arise naturally in many problems and proofs in discrete geometry. For example, the unit distance problem for convex polygons stimulated the extremal theory of 0–1 matrices. Similarly, the study of point-set configurations, known as the study of order types, plays an important role in geometric problems such as rectilinear crossing numbers and the happy ending problem.

Ordered structures arise naturally in many problems and proofs in discrete geometry. For example, the unit distance problem for convex polygons stimulated the extremal theory of 0–1 matrices. Similarly, the study of point-set configurations, known as the study of order types, plays an important role in geometric problems such as rectilinear crossing numbers and the happy ending problem.

In extremal, probabilistic, and structural combinatorics, many objects and arguments possess natural orderings. For example, the Erdős–Hajnal stepping-up argument for hypergraph Ramsey numbers processes vertices one by one according to a fixed order. Similarly, the resolution of the Stanley–Wilf conjecture relies on 0–1 matrices, which may be viewed loosely as ordered analogues of bipartite graphs.