This is the collection of extended abstracts for the 24 lectures and the open problems session at the third Oberwolfach workshop on Discrete Differential Geometry.

The workshop on Discrete Geometry was attended by 53 participants, many of them young researchers. In 13 survey talks an overview of recent developments in Discrete Geometry was given. These talks were supplemented by 16 ...

A number of remarkable recent developments in many branches of discrete geometry have been presented at the workshop, some of them demonstrating strong interactions with other fields of mathematics (such as algebraic ...

Factorization algebras are a new mathematical approach to quantum field theory. They are related to functorial field theories, another approach to quantum field theory. Factorization algebras also figure in current research ...

The 2007 Oberwolfach meeting “Geometric and Topological Combinatorics” presented a great variety of investigations where topological and algebraic methods are brought into play to solve combinatorial and geometric problems, ...

Spectral theory is a gateway to fundamental insights in geometry and mathematical physics. In recent years the study of spectral problems in discrete spaces has gained enormous momentum. While there are some relations to ...

The geometry of convex domains in Euclidean space plays a central role in several branches of mathematics: functional and harmonic analysis, the theory of PDE, linear programming and, increasingly, in the study of other ...

While arrangements of hyperplanes have been studied in algebra, combinatorics and geometry for a long time, recent discoveries suggest that they (and more generally arrangements of nonlinear subvarieties) play an even more ...

The purpose of this workshop was to bring together researchers with a common interest in the objects mentioned in the title from, respectively, the points of view of toric and tropical geometry, arrangement theory, and ...