# Wachspress Geometry

The workshop will take place on Tuesday and Wednesday, September 24 and 25, in SG 111 in the SeminargebĂ¤ude of the University of Leipzig right next to the Mensa am Park and the math department in the Augusteum.The workshop is supported by the DFG Priority Program SPP 2458 Combinatorial Synergies.

**Wachspress Geometry**is a young subject built on a circle of ideas that are currently emerging from Wachspress's work on generalized barycentric coordinates. At its core it is the study of

*Wachspress objects*, a family of closely related mathematical objects defined on convex polytopes. A central object, the

*Wachspress coordinates*, have their origin as generalized barycentric coordinates in geometric modelling. They have resurfaced in a surprising variety of contexts, including algebraic and convex geometry as well as polyhedral combinatorics and statistics. The

*adjoint polynomial*associated to Wachspress coordinates is the main ingredient for the canonical form of a convex polytope. As such it establishes Wachspress Geometry as one of the best understood instances of Positive Geometry. Most recently, Wachspress coordinates were also found to derive from a polytope parameter of higher rank now known as the

*Izmestiev matrix*, which in turn links the subject to rigidity theory and spectral graph theory.

The workshop has the following goals:

- to introduce Wachspress Geometry with its various constructions, approaches and open questions to a broader audience and to present its connection to Positive Geometry;
- to bring together experts on the various aspects of Wachspress Geometry to explore the interactions between their perspectives and to work towards a unifying explanation for the ubiquity of Wachspress phenomena across mathematics;
- to join experts on Wachspress Geometry and Positive Geometry to together develop the tools of Wachspress Geometry beyond convex polytopes.

## Organizers

Rainer SinnMartin Winter

## Confirmed Speakers

KathlĂ©n KohnElia Mazzucchelli

Dmitrii Pavlov

Raman Sanyal

Bernd Schulze

Bernd Sturmfels

Louis Theran