The proximal Galerkin finite element method is a high-order, low iteration complexity,
nonlinear numerical method that preserves the geometric and algebraic structure of …

Gibbs manifolds are images of affine spaces of symmetric matrices under the exponential
map. They arise in applications such as optimization, statistics and quantum physics, where …

We demonstrate the relevance of an algorithm called generalized iterative scaling (GIS) or
simultaneous multiplicative algebraic reconstruction technique (SMART) and its rescaled …

The Santaló point of a convex polytope is the interior point which leads to a polar dual of
minimal volume. This minimization problem is relevant in interior point methods for convex …

Kakade's natural policy gradient method has been studied extensively in the last years
showing linear convergence with and without regularization. We study another natural …

Using the dual formulation only, we show that regularity of unbalanced optimal transport
also called entropy-transport inherits from regularity of standard optimal transport. We then …

These notes are based on a series of lectures given by the author at the Max Planck Institute
for Mathematics in the Sciences in Leipzig. Addressed topics include affine and projective …

These are lecture notes for a minicourse taught by the author at the Hypergeometric school,
taking place at Kobe University on August 16-17, 2023. We study the positive and …

Abstract (EN) In recent years, algebraic geometry (both complex and real) has proven to be
useful in numerous applications in optimization, statistics, quantum information, and physics …

Gibbs Manifolds -0.22in Page 1 Gibbs Manifolds Bernd Sturmfels MPI Leipzig Paper with
Dmitrii Pavlov and Simon Telen Back-to-the-Roots Seminar KU Leuven, September 11 …