Pacific Interdisciplinary hub on Optimal Transport | PIMS - Pacific Institute for the Mathematical Sciences

2021 — 2024

The Pacific Interdisciplinary hub on Optimal Transport (PIHOT) is a Collaborative Research Group examining the research and applications of Optimal Transportation across a wide audience of researchers, students, industry, policy makers and the general public.

The Kantorovich Initiative is a dedicated website to help foster a community around the topic of Optimal Transportation.

While Einstein’s theory of gravity is formulated in a smooth setting, the celebrated singularity theorems of Hawking and Penrose describe many physical situations in which this smoothness must eventually breakdown. In positive-definite signature...

Optimal transport operates on empirical distributions which may contain acquisition artifacts, such as outliers or noise, thereby hindering a robust calculation of the OT map. Additionally, it necessitates equal mass between the two distributions...

Density functional theory (DFT) is one of the workhorses of quantum chemistry and material science. In principle, the joint probability of finding a specific electron configuration in a material is governed by a Schrödinger wave equation. But...

The Gromov-Wasserstein (GW) distance quantifies dissimilarity between metric measure (mm) spaces and provides a natural alignment between them. As such, it serves as a figure of merit for applications involving alignment of heterogeneous datasets...

I will try to present an overview of some results of unbalanced optimal transport for positive measures with different total masses, showing the crucial role of the so-called cone representation and of the corresponding homogeneous marginals. The...

Shifted divergences provide a principled way of making information theoretic divergences (e.g. KL) geometrically aware via optimal transport smoothing. In this talk, I will argue that shifted divergences provide a powerful approach towards unifying...

Deep learning-based approaches have succeeded surprisingly in various fields of sciences. In particular, one of the first and most successful achievements of them is image classification. Now, deep learning-based algorithms perform even better than...

The optimal transport problem provides a fundamental and quantitative way to measure the distance between probability distributions. Recently, it has been successfully used to analyze the evolutionary dynamics in physics and biology. Motivated by...

The theory of large deviations provides with a way to compute asymptotically the probability that an interacting particle system moves from a given configuration to another one over a fixed time interval. The problem of finding the most likely...

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Brendan Pass

Associate Professor of Mathematics, University of Alberta

Young-Heon Kim

Professor of Mathematics, University of British Columbia

Soumik Pal

Professor of Mathematics, University of Washington