The Summer Schools in Probability are a highlight of Canadian probability and are internationally significant.  Launched by PIMS in 2004, the school takes the form of two main 4-week courses along with three mini-courses. The schools have played a major role in the development of an exceptionally strong community of young probabilist in Canada, North America and overseas. This will be the 13th time this school has run.

This summer school offers an exceptional opportunity for participants to delve into the intricate realm of statistical optimal transport theory. This captivating field stands at the crossroads of multiple disciplines, drawing from a rich tapestry of mathematical insights from diverse subjects, including partial differential equations, stochastic analysis, convex geometry, statistics, and machine learning, crafting a vibrant and interdisciplinary landscape. The foremost objective of this summer school is to create a dynamic learning environment that unites students from diverse backgrounds such as PDE theory, probability, or optimal transport. 

The MSRI-UP summer program is designed to serve a diverse group of undergraduate students who would like to conduct research in the mathematical sciences.

In 2025, MSRI-UP will focus on Quantitative Justice. The research program will be led by Dr. Omayra Y. Ortega, Associate Professor in the Department of Mathematics at Sonoma State University.

From micro to macro, sea ice supports life in the polar regions. Left: illustration of the porous sea ice microstructure, home to a microbial community of ice endemic organisms including bacteria and algae. Right: two penguins on Antarctic sea ice.

In this summer school, students will be introduced to mathematical and computational modeling of sea ice and polar ecosystems. As a material, sea ice is a multiscale composite structured on length scales ranging from tenths of millimeters to tens of kilometers. From tiny brine inclusions and surface melt ponds of increasing complexity, to ice floes of varying sizes in a seawater host, a principal challenge is how to find sea ice effective properties that are relevant to larger scale models, given data on smaller scale structures. Similarly, the sea ice ecosystem ranges from algae living in the brine inclusions to charismatic megafauna like penguins and polar bears, whose diets depend critically, down the line, on the tiny sea ice extremophiles. The dynamics of sea ice microbial communities are regulated by the physics of the ice microstructure, and, in turn, many of these microbes modify their environment by secreting extracellular polymeric substances. In addition to sea ice and its ecosystems, we will consider broader mathematical models including energy balance models, tipping points, and global circulation models.