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.

<p>Flats and hyperbolic planes in a higher rank symmetric space</p> Drawn by Steve Trettel.

Lie groups are central objects in modern mathematics; they arise as the automorphism groups of many homogeneous spaces, such as flag manifolds and Riemannian symmetric spaces. Often, one can construct manifolds locally modelled on these homogeneous spaces by taking quotients of their subsets by discrete subgroups of their automorphism groups. Studying such discrete subgroups of Lie groups is an active and growing area of mathematical research. The objective of this summer school is to introduce young researchers to a class of discrete subgroups of Lie groups, called Anosov subgroups.

<p>Laminations arise naturally in hyperbolic geometry and (pseudo-) Anosov flows [Image by Jeffrey Brock]</p>

This school will serve as an introduction to the SLMath semester “Topological and Geometric Structures in Low-Dimensions”.  The school consists of two mini-courses: one on Teichmüller Theory and Hyperbolic 3-Manifolds and the other on Anosov Flows on Geometric 3-Manifolds.  Both topics lie at the interface of low-dimensional geometric topology (specifically, surfaces, foliations, and 3-manifolds) and low-dimensional dynamics.  The first course will be targeted towards students who have completed the standard first year graduate courses in geometry, topology, and analysis while the second course will geared towards more advanced students who are closer to beginning research. However, we expect that all students will benefit from both courses.