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A Mathematical Introduction to Nonlinear Wave Equations: Part I
A rigorous and intuitive foundation in nonlinear hyperbolic PDEs. Part I focuses on general linear wave equations, and lays the foundation for the general treatment of nonlinear wave equations.
Dave B. H. Verweg ·
Kapteyn Astronomical Institute ·
Luuk de Ridder ·
Korteweg-de Vries Institute for Mathematics ·
Date posted: April 6, 2026
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Coverages and Grothendieck Toposes
These notes detail the basics of the theory of Grothendieck toposes from the viewpoint of coverages. Typically one defines a site as a (small) category equipped with a Grothendieck topology. However, it is often desirable to generate a Grothendieck topology from a smaller structure, such as a Grothendieck pretopology, but these require some pullbacks to exist in your underlying category. There is an even more light-weight structure one can generate a Grothendieck topology from called a coverage.
Emilio Minichiello ·
CUNY CityTech ·
Date posted: October 6, 2025
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Moduli spaces of Riemann surfaces
Topics include the moduli space of Riemann surfaces and its Deligne-Mumford compactification, Jacobians and the period mapping, Teichmuller space and the Teichmuller and Weil-Petersson metrics, and the geometric Shafarevich and Mordell theorems.
These are course notes from a topics class first taught at Stanford University.
Alex Wright ·
University of Michigan ·
Date posted: October 6, 2025
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Course geometry and Teichmuller theory
Topics include Gromov hyperbolic spaces, curve graphs, Teichmuller spaces, mapping class groups, and hierarchical hyperbolicity.
These are student notes from a topics course taught at the university of Michigan.
Alex Wright ·
University of Michigan ·
Date posted: October 6, 2025
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Outer automorphism groups of free groups
Topics include folding, outer space, the Nielsen-Thurston classification of outer automorphisms, the free splitting and free factor complexes, and doubled handlebodies.
These are notes on a graduate topics course at the University of Michigan in Fall 2023. The notes were taken by students and edited by Alex Wright.
Alex Wright ·
University of Michigan ·
Date posted: October 6, 2025
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