Robert Lipshitz - ...and refinements of the *s*-invariant скачать в хорошем качестве

Robert Lipshitz - ...and refinements of the *s*-invariant

November 10, 2025 - Princeton University Surfaces and the Fourth Dimension Four-dimensional spaces are at the cusp of what humans can visualize, yet 4-dimensional topology remains one of the most mysterious topics in mathematics. One successful strategy for understanding 4-dimensional spaces has been to probe them with 2 dimensional ones---surfaces. This series will explore the interaction between 2 dimensional and 4-dimensional spaces, mediated by a particular algebraic tool called Khovanov homology. The first lecture will be a broad overview of 4-dimensional spaces, focused on how they are both concrete and mysterious. It will be largely accessible to anyone interested in mathematics. Later lectures will be more technical, introducing Khovanov homology and some of its refinements and applying them to 4-dimensional problems.