The series **"New Horizons in Undergraduate Mathematics"** showcases great lecturers speaking on topics from current research that are both important, accessible, and ready to enter the undergraduate curriculum.

These lectures provide an informal introduction to algebraic topology and show how the techniques can be adapted (via a construction called persistent homology) to study qualitative geometric properties of high dimensional data. The area described in the lectures form a part of computational topology, a rapidly expanding area of mathematics with a growing number of applications.

- Lesson 1: Introduction to Algebraic Topology - Running Time of 46 minutes
- Lesson 2: Applications of Topology - Running Time of 54 minutes

**Gunnar Carlsson**received his doctoral degree in mathematics in 1976 from Stanford University. He has taught at the University of Chicago, San Diego, Princeton University and Stanford University. He has written many research papers within algebraic topology, and in recent years turned his interest to applications of topological techniques in various domains, using computational methods.

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*This recording was produced through the VMath program at MSRI made possible by a grant from William R. Hearst.*