Course

MATH-488: Topology IV.b - Algebraic K-theory

Summary

Algebraic K-theory, which to any ring R associates a sequence of groups, can be viewed as a theory of linear algebra over an arbitrary ring. We will study in detail the first two of these groups and some of their applications to other areas of mathematics.

Lectures

Instructor

Kathryn Hess Bellwald

Kathryn Hess Bellwald received her PhD from MIT in 1989 and held positions at the universities of Stockholm, Nice, and Toronto before moving to the EPFL.Her research focuses on algebraic topology and its applications, primarily in the life sciences, but also in materials science. She has published extensively on topics in pure algebraic topology including homotopy theory, operad theory, and algebraic K-theory. On the applied side, she has elaborated methods based on topological data analysis for high-throughput screening of nanoporous crystalline materials, classification and synthesis of neuron morphologies, and classification of neuronal network dynamics. She has also developed and applied innovative topological approaches to network theory, leading to a powerful, parameter-free mathematical framework relating the activity of a neural network to its underlying structure, both locally and globally.In 2016 she was elected to Swiss Academy of Engineering Sciences and was named a fellow of the American Mathematical Society and a distinguished speaker of the European Mathematical Society in 2017. In 2021 she gave an invited Public Lecture at the European Congress of Mathematicians. She has won several teaching prizes at EPFL, including the Crédit Suisse teaching prize and the Polysphère d’Or.

Official source

https://edu.epfl.ch/coursebook/en/topology-iv-b-algebraic-k-theory-MATH-488

Moodle Page

http://go.epfl.ch/MATH-488

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Summary

Lectures

Instructor

Kathryn Hess Bellwald

Official source

https://edu.epfl.ch/coursebook/en/topology-iv-b-algebraic-k-theory-MATH-488

Moodle Page

http://go.epfl.ch/MATH-488

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