Part 17 of What is…quantum topology? | Daniel Tubbenhauer

???? What is…quantum topology? | Daniel Tubbenhauer

What is quantum topology? Why do mathematicians care about knots, categories, and strange new "quantum" ways of looking at space? And what does any of this have to do with algebra, logic, or physics?
In this new series, we explore quantum topology; a field that builds bridges between topology, algebra, number theory, logic, and quantum physics. Our central players will be quantum invariants of knots and links: mathematical quantities that not only distinguish between topological objects, but also encode deep algebraic and categorical structures.
The series is based on my lecture notes “Quantum Topology Without Topology”, where the goal is to understand these invariants from a categorical and diagrammatic point of view. We'll introduce categories, monoidal categories, braidings, duals, and fusion/modular structures; all through graphical calculus, with minimal assumptions about topology or algebra.

???? Lecture notes (PDF): https://www.dtubbenhauer.com/qinvariants.pdf
???? Keywords: quantum invariants, categorical algebra, diagrammatic methods, representation theory
???? Comments welcome! Corrections and suggestions can be sent via email and are very welcome!
Contents of the series will loosely follow:
1. What is a category? Why think categorically?
2. Monoidal categories and graphical calculus
3. Duality, braiding, and pivotal structure
4. Fusion and modular categories
5. Quantum invariants: diagrammatic and web approaches
6. Examples and applications: from knots to physics

About me.
Hi, I’m Daniel Tubbenhauer (but feel free to call me Dani, they/them). I’m a mathematician working at the interface of algebra, topology, and category theory. My work often involves diagrammatic and categorical approaches to representation theory, quantum invariants, and low-dimensional topology. I’m passionate about visual and conceptual ways of understanding abstract mathematics, and I enjoy sharing that perspective through informal talks, lecture notes, and videos like these.
???? Website: http://www.dtubbenhauer.com
???? TeX and slides: https://github.com/dtubbenhauer/My-TeX-files
???? #quantumtopology #categorytheory #representationtheory