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# Quantum metrics on the natural numbers (Katrine von Bornemann Hjelmborg, University of Southern Denmark)

## October 13, 2022 @ 4:00 pm - 5:00 pm

Quantum metrics in the sense of Rieffel were introduced to prove some statements arising in the high-energy physics literature. Since then, the area of quantum metric geometry has been used to answer questions stemming from within mathematics as well. To prove such results, it is often the case that certain properties of a quantum metric are sufficient enough, and explicit calculations of the quantum metric are rare. Thus, in this talk, we focus on certain quantum metrics introduced by Aguilar and Latrémolière on $c$, the space of complex-valued convergent sequences (which is isomorphic to the space of complex-valued continuous functions on the Alexandroff compactification of the natural numbers), and calculate exactly the metrics on the natural numbers that these quantum metrics induce. Moreover, we compare the quantum metrics of Aguilar and Latrémolière with a classical quantum metric on $c$ induced by the Lipschitz seminorm. (This is joint work with Konrad Aguilar).