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Department Colloquium

Fri., Jan. 22, 2021 3:30 p.m.

Location: Live Stream

Speaker: Anna Marie Bohmann (Vanderbilt University)

Title:  Detecting algebraic structures: K-theory and Lawvere theories (494 kB) PDF file


In the 1950s and 60s, mathematicians began constructing the invariants of rings that are called "K-theory." The K-theory of rings is hard to compute, but it contains lots of interesting information about algebra, number theory, and topology. For example, K-theory detects when rings are "the same" in the sense of having suitably equivalent categories of modules, which is called Morita invariance. In this talk, I will discuss the K-theory of rings as well as new work with Markus Szymik about the K-theory of a more general kind of algebraic structure, called a Lawvere theory. In the latter case, we show that while the K-theory of Lawvere theories contains lots of interesting information, it fails to satisfy Morita invariance!

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