A variety V is a Schreier variety if every if every subalgebra of a V-free algebra is free. I will explain a link between the concept of a Schreier variety and tame congruence theory. Namely, I will explain why a locally finite variety is a Schreier variety if and only if it consists of minimal algebras.

Locally finite Schreier varieties

Sep. 19, 2023 2:30pm (Math 3…

Lie Theory

ALT organizers

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The organizers of the ALT seminar (Flor Orosz Hunziker, Richard Green, and Nat Thiem) will give introductions to their research and their respective styles as advisors. All are welcome, but newer students exploring the various research groups in the department are especially encouraged to attend.

ALT Open House

Sep. 19, 2023 3:30pm (MATH 3…

Topology

Juan Moreno

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At its core, algebraic topology is about associating algebraic invariants to topological spaces. These are invariant in the sense that if you change your space by a homotopy equivalence you should get an isomorphic algebraic object. We will begin with the observation that often these invariants do not only respect homotopy, but also suspension, an operation that increases the dimension of a space. We call such invariants stable and will focus on the most important examples of them: generalized cohomology theories. The Brown representability theorem will then tell us that if we are interested in stable invariants then we should really be working with somethings called spectra instead of spaces.