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Events happening on February 28, 2023

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Feb. 28, 2023 1:25pm (Online)	Algebra/Logic Albert Vucaj (Technical University Vienna, Austria) View Online:https://cuboulder.zoom.us/j/96896272260 X Achieving a classification of all clones of operations over a finite set is one of the goals at the heart of universal algebra. Over the years, it has been shown that such a goal seems arduously reachable even if we only focus on clones over three-element sets. In a recent turn of events, the minor-equivalence relation on clones over finite sets gained importance both in universal algebra and in computer science: minor-equivalent clones satisfy the same set identities of the form , also known as minor-identities. Moreover, it was proved that the complexity of the CSP of a finite structure only depends on the set of minor-identities satisfied by the polymorphism clone of . In this talk, I will present a general overview of the poset arising by considering clones over some finite set with the following order: we write if there exist a minor-preserving map from to . In particular, I will focus on rather natural questions such as: is this poset a lattice? Is it countable? Does it have atoms or coatoms? Joint work with Manuel Bodirsky and Dmitriy Zhuk. Clones over finite sets up to minor-equivalence
Feb. 28, 2023 2:30pm (MATH 3…	Lie Theory Richard Green (CU) X A k-root is an easily defined type of polynomial that can be expressed as an integer linear combination of squarefree monomials of degree k in n indeterminates. The case k=1 corresponds to a root system of type D. As is the case for root systems, k-roots can be either positive or negative, and there is a basis for their span analogous to a set of simple roots. This talk will describe some interesting constructions that can be done by summing all the positive k-roots in certain judiciously chosen subsets. A generalization of the positive roots of type D_n
Feb. 28, 2023 3:30pm (MATH 3…	Topology Juan Moreno (CU Boulder) Duality for Morava E-Theory

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