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Events happening on October 17, 2023

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Oct. 17, 2023 1:25pm (online)	Algebra/Logic Erkko Lehtonen (Khalifa University, Abu Dhabi) View Online:https://cuboulder.zoom.us/j/96896272260 X Let $C1$ and $C2$ be clones on sets $A$ and $B$ , respectively. A set $K$ of functions of several arguments from $A$ to $B$ is called a $C1,C2)$ -clonoid if $K C1 ⊆ K$ and $C2 K ⊆ K$ . Sparks classified the clones $C$ on $0,1$ according to the cardinality of the lattice $L(JA, C)$ of $JA, C)$ -clonoids (here $J_{A}$ denotes the clone of projections on a finite set $A$ ): $L(JA, C)$ is finite if and only if $C$ contains a near-unanimity operation; $L(JA, C)$ is countably infinite if and only if $C$ contains a Mal'cev operation but no majority operation; $L(JA, C)$ has the cardinality of the continuum if and only if $C$ contains neither a near-unanimity operation nor a Mal'cev operation. We sharpen Sparks's result by completely describing the lattices $L(JA, C)$ and the $JA, C)$ -clonoids when $A = 0,1$ and $C$ contains a near-unanimity operation or a Mal'cev operation, i.e., when $L(JA, C)$ is finite or countably infinite. On clonoids of Boolean functions
Oct. 17, 2023 2:30pm (MATH 3…	Lie Theory Justine Fasquel (University of Melbourne) X W-algebras are a large family of vertex algebras associated to nilpotent elements of simple Lie algebras. They are usually constructed from affine Lie algebras by applying a quantum Hamiltonian reduction. In this talk, we will discuss the possibility to invert this process in order to reconstruct the representation theory of initial Lie algebras. We will illustrate the abstract theory with examples in small ranks. Inverse Hamiltonian Reduction : a tool for the representation theory of affine Lie algebras Sponsored by the Meyer Fund
Oct. 17, 2023 2:30pm (MATH 2…	Math Edu Leilani Arthurs (University of Colorado Boulder) X Conventionally, assessments are used to measure how much students have learned mid-semester or at the end of the semester; however, class assessments can also be used to promote student learning. In this 1-hour interactive workshop, participants will be introduced to alternative assessments that engage students in the learning process and can lead to improved outcomes compared to traditional instruction alone. By the end of this workshop, participants will be able to (i) differentiate three types of assessments, (ii) discuss the merits of alternative assessments, (iii) describe examples of alternative assessments, (iv) explain what it is like to experience such assessments from a student perspective, and (v) begin designing such assessments for use in their courses as early as this semester if they wish. Promote Student Learning Using Class Assessments
Oct. 17, 2023 3:30pm (MATH 3…	Topology Bridget Schreiner (University of Notre Dame) X A sequence of groups (or spaces) $G1 G2 G3…$ satisfies homological stability if $Hi(Gn)≅ Hi(Gn+1)$ for $n>>i$ . Regarding the sequence $G_{n}$ as the image of a functor from the category $N,+,0)$ and noting that stability occurs when $Hi(Gn+1,Gn)≅ 0$ , we can turn this into a statement about "differences" in the image of a functor $ℕ \to A b$ . This talk will introduce a generalization of the cross effects of Eilenberg and MacLane that is suited to answer questions about homological stability in this context. Cross effects and stability

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