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Events for the weeks of March 1st – 14th

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Tue, Mar. 3 2pm (online)	Algebra/Logic Ana Belen Avilez Garcia (Chapman University) View Online:https://cuboulder.zoom.us/j/96896272260 X Cozero elements of a frame play an important role in point-free topology. The set of cozero elements, Coz L, of a frame L is a sub -frame of L (that is, a sublattice closed under countable suprema and finite infima). Moreover, the lattice Coz L join-generates the frame L if and only if L is completely regular (a result analogous to the classical one for completely regular topological spaces). Within the setting of completely regular frames, we consider the Dedekind–MacNeille completion of the lattice of cozero elements, which in this context coincides with the Bruns–Lakser construction. The frame obtained through this process turns out to be a sublocale of the original frame, specifically, the smallest sublocale containing Coz L. A central aim of the talk is to compare this sublocale with the original frame and to present results and examples showing when the two coincide and when they differ. Viewing Coz L both as a join-generating sublattice and through its completion leads naturally to two related but distinct classes of frames: cozero frames and perfectly regular frames. We will examine the relationship between these notions and provide illustrative examples. This is an ongoing joint work with Guram Bezhanishvili and Joanne Walters-Wayland. Cozero frames and perfectly regular frames
Wed, Mar. 4 2:10pm (Math350)	Math Phys Markus J. Pflaum (CU Boulder) View Online:https://cuboulder.zoom.us/j/97049173677 TBA
Wed, Mar. 4 3:30pm (MATH 1…	Diversity Siddhant Agrawal, Robin Deeley, Sarah Petersen, Joseph Timmer (CU Boulder) X From adjunct positions to postdocs to faculty, there are a variety of academic jobs, and the application process for those jobs can be daunting. Join our panelists, Professors Siddhant Agrawal and Robin Deeley, Teaching Professor Joseph Timmer, and Postdoctoral Scholar Sarah Petersen, who will share their insights into navigating the academic job market. Designed for those entering the job market in the near future, this session aims to replace uncertainty with strategy and actionable guidance. Pizza will be served! Academic Job Panel
Tue, Mar. 10 1:20pm (MATH 3…	Homotopy Shauly Ragimov (University of Chicago) TBD
Tue, Mar. 10 2:30pm (MATH 3…	Lie Theory Spencer Daugherty (CU Boulder) X Gessel and Zhuang introduced the concept of shuffle-compatibility of statistics on permutations of subsets of \N to describe statistics whose multiset of values on the shuffles of two disjoint permutations is determined exactly by the size and statistic values of the two permutations being shuffled. Shuffle-compatibility implies the existence of an algebraic structure on the equivalence classes induced by the statistic. For example, the descent set statistic is shuffle-compatible, and the algebra on the equivalence classes it induces is isomorphic to the Hopf algebra of quasisymmetric functions. In this talk, we generalize shuffle-compatibility to objects such as words, parking functions, and set partitions using the Hopf monoids associated with these objects. We cover a variety of well-known statistics on each object. We define various algebraic structures on the equivalence classes formed by these statistics that are, in many cases, quotients of (or isomorphic to) well-known combinatorial Hopf algebras such as FQSym, WQSym, PQSym, and NCSym. Generalizing shuffle-compatibility using Hopf monoids

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