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Events happening on March 7, 2023

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Tue, Mar. 7 1:25pm (Online)	Algebra/Logic Michael Kinyon (University of Denver) View Online:https://cuboulder.zoom.us/j/96896272260 X The conjugacy equivalence relation in groups can be generalized to semigroups in various distinct ways. For example, in an inverse monoid $S$ , one might define $a,b∈ S$ to be conjugate if there exists $g∈ S$ such that $g-1ag = b$ and $gbg-1 = a$ . There are other semigroup generalizations of conjugacy which do not involve inverses at all. In this talk I will survey the various generalizations, focusing particularly on a notion known as \emph{natural conjugacy}, which, in inverse semigroups, coincides with the one defined above. Along the way, I will discuss connections with partial inner automorphisms and with the (universal algebra) center of an inverse semigroup. The work described herein is joint with J. Ara\'{u}jo, W. Bentz, J. Konieczny, A. Malheiro, V. Mercier and D. Stanovsk\'{y}. Conjugacy in semigroups
Tue, Mar. 7 2:30pm (MATH 3…	Lie Theory Nat Thiem (CU) X Symmetric functions appear throughout much of Stanley’s school of algebraic combinatorics. Algebraically, it is a combinatorial Hopf algebra indexed by integer partitions, and it is in fact a terminal object in the category of co-commutative combinatorial Hopf algebras. This talk explores a number of generalizations or variations on symmetric functions and how algebraic methods inform or confuse how these combinatorial Hopf algebras relate. This is ongoing work with F. Aliniaeifard. The problems with canonical maps
Tue, Mar. 7 3:30pm (MATH 3…	Topology Sheagan John (CU Boulder) X For f and g continuous and commuting self-maps of a Hausdorff space X, we investigate various conditions on X and on the pair (f , g) which provide existence of a coincidence value. We introduce generalized notions of the coincidence value property and use this added flexibility to determine how various coincidence properties of X are related to coincidence properties of associated fibre bundles and adjunction spaces. These investigations are motivated by the longstanding open question concerning whether Brouwer's classical fixed-point theorem has a coincidence value analog. "Lifts and Extensions" of Generalized Coincidence Value Properties