BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Danielle Bowerman (Missouri University of Science and Technology) DTSTART:20250912T153000Z DTEND:20250912T163000Z DTSTAMP:20260422T171847Z UID:CompMath/18 DESCRIPTION:Title: Extension Monads: Some Structure Theorems\nby Danielle Bowerman (Mis souri University of Science and Technology) as part of Relatorium seminar\ n\n\nAbstract\nTo some extent\, this presentation follows the seminar titl ed "Non-standard Methods and Universal Algebra" by Matt Insall presented b ack in February. In this presentation\, we take algebraic structures---a p air consisting of (1) a set of elements to compute upon and (2) a set of c omputational instructions\, called algebras heretofore---into the nonstand ard setting. This process can both enlarge and endense said algebra\, ofte n causing new elements to appear both "far away" from and "in between" the elements of the original algebra\, while preserving all of the same logic al properties of the original. \n\nThe additional elements are often clust ered around directly mapped elements from the standard (original) setting. In the case of these algebras\, we define a third structure\, the extensi on monad\, of the elements that are very close to the original algebra. Th is extension monad is\, as a set\, in between the standard and nonstandard version of the algebra and while not logically identical\, captures the l ocal behavior of the computational instructions\, known as operations.\n\n Bio: Danielle Bowerman studied mathematics at Evangel University and earne d a bachelor of science in 2019. She then went on to join a mathematics Ph D program as a Chancellor's Distinguished Fellow at the Missouri Universit y of Science and Technology and expects her PhD in the fall of 2025. She t aught a few sections of College Algebra at some point.\n\nModerator: This talk will be moderated by Matt Insall. Matt Insall is a mathematician\, f ather of four (two sons and two daughters)\, and grandfather of four boys and two girls. He’s written poems and a song\, and performs occasionally at open mic events. Matt retired in September 2024 from his position in t he faculty of the Missouri University of Science and Technology Department of Mathematics and Statistics after 35 years in that position.\n LOCATION:https://researchseminars.org/talk/CompMath/18/ END:VEVENT END:VCALENDAR