Grad Student Seminar - Niko Schonsheck

January 17, 2019
Tuesday, January 22, 2019 - 5:15pm to 6:30pm
Cockins Hall 240
Niko Schonsheck

Title: Homotopy Theory -- from the Fundamental Group to Structured Ring Spectra

SpeakerNiko Schonsheck (Ohio State University)

Abstract: Have you ever found yourself lying awake at night haunted by the fact that all homotopy theorists seem to do is draw complicated diagrams and then nod sagely as if the turbid mysteries of the universe have been suddenly illuminated? Well then you're in luck! In this talk, we'll begin at the beginning -- with the fundamental group of a space as first defined by Poincare in 1905. Seeking to improve this algebraic invariant of topological spaces will lead us naturally to the higher homotopy groups, spectra, and the so-called stable homotopy category. A great deal of research sought to understand this category and spawned the "brave new algebra" of structured ring spectra. In the latter stages of this talk, will discuss these recent developments and conclude with a direction of current research.

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