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Geometry-Topology Seminar

Thursday, February 10, 2022 - 5:15pm

Saad Slaoui

U Texas


University of Pennsylvania

via Zoom

The Zoom link for this talk is available via e-mail from After the talk, we will stay online for a while to socialize.

This talk will be concerned with a particularly successful enterprise in algebraic topology known as rational homotopy theory, as well as some of its extensions and applications. Developed by Quillen (1969) and Sullivan (1977), rational homotopy theory locates a full subcategory of the homotopy category of spaces - called the rational homotopy category - which admits a lossless translation into purely algebraic structures, namely commutative differential graded algebras (cdga’s) over the rational numbers. We will focus on Sullivan’s perspective on the story, and hint at an application of this dictionary to geodesic counts in closed Riemannian manifolds. Time permitting, we shall discuss modern extensions of this yoga by Mandell (2001) and Yuan (2019), the former establishing analogous results “p-adically” rather than rationally, and the latter completing the program so to speak by exhibiting a lossless translation for all simply connected spaces of finite types within the framework of higher algebra.