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Colloquium: Diffusion and diffraction in algebraic topology

Event Type
245 Altgeld
Mar 3, 2022   4:00 pm  
Paul G. Goerss, Northwestern University
Jozsef Balogh

Algebraic topologists compute the very basic geometric invariants, such as the genus of a surface or the Euler characteristic of a finite simplicial complex. The most basic invariant of all is the stable homotopy groups of spheres, but these have a well-earned reputation of being a chaotic mess, seemingly without any discernible order. It turns out, however, that with the right diffraction principle and a good deal of hard computation, we can separate out some very intriguing large-scale patterns. What these patterns are and how they should fit together is the subject of a number of conjectures, some of which have seen remarkable progress in the past few years. In this talk I’ll display the patterns, lay out the conjectures, and talk about the recent progress, touching on the work of a whole host of people, many of whom live and work here in the Midwest.

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