UW Madison mathematics Colloquium is on Fridays at 4:00 pm.

Fall 2021

September 17, 2021, B239 + Live Stream, Mark Shusterman (Harvard)

(hosted by Gurevich)

Finitely Presented Groups in Arithmetic Geometry

I will report on recent works, in part joint with Esnault—Srinivas, and with Jarden, on the finite presentability of several (profinite) groups arising in algebraic geometry and in number theory. These results build on a cohomological criterion of Lubotzky involving Euler characteristics. I will try to explain the analogy, rooted in arithmetic topology, between these results and classical facts about fundamental groups of three-dimensional manifolds.

September 24, 2021, B239, Sean Paul (UW-Madison)

October 1, 2021, B239, Andrei Caldararu (UW-Madison)

October 8, 2021, Zoom, Jon Chapman (University of Oxford)

(Wasow lecture; hosted by Thiffeault)

Asymptotics beyond all orders: the devil's invention?

"Divergent series are the invention of the devil, and it is shameful to base on them any demonstration whatsoever." --- N. H. Abel.

The lecture will introduce the concept of an asymptotic series, showing how useful divergent series can be, despite Abel's reservations. We will then discuss Stokes' phenomenon, whereby the coefficients in the series appear to change discontinuously. We will show how understanding Stokes' phenomenon is the key which allows us to determine the qualitative and quantitative behaviour of the solution in many practical problems. Examples will be drawn from the areas of surface waves on fluids, crystal growth, dislocation dynamics, and Hele-Shaw flow.