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$\xi$-stability and the Weighted Fundamental Lemma
Algebraic Geometry and Number Theory| Speaker: | Connor Halleck-Dube, UC Berkeley |
| Related Webpage: | https://math.berkeley.edu/~chd/ |
| Location: | 2112 MSB |
| Start time: | Wed, Feb 4 2026, 12:10PM |
Description
The Weighted Fundamental Lemma and its nonstandard variant are the remaining conditional pieces underlying a large body of work in automorphic theory. After briefly motivating with the problem of stabilizing the trace formula, we will discuss weighted stability conditions on generically regular-semisimple Higgs bundles and their connection to weighted orbital integrals. We will then outline how this framework allows an extension of Ng\^{o}'s work into a proof of the weighted fundamental lemma for Lie algebras.