ERC Consolidator Grant · 2025
Igusa Stacks and the Langlands program
The Langlands program, often called a ``grand unified theory of mathematics'', predicts reciprocity laws that relate very different kinds of mathematical objects: automorphic forms and Galois representations. Shimura varieties play a fundamental role in constructing and propagating instances of Langlands reciprocity. In the past decade, advances in p-adic geometry have revolutionised the study of Shimura varieties. This recently led to the introduction of certain p-adic analytic varieties called Igusa stacks, which connect Shimura varieties to ideas from geometric Langlands via the work of Fargues--Scholze. This gives access to powerful new tools and makes Igusa stacks seem as fundamental…
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