In spring 2026, the UA Grad ANT Seminar is organized by Nick Pilotti. This website is maintained by Napoleon Wang.
We meet Mondays, 3–4 PM Arizona time, in Math 402, unless otherwise noted.
Feb 16 Xinyu Zhou (Boston University)
Title: Dualities between integral local Shimura varieties
Abstract: Generalizing earlier results of Faltings and Fargues on Lubin–Tate spaces and Drinfeld symmetric spaces, Scholze and Weinstein show in the "Berkeley lecture notes" that there is a "duality" between local Shimura varieties associated to a reductive group G and those associated to an inner twist G′, by proving that at the infinite level, they admit isomorphic moduli interpretations in terms of p-adic shtukas.
In this talk, I will review Scholze-Weinstein's approach and show how to generalize this duality result further to the integral models of local Shimura varieties. If time permits, we also discuss an application to cohomology of p-adic groups with some natural mod-p coefficients.
Feb 9 Haochen Cheng (Northwestern)
Title: Non-liftability of abelian schemes and beyond
Abstract: In the complex setting, the embedding of a subvariety into a Shimura variety is largely governed by its monodromy group. In particular, subvarieties with small monodromy groups do not occur inside Shimura varieties. This rigidity phenomenon breaks down in characteristic p: for instance, Moret–Bailly constructed a nontrivial family of supersingular abelian surfaces over the projective line. In this talk, we study the moduli of abelian varieties in characteristic p. We show that any subvariety with trivial l-adic monodromy group is necessarily contained in an isogeny leaf in the sense of Oort. Moreover, we prove that such subvarieties do not even admit a lift to W2(k) by using non-abelian Hodge theory in positive characteristic. Finally, I will discuss ongoing ideas toward extending these results to (exceptional) Shimura varieties, building on recent works of Patrikis, Bakker–Tsimerman–Shankar, et al.
Notes
Feb 2 Chapman Howard
Title: Parabolic Induction, Jacquet Modules, and Mackey Theory, oh my!
Abstract: The central object in the local Langland's Correspondence (for GLn) is the “irreducible admissible representation” (of GLn). LLC for GLn is now a theorem (Harris-Taylor, Henniart), so it makes sense to study the associated functorial lifts. Two examples are the base change induced from the inclusion GLn(F) ↪ GLn(E) for some E/F, and the Jacquet-Langlands transfer induced from the inclusion GLn(F) ↪ GLn(D) for some central division algebra D/F. In this talk, we’ll break down the tools that allow one to study these instances of functoriality, and maybe present an argument from our thesis project.
Jan 26 Napoleon Wang
Title: Title: Vector bundles on Fargues-Fontaine curves
Abstract: The Fargues–Fontaine curve XFF is a p-adic analogy to the projective line ℙ1, constructed by Fargues-Fontaine in a way that p-adic Hodge theoretic objects can be expressed via vector bundles with additional structure at a distinguished point x∞. In analogy with the Beauville-Laszlo gluing description of Hecke modifications via the affine Grassmannian, modifications of G-bundles at x∞ are described by the B+dR-affine Grassmannian (Fargues-Scholze). By Fargues-Fontaine and Anschütz, vector bundles on XFF are classified and formulated as an equivalence with isocrystals. More recent work by Birkbeck et al. and Hong refines this by studying extensions, subbundles, and quotient bundles using the Harder-Narasimhan polygons. In the end, we will briefly discuss the relative versions of the Fargues-Fontaine curve over a perfectoid base following Kedlaya-Liu and Fargues-Scholze.
