My name is Pol van Hoften and I'm an assistant professor (universitair docent) at
I am interested in the Langlands programme, in particular in the mod p and p-adic geometry of Shimura varieties.
Previously I was a postdoctoral fellow at Stanford University
mentored by Richard Taylor
. Before that, I completed my PhD in mathematics at the London School of Geometry and Number Theory
and King's College London
. I was supervised by James Newton
and Ana Caraiani
My e-mail address is p dot van dot hoften at vu dot nl.
Publications and Preprints
- On exotic Hecke correspondences, with Jack Sempliner, in preparation. recorded talk describing our main results.
- Igusa stacks for Shimura varieties of Hodge type (preliminary title), with Dongryul Kim, Patrick Daniels and Mingjia Zhang, in preparation.
- On the Piatetski--Shapiro construction for integral models of Shimura varieties, with Jack Sempliner, in preparation.
- Hecke orbits on Shimura varieties of Hodge type , with Marco D'Addezio (arxiv, pdf), submitted.
- On the ordinary Hecke orbit conjecture (arxiv, pdf), to appear in Algebra & Number Theory.
- Monodromy and irreducibility of Igusa varieties , with Luciena Xiao Xiao (arxiv, pdf), submitted.
Mod p point on Shimura varieties of parahoric level, with an appendix by Rong Zhou (arxiv, pdf), submitted.
A geometric Jacquet-Langlands correspondence for paramodular Siegel threefolds, Mathematische Zeitschrift (2021). Journal version, arxiv preprint.
Seminars and teaching
In the Winter of 2023, I taught Math 245B: "Topics in Algebraic geometry" on Deligne-Lusztig theory.
In the Fall of 2022 and the Winter of 2023, Lie Qian and I organised the Berkeley-Stanford number theory learning seminar on the Emerton-Gee stack, following the book of Emerton-Gee.
In the spring of 2022, I organised the Berkeley-Stanford number theory learning seminar on moduli spaces of Langlands-parameters, following the identically named paper of Dat-Helm-Kurinczuk-Moss.
In Winter of 2020, I co-organized a reading group on Deligne-Lusztig theory with Miriam Norris.
In Winter 2019, I co-organized the London Number Theory Study Group with Carl Wang-Erickson, Ashwin Iyengar and Alice Pozzi. The topic of the study group was the work of Akshay Venkatesh, in particular his work on derived structures in the Langlands program, specifically his Galois deformation theory paper with Soren Galatius and his Hecke algebra paper.
Notes / Miscellaneous
- Introduction to the Emerton-Gee stack. These are the notes from the first talk in the Stanford--Berkeley number theory learning seminar on the Emerton-Gee stack of the fall of 2022.
- Introduction to moduli spaces of local Langlands parameters. These are the notes from the first talk in the identically named Stanford--Berkeley number theory learning seminar in the spring of 2022.
- Higher Coleman Theory : These are the notes from two talks I gave in the London number theory study group in the fall of 2020, attempting to summarise the recent identically named work of Boxer and Pilloni. The first part of the talk is a general introduction to their results and techniques, and in the second part of the talk I specialise to Siegel threefolds and make everything as explicit as possible.
Construction of moduli schemes: smooth case: These are the notes from a talk I gave in the LTXZZ study group at Imperial in Winter 2020, which discusses the following recent work of Liu-Tian-Xiao-Zhang-Zhu. In the talk I start by discussing a baby case of what happens in Section 4 of the aforementioned paper and then discuss Section 4 in more detail.
Igusa Varieties & Mantovan's Formula: These are the notes from a talk I gave in the London number theory study group in summer 2019. I briefly review the Newton stratification on the mod p fiber of a PEL type Shimura variety (with good reduction at p) and then introduce Oort's foliation. After giving some background on completely slope divisible Barsotti-Tate groups I define Igusa varieties and prove that they are ètale covers of the leaves of the foliation. I end by defining the `product structure' on the Newton strata, which is a finite surjective map from the product of an Igusa variety with a truncated Rapoport-Zink space to a Newton stratum.
Perverse Sheaves and nearby cycles: These are the notes from a talk I gave in the London number theory study group in fall 2018. I introduce the triangulated category of l-adic sheaves with constructible cohomology and discuss the six functor formalism in this context. I then define the perverse t-structure and talk about the intermediate extension functor. In the last section I discuss Milnor fibers, nearby cycles and discuss the fact that nearby cycles 'preserve perversity'.
Perfectoid rings, A_inf, and the pro-ètale site: These are the notes from a talk I give in the London number theory study group in summer 2018. The first half follows Section 3 of Bhatt-Morrow-Scholze and the second half is about the pro-ètale site of an adic space (notes by James Newton).
Classical Motives: These are the notes from a talk I gave in the London number theory study group in spring 2018. I start by giving a quick introduction to intersection theory and then define various categories of Chow motives. I end by discussing the proof of Theorem 1 of Jannsen's paper Motives, numerical equivalence, and semi-simplicity.
Mixed Complexes: These are the notes from a talk I gave in the seminar on perverse sheaves in the spring of 2017 in Nijmegen. I introduce the notion of weight for an l-adic sheaf and define pure and mixed sheaves. I then discuss the derived category of such mixed sheaves and its stability properties under the six operations. I end by proving Proposition 5.12 of Beilinson-Bernstein-Deligne.
Descent of Morphisms: These are the notes from a talk I gave for topics in algebraic geometry in Spring 2016 in Leiden.
This website design was stolen (with permission) from Ashwin Iyengar.