http://www-math.umd.edu/research/seminars.html http://www-math.umd.edu/research/seminars.html Wed, 08 Oct 2025 14:00:00 EDT Where: Kirwan Hall 3206
Speaker: Zev Rosengarten (The Hebrew University of Jerusalem) - https://sites.google.com/view/zevrosengarten

Abstract: In 1984, Oesterle asked whether a wound unipotent group admitting infinitely many rational points over a global function field necessarily contains a nontrivial unirational subgroup -- that is, do rational points only arise for a good geometric reason? Though he formulated the question for wound unipotent groups, it makes sense for arbitrary linear algebraic groups -- although one may show that the more general question ultimately boils down to the wound unipotent case. Using some recent work of mine on the structure of wound unipotent groups, I shall outline a positive answer to Oesterle's question, and in fact discuss a stronger result which holds over more general fields of arithmetic interest. Time permitting, I will also discuss how these structural results can be combined with local Tate duality to give a criterion for which linear algebraic groups over local function fields have finite cohomology.
]]> http://www-math.umd.edu/research/seminars.html Wed, 15 Oct 2025 14:00:00 EDT Where: Kirwan Hall 3206
Speaker: Guido Bosco (Princeton University ) - https://guests.mpim-bonn.mpg.de/bosco/

Abstract: In the past decade, p-adic Hodge theory has been transformed by the discovery of perfectoid spaces and the Fargues–Fontaine curve. One area, however, that has remained almost untouched by these breakthroughs is the theory of p-adic differential equations, as initiated by Dwork and Robba. After all, perfectoid spaces do not carry interesting differential forms in the naive sense. In this talk, I will explain how to address this issue and, more generally, how one can define D-modules on arc-stacks living over Q_p. I will then focus on D-modules on the Fargues–Fontaine curve and sketch a new proof of the cornerstone of the theory of p-adic differential equations, namely the p-adic monodromy theorem. Finally, I will outline how this perspective also leads to new results and conjectures on p-adic cohomology theories, such as Hyodo–Kato cohomology.
Based on joint work with Anschütz, Le Bras, Rodriguez Camargo, and Scholze.
]]> http://www-math.umd.edu/research/seminars.html Wed, 29 Oct 2025 14:00:00 EDT Where: Kirwan Hall 3206
Speaker: Matt Broe (Boston University) - https://sites.google.com/view/mattbroe/home

Abstract: The Beilinson-Bloch conjecture is a generalization of the Birch and Swinnerton-Dyer conjecture, which relates the ranks of Chow groups of smooth projective varieties over global fields to the order of vanishing of L-functions. We construct classes of non-isotrivial hypersurfaces over global function fields for which the conjecture can be verified. These include some quartic K3 surfaces, whose groups of zero-cycles of degree zero we prove to be finite. We also prove that the Chow motive of a smooth cubic threefold over any field has a certain summand coming from its intermediate Jacobian, which is an associated abelian fivefold. We thus deduce the Birch and Swinnerton-Dyer conjecture for the intermediate Jacobians of cubic threefolds constructed in the previous step. Finally, combining this case of BSD with results of Roulleau and Geisser, we prove some new cases of the Tate conjecture over finite fields.
]]> http://www-math.umd.edu/research/seminars.html Mon, 10 Nov 2025 14:00:00 EST Where: Kirwan Hall 3206
Speaker: Jared Weinstein (Boston University) - https://sites.google.com/view/jared-weinstein/home

Abstract: The complex unit disc is conformally equivalent to the upper half-plane.  In 2002, Faltings proved a p-adic version:  the p-adic unit disc is isomorphic to Drinfeld’s upper half-plane, up to the action of some profinite groups.  We present a family of Faltings-style isomorphisms, occurring entirely in characteristic p, which relates a moduli space of formal groups to a "mod p period domain".  The motivation is entirely from chromatic homotopy theory, but along the way there is much interesting p-adic geometry and mod p representation theory of p-adic groups.  This is joint work with many people.
]]> http://www-math.umd.edu/research/seminars.html Wed, 12 Nov 2025 14:00:00 EST Where: Kirwan Hall 3206
Speaker: Tess Bouis (Institute for Advanced Study) - https://tessbouis.com/

Abstract: Serre's classical GAGA theorem states that coherent sheaves on a proper complex algebraic variety are the same as those of its analytification. In particular, one finds that the algebraic and analytic Picard groups agree for proper varieties. The Picard group being the degree-two weight-one motivic cohomology group, one may wonder to what extend motivic cohomology does satisfy some GAGA comparison in general. In this talk, I want to discuss some answers to the non-archimedean analogue of this question. In particular, I will explain how to use recent progress in motivic cohomology to define a good notion of "analytic cycles" on rigid-analytic varieties, and report on a GAGA theorem between algebraic and analytic zero-cycles. This is based on joint work in progress with Elden Elmanto, Brian Shin, and Mahdi Rafiei.
]]> http://www-math.umd.edu/research/seminars.html Mon, 17 Nov 2025 14:00:00 EST Where: Kirwan Hall 3206
Speaker: Michael Temkin (The Hebrew University of Jerusalem) - https://math.huji.ac.il/~temkin/

Abstract: Since Hironaka's famous resolution of singularities in characteristics zero in 1964, it took about 40 years of intensive work of many mathematicians to simplify the method, describe it using conceptual tools and establish its functoriality. However, one point remained quite mysterious: despite different descriptions of the basic resolution algorithm, it was essentially unique. Was it a necessity or a drawback of the fact that all subsequent methods relied on Hironaka's ideas essentially?

The situation changed in the last decade, when a logarithmic, a weighted and a foliated analogues and generalizations were discovered in works of Abramovich-Temkin-Wlodarzcyk, McQuillan, Quek, Abramovich-Temkin-Wlodarzcyk-Belotto and others. At this stage we can already try to figure out general ideas and principles shared by all these methods and the picture is quite surprising -- it seems that each method is quite determined by its basic setting consisting of the class of geometric objects and basic blowings up one works with. In particular, the classical method is probably the only natural resolution (via principalization) method obtained by blowing up smooth centers in the ambient manifold.

In my talk I'll describe the settings and the methods on a very general level. If time permits, I will add some details about the simplest dream (or weighted) method, which has no memory and improves the singularity invariant by each weighted blowing up. Thus, the algorithm becomes simplest possible and the (modest) price one has to pay consists of extending the setting of varieties (or schemes) and blowings up along smooth centers to the setting of orbifolds and blowings up weighted centers.
]]> http://www-math.umd.edu/research/seminars.html Wed, 19 Nov 2025 14:00:00 EST Where: Kirwan Hall 3206
Speaker: Linus Hamann (Harvard University) - https://people.math.harvard.edu/~hamann/

Abstract: Shimura Varieties are of fundamental importance in number theory, by virtue of the fact that their cohomology provides the only known geometric incarnations of the global Langlands correspondence over number fields. When the Shimura Variety is non-compact, it is often very desirable to work with the intersection cohomology of its minimal compactification, as this can be related to L^2-cohomology of the associated symmetric space, and the latter is computed in terms of the (g,K)-cohomology of the discrete spectrum of the space of automorphic forms via the work of Borel-Cassleman. In this talk, we investigate the relationship of intersection cohomology with a structure coming from the incarnation of the Shimura variety as a p-adic manifold. Namely, we study how the intersection cohomology interacts with Mantovan’s filtration, which generalizes the filtration on the cohomology of the modular curve coming from excision with respect to the ordinary and supersingular locus. We accomplish this by describing the intersection cohomology as a certain Hecke operator applied to a sheaf on Bun_{G}, the moduli stack of G-bundles of the Fargues-Fontaine curve and then explicitly describing the stalks in terms of an intermediate extension from Igusa varieties to their affine partial minimal compactifications.  The aforementioned filtration can then be understood via excision applied to the Harder-Narasimhan stratification of this sheaf on Bun_{G}. This leads to the hope that Borel-Cassleman’s description of the L^{2}-cohomology can be refined to a description of our sheaf in terms of direct sums of certain “sheared” Hecke eigensheaves on Bun_{G}, where the shearing encodes the known relationship between the (g,K)-cohomology and the Arthur SL_{2} of the A-parameters attached to the discrete spectrum via the work of Adams-Johnson and Vogan-Zuckerman. This is joint work in progress with Ana Caraiani and Mingjia Zhang.
]]> http://www-math.umd.edu/research/seminars.html Wed, 10 Dec 2025 14:00:00 EST Where: Kirwan Hall 3206
Speaker: Sean Howe (University of Utah) - https://www.math.utah.edu/~howe/

Abstract: For S a smooth rigid analytic variety over a complete extension of Q_p, we define a category of variations of twistors bundles on the relative thickened Fargues-Fontaine curve over S that plays a role in relative p-adic Hodge theory similar to Simpson’s theory of variations of twistor structures over complex manifolds. When the base field is discretely valued, we construct a fully faithful functor from Q_p-local systems on S to this category and, as an application, describe Banach-Colmez tangent bundles for p-adic Lie group torsors and differentiate period maps for de Rham torsors.  Along the way we will highlight connections with other recent advances in relative p-adic Hodge theory including geometric Sen theory, the p-adic Simpson and Riemann-Hilbert correspondences, and analytic prismatization.
]]> http://www-math.umd.edu/research/seminars.html Mon, 02 Feb 2026 14:00:00 EST Where: Kirwan Hall 3206
Speaker: Naomi Sweeting (Princeton University) - https://sweeting.scholar.princeton.edu/

Abstract: Quaternionic modular forms on G_2 carry a surprisingly rich arithmetic structure. For example, they have a theory of Fourier expansions where the Fourier coefficients are indexed by totally real cubic rings. For quaternionic modular forms on G_2 associated via functoriality with certain modular forms on PGL_2, Gross conjectured in 2000 that their Fourier coefficients encode L-values of cubic twists of the modular form (echoing Waldspurger's work on Fourier coefficients of half-integral weight modular forms). This talk will report on recent work proving Gross's conjecture when the modular forms are dihedral, giving the first examples for which it is known. Everything in the talk is joint work with Petar Bakic, Alex Horawa, and Siyan Daniel Li-Huerta.
]]> http://www-math.umd.edu/research/seminars.html Mon, 09 Feb 2026 14:00:00 EST Where: Kirwan Hall 3206
Speaker: Sean Cotner (University of Michigan) - https://public.websites.umich.edu/~stcotner/

Abstract: We will recall some features of the local Langlands program, as well as recent work in reformulating it in a categorical framework. We will discuss partial calculations of the Fargues–Scholze L-parameters associated to tame supercuspidal representations of reductive p-adic groups, by chaining together some instances of "modular functoriality". This is joint work with Tony Feng.
]]> http://www-math.umd.edu/research/seminars.html Mon, 16 Feb 2026 14:00:00 EST Where: Kirwan Hall 3206
Speaker: Keerthi Madapusi (Boston College) - https://sites.google.com/a/bc.edu/keerthi/
Abstract: Counting mod p points on Shimura varieties has been for a few decades the main avenue for establishing non-abelian reciprocity laws. This began with the work of Deligne and Langlands on the modular curve, continued with that of Kottwitz on PEL type Shimura varieties, and has culminated in recent work of Kisin and Kisin-Shin-Zhu (KSZ) on varieties of abelian type. All of these results depend ultimately on a serious use of isogenies between abelian varieties with additional structure. In this talk, I’ll explain how to prove variants of the Langlands-Rapoport conjectures formulated by KSZ using structural properties of integral models that avoid any discussion of abelian varieties or even p-divisible groups, and works also for many exceptional Shimura data for large enough p. This is based on joint work with Alex Youcis and also with Si Ying Lee.
]]> http://www-math.umd.edu/research/seminars.html Wed, 04 Mar 2026 14:00:00 EST Where: Kirwan Hall 3206
Speaker: Kęstutis Česnavičius (Institut de Mathématique d'Orsay) - https://www.imo.universite-paris-saclay.fr/~kestutis.cesnavicius/

Abstract: I will present a purely algebraic method for arguing the Cartan decomposition and the variant of the Grothendieck—Serre conjecture about generically trivial torsors over arbitrary Henselian valuation rings. In special cases, these results can also be argued using Bruhat—Tits theory. Instead, I will discuss how the general case of Henselian valuation rings of arbitrary rank directly follows from suitable extension techniques for torsors and invariance results for stacky Henselian pairs.
]]> http://www-math.umd.edu/research/seminars.html Mon, 23 Mar 2026 16:00:00 EDT Where: Kirwan Hall 3206
Speaker: Peter Dillery (University of Bonn) -
Abstract: A major goal of the Langlands program is to describe the
multiplicity of an irreducible discrete automorphic representation of a
connected reductive group G in its discrete L2-spectrum. The first goal of
this talk is to explain work from the last few years which gives the first
conjectural formula for this multiplicity for general G over a global
field, as envisioned by Kottwitz in 1984. We then discuss recent work
which we hope lays the foundations for proving cases of these formulas
using the geometric framework of Fargues and Scholze.
]]> http://www-math.umd.edu/research/seminars.html Wed, 25 Mar 2026 14:00:00 EDT Where: Kirwan Hall 3206
Speaker: Tsao-Hsien Chen (University of Minnesota) -  https://sites.google.com/site/tsaohsienchen/
Abstract:  I will first give a review of the well-studied relationship between  Loop groups, vector bundles on complex P^1 and Langlands duality for reductive groups. Then I will discuss recent progress on establishing a similar relationship in the setting of loop spaces of symmetric spaces (or spherical varieties), vector bundles on twistor P^1  (or real projective line RP^1) and Langlands duality for real groups (or Relative Langlands duality). The key ingredients include a Matsuki duality for loop groups and a version of derived Satake equivalence for ramified groups. I will discuss  applications of such connections to Ben-Zvi-Nadler's conjecture on Betti Geometric Langlands for real groups and Ben-Zvi-Sakellaridis-Venkatesh's conjecture on relative derived Satake equivalence for symmetric spaces. If time permits, I will mention a hope / speculation in the mixed characteristic setting.
]]> http://www-math.umd.edu/research/seminars.html Mon, 30 Mar 2026 14:00:00 EDT Where: Kirwan Hall 3206
Speaker: Linquan Ma (Purdue University) - https://www.math.purdue.edu/~ma326/

Abstract: We introduce a mixed characteristic analog of F-pure singularities, which we call perfectoid pure singularities. We will present some basic and expected properties of these singularities including their connections with log canonical singularities. We will then show how to produce examples of these singularities via deformation to positive characteristic and discuss some related open questions. This talk is based on joint work with Bhargav Bhatt, Zsolt Patakfalvi, Karl Schwede, Kevin Tucker, Joe Waldron, and Jakub Witaszek.
]]> http://www-math.umd.edu/research/seminars.html Mon, 20 Apr 2026 14:00:00 EDT Where: Kirwan Hall 3206
Speaker: Devarshi Mukherjee (University of Oxford) - https://sites.google.com/view/devarshimukherjee
Abstract: We discuss several categories of analytic stacks relative to the category of bornological modules over a Banach ring. When the underlying Banach ring is a nonarchimedean valued field, this category contains derived rigid analytic spaces as a full subcategory. When the underlying field is the complex numbers, it contains the category of derived complex analytic spaces. We then consider localising invariants of rigid categories associated to bornological algebras. The main results in this part include Nisnevich descent for derived analytic spaces and a version of the Grothendieck-Riemann-Roch Theorem for derived dagger analytic spaces over an arbitrary Banach ring.
]]> http://www-math.umd.edu/research/seminars.html Tue, 21 Apr 2026 15:30:00 EDT Where: Kirwan Hall 1308
Speaker: Baidehi Chattopadhay (UMD) -

]]> http://www-math.umd.edu/research/seminars.html Wed, 22 Apr 2026 14:00:00 EDT Where: Kirwan Hall 3206
Speaker: Longke Tang (Princeton University ) - https://web.math.princeton.edu/~longket/

Abstract: For smooth manifolds, the Gysin map of a closed immersion is defined as the cohomology applied on the Pontryagin–Thom collapse map, which collapses the ambient manifold to the one-point compactification of the tubular neighborhood of the closed submanifold. In this talk, I will present a version of the Pontryagin–Thom collapse map in algebraic geometry, more precisely in 𝐏¹-homotopy theory, using a compactified deformation to the normal cone. This yields the Gysin map for all known or unknown cohomology theories with 𝐏¹-homotopy invariance, including étale, Hodge, crystalline, prismatic, etc. I will also survey applications of my Gysin map to more concrete arithmetic questions, including recent work of Carmeli–Feng on Brauer groups of surfaces over finite fields.
]]> http://www-math.umd.edu/research/seminars.html Mon, 27 Apr 2026 14:00:00 EDT Where: Kirwan Hall 3206
Speaker: Casimir Kothari (University of Chicago) - https://math.uchicago.edu/~ckothari/

Abstract: Dieudonné theory is the study of families of group schemes via linear-algebraic data.  In this talk, I will begin by recalling some motivation for Dieudonné theory, with examples.  Then I will explain some new classification and smoothness results for certain close relatives of p-divisible groups known as n-smooth groups, which affirmatively answer conjectures of Drinfeld. This is joint work with Joshua Mundinger.
]]> http://www-math.umd.edu/research/seminars.html Wed, 29 Apr 2026 14:00:00 EDT Where: Kirwan Hall 3206
Speaker: Dongryul Kim (Stanford University) - https://web.stanford.edu/~dkim04/

Abstract: Igusa stacks are $p$-adic geometric objects, recently introduced byMingjia Zhang, that roughly parametrize ways to $p$-adically
uniformize (global) Shimura varieties by local Shimura varieties. In
joint work with Patrick Daniels, Pol van Hoften, and Mingjia Zhang, we
construct Igusa stacks for all abelian type Shimura data and use them
to the study of $\ell$-adic cohomology of Shimura varieties. I will
discuss the geometric ingredients that go into the construction as
well as how it naturally fits into Fargues--Scholze's framework of
categorical local Langlands.
]]>