CRC 326 - GAUS

AGTZ Kolloquium
2026-04-23 14:15 - 15:15 (Europe/Berlin) | Mainz, Hilbertraum 05-432
Kaif Hilmann (Uni Bonn)
Titel: Equivariant localizing motives for finite groups and applications
Abstract: In this talk, I will give a proposal for a definition of genuine equivariant lozalizing motives for finite groups G. Using isotropy separation arguments on equivariant cubes and the recent insights of Ramzi-Sosnilo-Winges, we use this version of motives to enhance the algebraic K-theory functor with the structure of multiplicative norms.
Among other things, we use our results to give a new and much simplified proof that K-theory admits polynomial functoriality, first proved in a celebrated paper of Barwick-Glasman-Mathew-Nikolaus. Time permitting, we will also discuss other applications such as constructing an equivariant Dennis trace map and showing that all genuine G-spectra are the K-theory of a G-stable category. This reports on joint work with Maxime Ramzi.

Symmetric Power Functoriality
2026-04-23 14:15 - 16:00 | Heidelberg
14:15 Talk 1: Unitary Groups: Alireza Shavali

Duality for the condensed cohomology of the Weil group of a p-adic field
2026-04-24 13:30 - 14:30 | Heidelberg, Mathematikon, SR A and Livestream
Marco Artusa (CIRM (Luminy) and I2M (Marseille))
Duality theorems are among the central results in arithmetic geometry. For $p$-adic fields, the earliest example is due to Tate, dealing with Galois cohomology of finite Galois modules. To extend this result to more general coefficients, one is forced to modify the original cohomology groups. This underlines some shortcomings of Galois cohomology, such as the lack of a natural topology on cohomology groups. In this talk, we build a new topological cohomology theory for p-adic fields, thanks to the Weil group and Condensed Mathematics. Moreover, we see how to use this cohomology theory to extend Tate’s result to more general topological coefficients. This new duality takes the form of a Pontryagin duality between locally compact abelian groups. As a particular case, one gets the reciprocity isomorphisms of local class field theory “à la Weil”, which identifies the units of a $p$-adic field and the abelianised Weil group. One could try to apply similar techniques to higher local fields. Inspired by Kato’s work, the hope is to obtain a condensed-Weil version of higher local class field theory, which would identify $d$-th Milnor $K$-theory of a higher local field with its abelianised Weil group.

Variation of crepant resolutions of Kleinian singularities
2026-04-24 14:00 - 16:00 | Heidelberg, MATHEMATIKON, SR 007, Im Neuenheimer Feld 205, Heidelberg, 69120, Germany
The McKay correspondence establishes a strong relationship between the classical minimal resolution and the standard orbifold resolution of a Kleinian surface singularity. Based on joint work with Ruth Wye, I will explain how the McKay correspondence extends to a larger class of crepant stacky resolutions of the singularity, and how their Hilbert schemes of points are related through variation of GIT quotients (VGIT). Time permitting, I will also sketch some recent ideas from work in progress with Austin Hubbard on how to relate the resolutions themselves via VGIT by taking into account the variation of monoidal structures on their mutual derived category.

Seminar on Arithmetic Geometry
2026-04-24 15:30 - 17:00 | Darmstadt, Room 401 and Zoom, Schlossgartenstraße 7, Darmstadt, 64289, Germany
Lucas Gerth (IMJ Paris): Moduli spaces of analytic p-divisible groups
Abstract: We prove a classification of families of analytic p-divisible groups on adic spaces S over Qp in terms of Hodge–Tate triples on S, generalizing a theorem of Fargues. From this, for S a perfectoid space, we construct an analytic Dieudonné theory with values in mixed characteristic Shtukas over the Fargues–Fontaine disc. As applications, we realize the local Shimura varieties of EL and PEL type of Scholze–Weinstein as moduli spaces of analytic p-divisible groups with framed universal cover, and we reinterpret the Hodge–Tate period map of Scholze in terms of topologically p-torsion subgroups of abelian varieties.
Zoom (635 7328 0984, Kenncode: kleinste sechsstellige Primzahl)

de Rham-Witt complex
2026-04-27 10:15 - 11:45 | Mainz, Hilbertraum 05-432
Niklas Stelzer:
§2 Dieudonné complexes 2/2
Some homological algebra.
Define Dieudonné complexes of Cartier type (Definition 2.4.1) and discuss Theorem 2.4.2. define completion of Dieudonné complexes (Construction 2.5.1) and strictness (Definition 2.5.4). Prove Proposition 2.6.5 in the particular case of W(M) ∗ for M∗ saturated (without mentioning strict Dieudonné towers). Cover §2.7 and §2.8.

Poincaré-Dualität in Charakteristik p
2026-04-30 09:00 - 11:00 | Heidelberg, Mathematikon, SR 8, Heidelberg, Germany
Vortrag 3: Logarithmische deRham-Witt-Garben II – tba

The K-theory of Z/p^n
2026-04-30 11:15 - 12:45 | Heidelberg, Mathematikon, SR 8 and Zoom, INF 205, Heidelberg, Germany
Talk 3: The prismatic crystal – Marvin Schneider / Rustam Steingart (Universität Heidelberg)

Symmetric Power Functoriality
2026-04-30 14:15 - 16:00 | Heidelberg
14:15 Talk 2: Background on p-adic Modular Forms: Timo Kränzle

de Rham-Witt complex
2026-05-04 10:15 - 11:45 | Mainz, Hilbertraum (05-432)
Andreas Gieringer:
§3: Dieudonné algebras
More homological algebra and our main examples.
Define Dieudonné algebras (Definition 3.1.2). Discuss Examples 3.1.8, 3.2, and that of the completed de Rham complex as a Dieudonné algebra (Variant 3.3.1, Corollary 3.3.8). Discuss Propositions 3.4.2 and 3.4.3. Prove Propositions 3.5.5 and 3.5.8, and Corollaries 3.5.9 and 3.5.10.

International Seminar on Automorphic Forms
2026-05-05 16:00 - 17:00
Clayton Williams (UIUC): Eisenstein series modulo prime powers
Eisenstein series modulo p are known classically, and recent work of Ahlgren, Hanson, Raum, and Richter determine these series modulo p2. Classical bounds for the weight of a modular form determining an Eisenstein series modulo prime powers pm are roughly pm. I will present joint work with Ahlgren and Castillo showing Eisenstein series are determined modulo pm by a modular form of weight no more than mp, together with an explicit recurrence.
Zoom (680 4828 0736, The password is the first Fourier coefficient of the modular j-function (as digits)).

Specialization of iterated Galois groups
2026-05-06 14:00 - 17:00 | Frankfurt, Robert-Mayer-Str. 6-8, Raum 308
14:00 – 15:15 Talk 1: Leonie Nienhaus (Goethe Universität Frankfurt): Overview of seminar
15:45 – 17:00 Talk 2: Jakob Stix (Goethe Universität Frankfurt): Introduction to arboreal Galois representations

Poincaré-Dualität in Charakteristik p
2026-05-07 09:00 - 11:00 | Heidelberg, Mathematikon, SR 8, Heidelberg, Germany
Vortrag 4: Logarithmische deRham-Witt-Garben III – tba

WKB Analysis: From Quadratic Differentials to Stokes matrices
2026-05-07 10:00 - 12:30 | Frankfurt, Robert-Mayer-Str. 6-8, Raum 309
10:00 – 11:00 Talk 1: Miguel Prado (Goethe Universität): Meromorphic differentials and their trajectories
11:30 – 12:30 Talk 2: Nicole Müller (Goethe Universität): CP1-structures and Schrödinger equations

The K-theory of Z/p^n
2026-05-07 11:15 - 12:45
Talk 4: The Nygaard filtration, syntomic cohomology and the prismatic package –
Marvin Schneider / Rustam Steingart (Universität Heidelberg)

CRC-Colloquium
2026-05-07 15:30 - 18:30 | Darmstadt
15:00 Coffee
15:30 – 16:30 Sabrina Pauli (TU Darmstadt): Tropical and Arithmetic Perspectives
16:30 Coffee and Cake
17:00 – 18:00 Jakob Stix (Goethe Universität Frankfurt): The Anabelian Section Conjecture
18:30 Dinner

Symmetric Power Functoriality
2026-05-08 09:15 - 11:00 | Heidelberg
09:15 Talk 3 Background on p-adic Hodge Theory: Miriam Philipp

Syntomic descent spectral sequence for arithmetic p-adic varieties
2026-05-08 13:30 - 14:30 | Heidelberg, Mathematikon, SR A and Livestream
Yicheng Zhou (Paris-Saclay)
For a “large” class of rigid-analytic varieties over a p-adic local field, we explain how to construct a natural syntomic descent spectral sequence compatible with the Hochschild-Serre spectral sequence. As a consequence, for proper rigid-analytic varieties, the étale regulators maps on suitable K-theoretic groups factor through their syntomic counterparts, for suitably defined syntomic Chern class maps.

de Rham-Witt Complex
2026-05-11 10:15 - 11:45 | Mainz, Hilbertraum (05-432)
Julie Bannwart
§4: Definition of the complex
The de Rham–Witt complex, its universal property, and relation to the de Rham complex. Cover §3.6 (discuss in particular Lemma 3.6.1 and Proposition 3.6.3). Define the saturated de Rham–Witt complex (Definition 4.1.1, Proposition 4.1.4). State Corollary 4.1.5. Prove Theorem 4.2.4. Prove Theorem 4.3.1 (make sure to state Corollary 4.3.5), and discuss Remark 4.3.6.

AGTZ-Kolloquium
2026-05-12 12:30 - 13:30 | Mainz, Hilbertraum (05-432)
Carl Mautner (University of California, Riverside, USA)
Hilbert schemes, perverse sheaves and a new Schur algebra
The Schur algebra is a finite-dimensional algebra that connects the representation theory of the symmetric and general linear groups. In joint work with Tom Braden, we give an algebraic description of the category of perverse sheaves with coefficients in a field of characteristic p on S^n(C^2), the n-fold symmetric product of the plane, in terms of a new, enhanced version of the Schur algebra. This work is motivated by a geometric description of the standard Schur algebra and the theory of symplectic duality.

International Seminar on Automorphic Forms
2026-05-12 16:00 - 17:00
Martin Raum (Goteborg): The geometric unitary Kudla Conjecture
Kudla and Millson proved that the generating series of cohomology classes associated with special cycles on orthogonal and unitary Shimura varieties is modular. This yields Siegel modular forms and Hermitian modular forms. In later work, Kudla conjectured that the analogous generating series of cycles in the Chow group is modular, too. The orthogonal case of the conjecture was established more than 10 years ago. We resolve the conjecture in the unitary case. In this talk, we explain in particular the role of automatic convergence results in the theory: how they arise and what techniques we currently have to prove them.
Zoom (680 4828 0736, The password is the first Fourier coefficient of the modular j-function (as digits)).

de Rham-Witt complex
2026-05-18 10:15 - 11:45 | Mainz, Hilbertraum (05-432)
Nutsa Gegelia
§5: Extension to schemes
The de Rham–Witt complex as a sheaf. The main goal is to prove Theorem 5.2.2 and Proposition 5.2.4. In pariticular, cover §5.1. As time permits, discuss §5.3 (étale behaviour).

Oberseminar Algebra und Geometrie
2026-05-18 16:00 - 18:00 | Frankfurt, Robert-Mayer-Str. 6-8, Raum 309
Michael Temkin (MPI Bonn): Wild Hurwitz spaces and level structures

Abstract: Hurwitz moduli spaces of covers of curves of degree d are classical and well studied objects if one assumes that d! is invertible and hence no wild ramification phenomena occur. There were very few attempts to study the wild case. In the most important one Abramovich and Oort started with the classical space H_{2,1,0,4} of double covers of P^1 ramified at four points and (following an idea of Kontsevich and Pandariphande) described its schematic closure H in the space of stable maps over Z. The result over F_2 was both strange and informative, but lacked a modular interpretation.
In the first part of my talk I will describe the example of Abramovich-Oort and then tell about a work in progress of Hippold, where a (logarithmic) modular version of compactified Hurwitz space of degree p is constructed when only (p-1)! is invertible. In particular, this conceptually explains phenomena observed by Abramovich-Oort. In the second part I will describe another outcome of the same ideas. It was observed by Abramovich-Oort that H is the blowing up of the modular curve X(2). This is not a coincidence, and the same ideas can be used to refine the wild level structures of Drinfeld and construct modular interpretation of the minimal modifications of the curves X(p^n) which separate ordinary branches at any supersingular point. This is a very recent work in progress and the precise description of the obtained spaces is still to be found.

International Seminar on Automorphic Forms
2026-05-19 16:00 - 17:00
Quasimodular forms for the orthogonal group and Gromov-Witten theory
Georg Oberdieck (Heidelberg)
In this talk we begin by introducing quasimodular forms for orthogonal groups as constant terms of almost-holomorphic modular forms. For this we introduce orthogonal lowering and raising operators. Basic results are the description of the spaces of quasimodular forms in terms of vectorvalued modular forms and the interaction with the theta lift. In particular, we give a criterion when the theta lift of a quasimodular form is again quasimodular (it is not always the case). In the second part of the talk I will explain how these quasimodular forms appear in the Gromov-Witten theory of Enriques surfaces. They also want to appear in the Gromov-Witten theory of K3 surfaces, but actually more general automorphic objects there. Based on joint work with Brandon Williams.
Zoom (680 4828 0736, The password is the first Fourier coefficient of the modular j-function (as digits)).

Poincaré-Dualität in Charakteristik p
2026-05-21 09:00 - 11:00 | Heidelberg, Mathematikon, SR 8, Heidelberg, Germany
Vortrag 5: Poincaré-Dualität – Christian Dahlhausen

WKB Analysis: From Quadratic Differentials to Stokes matrices
2026-05-21 10:00 - 12:30 | Frankfurt, Robert-Mayer-Str. 6-8, Raum 309
10:00 – 11:00 Talk 3: Lukas Schneider (Goethe Universität): WKB analysis 1: From Schrödinger equation to the Stokes grap
11:30 – 12:30 Talk 4: Martin Möller (Goethe Universität): WKB analysis 2: Borel summation and summability of the WKB solution

The K-theory of Z/p^n
2026-05-21 11:15 - 12:45
Talk 5: Crystalline degeneration and relative-to-absolute descent I – Anna Blanco Cabanillas (Universität Heidelberg)

AGTZ Kolloquium
2026-05-21 14:15 - 15:15 | Mainz, Hilbertraum (05-432)
Marc Hoyois (Uni Regensburg)
Poincaré localizing invariants of schemes
In joint work with Markus Land, we investigate motivic properties of Poincaré localizing invariants of schemes, like Grothendieck-Witt theory, and we establish that they satisfy a projective bundle formula and descent for the Nisnevich topology. This implies that the motivic sphere spectrum over (almost) any local ring R admits a faithful action of the Grothendieck-Witt group of nondegenerate symmetric bilinear forms over R.

Symmetric Power Functoriality
2026-05-21 14:15 - 16:00 | Heidelberg
14:15 Talk 4 Background on Galois Deformation Theory: Mingkuan Zhang

Construction of logarithmic cohomology theories
2026-05-22 13:30 - 14:30 | Heidelberg, Mathematikon, SR A and Livestream
Doosung Park (Wuppertal)
In this talk, I will explain a functor extending cohomology theories from schemes to log schemes. Using this functor, we can obtain the log cyclotomic trace, and we can represent K-theory in the logarithmic motivic homotopy category. I will also explain an application to the p-adic deformation problem for the K-theory of semistable schemes.
