CRC 326 - GAUS

Prismatization
2023-05-08 14:00 - 15:30 (Europe/Berlin) | Darmstadt and Mainz and Zoom
Tom Bachmann (Uni Mainz): Filtrations and endomorphisms via stacks
Main references: [Bhatt, Section 2.2.1 and 2.2.2], [BL1, App. D], and
[Mou].
(1) Explain quotient stacks of a scheme by a functor of groups, see for instance
[Kha, Section 4.4, in particular Theorem 4.28]8.
(2) Explain the notion of a graded and a filtered derived category. Explain
completeness, canonical and stupid filtration, mention its symmetric monoidal structure without defining precisely what a symmetric monoidal
structure is9, and explain the standard and the Beilinson t-structure.
3(3) Introduce the quotient stack A1=Gm, explain that it classifies generalized
Cartier divisors, see [Bhatt, 2.2.5] or [KhRy, 3.2].
(4) Formulate and prove [Bhatt, 2.2.6 + 2.2.8].
(5) Explain Gca and V(E) for a vector bundle E.
(6) Explain [Bhatt, 2.2.12 + 2.2.13] without going too much into detail although it would be nice to see, where characteristic zero” is needed.
(7) If time permits, explain [Bhatt, 2.2.14 { 2.2.16].
(8) In any case, explain [Bhatt, 2.2.17].
https://tu-darmstadt.zoom.us/j/62421505417?pwd=[REDACTED]
Meeting-ID: 624 2150 5417
Kenncode: [REDACTED]

Vectorial Drinfeld modular forms over Tate algebras
2023-05-09 13:30 - 15:00 | Heidelberg, Mathematikon, SR 8 and Zoom, INF 205, Heidelberg, Germany
Paola Francesca Chilla: Introduction to weak vectorial Drinfeld modular forms
Our goal in this talk is to introduce weak vectorial Drinfeld modular forms which will
have a crucial role to determine special values of Goss L-functions. We need to emphasize
that VDMFs given in [Pel12, Def. 12] are indeed seen as weak VDMFs in [PP18, Def. 3.4].
Throughout the seminar, we will borrow this terminology and call them weak VDMFs. Our
main goal for the talk is to analyze the C∞-vector spaces of a certain subclass of weak
VDMFs studied in [Pel12]. The talk will start with basic definitions. Later on we prove
[Pel12, Lem. 13] which indeed implies that one dimensional weak VDMFs corresponding to
the trivial representation 1 are nothing but weak Drinfeld modular forms tensored with T.
This will imply that the space of Drinfeld modular forms tensored with T is equal to the
space of VDMFs corresponding to 1. Thus one needs to focus on the higher dimension case
to produce non-trivial examples. For this aim, we define the functions F and F∗ given in
[Pel12, §2.2, 2.3], which are examples of weak VDMFs of dimension two constructed by using
Anderson generating functions. We also define the deformation of the Eisenstein series. We will finalize the talk with a sketch of the proof of [Pel12, Prop. 19]. The main references are[Pel12, §1,2] and [Pel14, §2,3]

Superconnections, Theta series and period domains
2023-05-10 13:15 - 14:45 | Darmstadt, Room 244 and Zoom, Schlossgartenstraße 7, Darmstadt, 64289
Some classical results of Kudla and Millson.
Fabian Scherf
Zoom meeting ID 667 3384 5311
Password in request.

Prismatization
2023-05-15 14:00 - 15:30 | Darmstadt and Mainz and Zoom
Rizacan Ciloglu (TU Darmstadt): Warm-Up: De Rham cohomology in characteristik 0
https://tu-darmstadt.zoom.us/j/62421505417?pwd=[REDACTED]
Meeting-ID: 624 2150 5417
Kenncode: [REDACTED]

Vectorial Drinfeld modular forms over Tate algebras
2023-05-16 13:30 - 15:00 | Heidelberg, Mathematikon, SR 8 and Zoom, INF 205, Heidelberg, Germany
Alireza Shavali Kohshor: Special values of L-functions

Superconnections, Theta series and period domains
2023-05-17 13:15 - 17:00 | Darmstadt, Room 244 and Zoom, Schlossgartenstraße 7, Darmstadt, 64289
Superconnections
Mingkuan Zhang (TU Darmstadt)

Zoom meeting ID 667 3384 5311
Password on request.

Prismatization
2023-05-22 14:00 - 15:30 | Darmstadt and Mainz and Zoom
Patrick Bieker: G# a and GdR
https://tu-darmstadt.zoom.us/j/62421505417?pwd=[REDACTED]
Meeting-ID: 624 2150 5417
Kenncode: [REDACTED]

Vectorial Drinfeld modular forms over Tate algebras
2023-05-23 13:30 - 15:00 | Heidelberg, Mathematikon, SR 8 and Zoom, INF 205, Heidelberg, Germany
Gebhard Böckle: Vectorial Drinfeld modular forms
Our fifth talk is to start investigating VDMFs as well as discussing their several propertieswhich will be later used to reveal some applications for Drinfeld modular forms. They areweak VDMFs corresponding to a certain character with a regularity condition introduced in[PP18, Def. 3.4(2)]. After defining VDMFs, we revisit the deformation of Eisenstein seriesand prove [PP18, Prop. 3.7] which gives the Fourier expansion of their each entry (see also[Pel12, Lem. 21]). An equivalent condition for the regularity [PP18, Cor. 2.6] should alsobe analyzed. Later on, we introduce the function F discussed in the previous talk and showthat it is indeed not a VDMF in the sense of [PP18]. The final goal is to prove [PP18, Thm.3.9] which allows one to decompose a certain space of VDMFs into components generatedby an Eisenstein series E1 and its twist, the image of E1 under the q-th power Frobenius
automorphism of T.

Superconnections, theta series, and period domains
2023-05-24 13:15 - 14:45 | Darmstadt, Room 244 and Zoom, Schlossgartenstraße 7, Darmstadt, 64289
Period domains and invariant forms
Jiaming Chen
Zoom meeting ID 667 3384 5311
Password on request.

Six functor formalism and Poincaré duality
2023-05-25 09:30 - 11:00 | Heidelberg, Mathematikon, SR 8 und Zoom, Germany
Talk 4: Christian Dahlhausen (Universität Heidelberg): 6FF: ∞-categorical background

Bridgeland stability conditions and applications
2023-05-25 15:15 - 17:45 | Frankfurt, Robert-Mayer-Str. 10, Raum 711 groß
Talk 5: K. Kühn (Goethe Universität Frankfurt): Stability conditions on triangulated categories
Talk 6: J. Horn (Goethe Universität Frankfurt): The stability manifold

Vectorial Drinfeld modular forms over Tate algebras
2023-05-30 13:30 - 15:00 | Heidelberg, Mathematikon, SR 8 and Zoom, INF 205, Heidelberg, Germany
Sriram Chinthalagiri Venkata: Drinfeld modular forms of prime power levels via vectorial modular forms
We now focus on another application of VDMFs for obtaining Drinfeld modular forms of
certain level. This will be done by evaluating T-valued functions on a particular point of C∞
as well as taking the hyperderivatives of entries of VDMFs. More precisely, the talk should
cover the content of [PP18, Prop. 4.11] and [PP18, Prop. 4.19]. Hence it should be organized
so that all necessary background, such as Drinfeld modular forms for congruence subgroups and notion of hyperderivatives, to achieve the above mentioned results are introduced. The main references are [PP18, §4.1–4.2.4] and [PP18, §4.4–4.4.2].

Superconnections, Theta series and period domains
2023-05-31 13:15 - 17:00 | Darmstadt, Room 244 and Zoom, Schlossgartenstraße 7, Darmstadt, 64289
Relations with the Kudla–Millson forms
Gabriele Bogo (TU Darmstadt)
Zoom meeting ID 667 3384 5311
Password on request.

Six functor formalism and Poincaré duality
2023-06-01 09:30 - 11:00 | Heidelberg, Mathematikon, SR 8 und Zoom, Germany
Talk 5: Morten Lüders (Universität Heidelberg): Symmetric monoidal ∞-categories and 6FF

Bridgeland stability conditions and applications
2023-06-01 15:15 - 17:45 | Frankfurt, Robert-Mayer-Str. 10, Raum 711 groß
Talk 7: R. Zuffetti (TU Darmstadt): Stability conditions on surfaces
Talk 8: J. So (GU Frankfurt): Walls and chambers

Prismatization
2023-06-05 14:00 - 15:30 | Darmstadt and Mainz and Zoom
Lorenzo Mantovani (Uni Mainz): G# a and GdR
https://tu-darmstadt.zoom.us/j/62421505417?pwd=[REDACTED]
Meeting-ID: 624 2150 5417
Kenncode: [REDACTED]

Vectorial Drinfeld modular forms over Tate algebras
2023-06-06 13:30 - 15:00 | Heidelberg, Mathematikon, SR 8 and Zoom, INF 205, Heidelberg, Germany
Oğuz Gezmiş: Hecke operators
Our goal in the last talk is to study Hecke operators acting on the space of VDMFs and consequences of such an action for Drinfeld modular forms. In particular, applying hyperderivatives and evaluating the coordinates of vectorial modular forms at roots of unity, we will obtain Hecke eigenforms for certain congruence subgroups of GL2(A). We start with defining the slash operator and the Hecke operator Tp for each monic irreducible polynomial p in A. Later on, we give the necessary ideas for the proof of [PP18, Prop. 5.12, Prop. 5.18] and briefly mention why the regularity condition is required for the stability of the space of VDMFs under Hecke operators [PP18, Rem. 5.13]. We continue with giving some examples of Hecke eigenforms in our setting and analyze the behavior of vectorial Eisenstein series under Tp as well as provide a sketch of a proof for [PP18, Cor. 5.23-5.24]. The main reference for the talk is [PP18, §5–5.3].

Prismatization
2023-06-12 14:00 - 15:30 | Darmstadt and Mainz and Zoom
Marcin Lara (Uni Frankfurt): Hodge filtered de Rham cohomology of p-adic formal schemes
https://tu-darmstadt.zoom.us/j/62421505417?pwd=[REDACTED]
Meeting-ID: 624 2150 5417
Kenncode: [REDACTED]

Superconnections, Theta series and period domains
2023-06-14 13:15 - 14:45 | Darmstadt, Room 244 and Zoom, Schlossgartenstraße 7, Darmstadt, 64289
Weil Representation and Modularity
Christina Röhrig (TU Darmstadt)
Zoom meeting ID 667 3384 5311
Password on request.

Prismatization
2023-06-19 14:00 - 15:30 | Darmstadt and Mainz and Zoom
Christopher Lang (TU Darmstadt): The conjugate filtration in characteristic p
https://tu-darmstadt.zoom.us/j/62421505417?pwd=[REDACTED]
Meeting-ID: 624 2150 5417
Kenncode: [REDACTED]

Superconnections, Theta series and period domains
2023-06-21 13:15 - 14:45 | Darmstadt, Room 244 and Zoom, Schlossgartenstraße 7, Darmstadt, 64289
Green Forms for Special Cycles I.
Riccardo Zuffetti (TU Darmstadt)
Zoom meeting ID 667 3384 5311
Password on request.

Bridgeland stability conditions and applications
2023-06-22 15:15 - 17:45 | Purely Online (Exceptional)
Talk 9: A. Bud (GU Frankfurt): Moduli spaces of Bridgeland semistable objects
Talk 10: J. Chen (GU Frankfurt): The Positivity Lemma

Prismatization
2023-06-26 14:00 - 15:30 | Darmstadt and Mainz and Zoom
Thibaud van den Hove (TU Darmstadt): Prismatization in characteristic p
https://tu-darmstadt.zoom.us/j/62421505417?pwd=[REDACTED]
Meeting-ID: 624 2150 5417
Kenncode: [REDACTED]

Superconnections, Theta series and period domains
2023-06-28 16:00 - 17:00 | Darmstadt, Room 244 and Zoom, Schlossgartenstraße 7, Darmstadt, 64289
Green Forms for Special Cycles II.
Yingkun Li (TU Darmstadt)
Zoom meeting ID 667 3384 5311
Password on request.

Six functor formalism and Poincaré duality
2023-06-29 09:30 - 11:00 | Heidelberg, Mathematikon, SR 8 und Zoom, Germany
Talk 6: Lukas Waas (Universität Heidelberg): 6FF: construction via compacti cation

Bridgeland stability conditions and applications
2023-06-29 15:15 - 17:45 | Darmstadt, S2|15, Room 201 and Zoom
Talk 11: M. Möller (GU Frankfurt): The projectivity of the Bridgeland moduli space for K3
Talk 12: Emanuele Marci (Université Paris-Saclay, Orsay): Bridgeland stability conditions on Calabi-Yau manifolds
Abstract:
I will give a short overview on Bridgeland stability conditions on Calabi-Yau manifolds, presenting in particular the case of the quintic threefold (C. Li’s Theorem) with applications and, if time permits, of abelian and hyper-Kähler varieties.

Prismatization
2023-07-03 14:00 - 15:30 | Darmstadt and Mainz and Zoom
Manuel Blickle (Uni Mainz): Nygaard filtered prismatization over a perfect field
https://tu-darmstadt.zoom.us/j/62421505417?pwd=[REDACTED]
Meeting-ID: 624 2150 5417
Kenncode: [REDACTED]

Superconnections, Theta series and period domains
2023-07-05 13:15 - 14:45 | Darmstadt, Room 244 and Zoom, Schlossgartenstraße 7, Darmstadt, 64289
Green forms and the Siegel–Weil formula
Jan Hendrik Bruinier (TU Darmstadt)
Zoom meeting ID 667 3384 5311
Password in request.

Prismatization
2023-07-10 | Darmstadt and Zoom
Talk 1: Can Yaylali (TU Darmstadt): Prismatic gauges over a perfect field (10:00 in S2|15 051, TU Darmstadt)
Lunch (12:00, Mensa TU Darmstadt)
Talk 2: Torsten Wedhorn (TU Darmstadt): Syntomification of smooth schemes over perfect fields (14:00 in S2|15 051, TU Darmstadt)
Talk 3: Anton Güthge (TU Darmstadt): F-Gauges and syntomic cohomology (16:00 in S2|15 051, TU Darmstadt)
Dinner (18:00)
https://tu-darmstadt.zoom.us/j/62421505417?pwd=[REDACTED]
Meeting-ID: 624 2150 5417
Kenncode: [REDACTED]

Superconnections, Theta series and period domains
2023-07-12 13:15 - 14:45 | Darmstadt, Room 244 and Zoom, Schlossgartenstraße 7, Darmstadt, 64289
tba
Luis Garcia (University College London)
Zoom meeting ID 667 3384 5311
Password in request.
