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This semester we want to understand the paper "Projectivity of the Witt vector affine Grassmannian" by Bhatt and Scholze.

Program: program GrWaff.

Dates and location: Tuesdays, 14:00-15:30, in 05-426. It is also possible to participate via Zoom.

Zoom coordinates: Meeting ID: 912 4572 6486. Passcode: affinewitt

List of talks:

-- in case our poster made you thirsty try one of these

SFB/TRR 45 Summer School, July 9--13 2018, Mainz, Germany

The purpose is to familiarize the participants with techniques from Hodge Theory, in particular mixed Hodge modules, and their applications to problems in birational geometry.

Speakers

Mihnea Popa (Northwestern) (mini-course)

Mircea Mustata (Michigan) (mini-course)

Florian Ivorra (Rennes) (mini-course)

Jean Babtiste Teyssier (Leuven) (intro nearby cycles)

Nero Budur (Leuven)

Christian Schnell (Stony Brook)

Lei Wu (Utah) (problem sessions)

Organizer

Manuel Blickle (Mainz) (blicklem@uni-mainz.de)

Registration and financial support

Full financial support is available for members of the SFB/TRR 45. There is limited financial support available for local expenses (hotel costs) only. Please indicate on the application form if you require financial support:

Registration is closed.

With questions of non-mathematical nature please contact our secretarial support Ms Gonska (gonska@uni-mainz.de)

Venue

The conference takes place at the Institute of Nuclear Physcis at the Johannes Gutenberg-Universität Mainz (see Campus Map).

Preparation workshop in Freiburg

There is a series of introductory talks about D-modules and Hodge modules shortly before the workshop at FRIAS in Freiburg, Germany. Click here for more information.

Schedule

(*) the semifinals of the soccer worldcup can be watched on Campus at the Kulturcafe or in town: see map

Abstracts and Notes

Florian Ivorra: Introduction to mixed Hodge Modules

1. Overview and motivation
The goal of this lecture is to motivate the introduction of Hodge modules. I will make a short incursion into the l-adic theory over finite field which provided a model for the theory. I will then recall some basic notions in Hodge theory and outline the strategy behind the definition of a Hodge module.

2. Perverse sheaves and intersection complexes
In this lecture, I will focus on perverse sheaves, recalling the definition and their relations with D-modules. I will introduce also intermediate extensions, intersection complexes and explain the structure theorem for simple perverse sheaves.

3. Around the definition of Hodge modules
In the this lecture, I will explain the inductive definition of a (pure) Hodge module and introduce two of the main theorems. If time permits, I will give an overview of the mixed case.

Mihnea Popa: Hodge modules, birational geometry, and families of varieties

Mircea Mustata: Hodge modules, birational geometry, and singularities

Jean Babtiste Teyssier: Introduction to Nearby Cycles for D-modules

We will explain the construction of nearby cycles for D-modules relevant to the theory of Hodge modules, as well as its main properties.

Teyssier: Intro Nearby Cycles

Nero Budur: Absolute sets and the Decomposition Theorem

The celebrated Monodromy Theorem states that the eigenvalues
of the monodromy of a polynomial are roots of unity. In this talk we
give on overview of recent results on local systems giving a
generalization of the Monodromy Theorem. We end up with a conjecture
of André-Oort type for special loci of local systems. The conjecture
is true in rank one. If true in general, it would provide a simple conceptual
proof for all semi-simple perverse sheaves of the Decomposition Theorem, assuming only the geometric case (Beilinson-Bernstein-Deligne-Gabber) or the MHM case (Saito). Joint work with Botong Wang.

Christian Schnell: Extension theorems for holomorphic forms on singular spaces

Lei Wu: Afternoon Problem Sessions

Local Information

Hotel

Regardless of whether they receive funding from us or not, participants have to book accommodation themselves. Here are some suggestions:

• Hotel Hammer
• Hotel Advena
• Hotel Römerstein
• Hotel Königshof
• Intercity Hotel Mainz
• Jugendhaus Don Bosco

Travel

Closest airport is located at Frankfurt/Main. From there, there are frequent trains to Mainz central station (Hauptbahnhof). One possibility would be to take the S8 from Frankfurt airport to Mainz.

The following lines serve the university from the main station (get off at the stop "Friedrich-von-Pfeiffer-Weg"):

• tram 51 (towards Lerchenberg)
• tram 53 (towards Lerchenberg)
• bus 54 (towards Klein-Winternheim)
• bus 55 (towards Finthen)
• bus 56 (towards Finthen/Wackernheim)
• tram 59 (towards Hochschule Mainz)
• bus 75 (towards Schwabenheim/Ingelheim)
• bus 650 (towards Sprendlingen)

Free afternoon on wednesday

On the free afternoon on Wednesday you may participate in a trip along the rhine river.

We will organize bus and boat transfer from the University to the city of St. Goar up the Rhine valley.
From there you have two options:

1. Visit the Castle Rheinfels, have dinner at a local restaurant and return to Mainz by yourself with the train
2. Take a challenging a hike along the Rheinburgenweg from St Goar to Oberwesel then have dinner in Oberwesel and ruturn to Mainz by train.

In any case: after the ca. 2h boat ride up the rhine river, passing the castle and the famous rock of Loreley, you are on your own (but information will be provided).

Thursday night dinner

There will be a dinner in a restaurant organized on Thursday (probably at Heiliggeist). We will meet at 18:30 inside the restaurant (so that we do not block the street waiting altogether outside). You can sign up for dinner with your dietary requirements at the summer school until Wednesday at noon.

List of Participants (as of June 20, 2018):

Miscellaneous:

• Map of Campus
• Location of Campus within the City of Mainz
• Weather in Mainz
• Deutsche Bahn website