# Joint Seminar

# Joint Seminar on Complex Algebraic Geometry and Complex Analysis

(Bochum - Essen - Köln - Münster - Wuppertal)

Photo by Max Greve and Timo Bobert

# The Seminar

The "Joint Seminar on Complex Algebraic Geometry and Complex Analysis" is a research seminar, organised by the algebraic and complex geometry research groups in Bochum, Essen, Cologne, Münster, and Wuppertal. The seminar meets roughly twice per semester for a full day at one of the participating departments. There are three talks per meeting, both by invited guests and by speakers from the organising universities. We aim to leave ample room for discussions.

The talks are open for everyone. Contact one of the organisers if you are interested in attending the meeting. We have some funds that might help to support travel for some junior participants.

Meetings of the seminar are partially supported by

- DFG-GRK 2553 "Symmetries and Classifying Spaces - analytic, arithmetic, and derived" (Essen)
- DFG-SFB/TR 191 "Symplectic structures in geometry, algebra and dynamics" (Bochum-Cologne-Heidelberg)
- ANR-DFG-Projekt QuaSiDy - "Quantization, Singularities, and Holomorphic Dynamics"
- Mathematics Münster

# Next Meeting

### DATE AND PLACE

The next meeting will take place on **Friday, April 26th, 2024** at **Cologne**.

### TALKS

**Cécile Gachet (Berlin) :**Orbifold fundamental groups of log canonical Calabi-Yau surface pairs

Abstract:

In algebraic topology, the Galois correspondence allows to view the fundamental group $\pi_1(X)$ of a topological manifold $X$ as parametrizing unramified covers of $X$, via its subgroups. A notion of orbifold fundamental group for pairs $(X, D)$ has been circulating in the algebro-geometric literature since the 1990ies to play a similar role to the usual fundamental group for non necessarily étale covers. It exhibits a correspondence à la Galois: For a complex projective variety X with relatively mild singularities, and an effective divisor D on X with rational coefficients in [0,1], the normal finite index subgroups of the orbifold fundamental group $\pi_1(X, D)$ correspond to finite Galois covers of $X$ whose ramification is controlled, both geometrically and numerically, by the divisor D. In this talk, we explain how mild positivity conditions on the curvature of a pair $(X, D)$ and on its singularities force the group $\pi_1(X, D)$ to be "rather small". We review a recent result by L. Braun for klt Fano pairs, state some open questions, and present our recent contribution for log canonical Calabi-Yau pairs of dimension 1 and 2. In particular, we explain that the orbifold fundamental group of a log canonical Calabi-Yau surface pair admits a normal subgroup of index at most 7200 that is either abelian of rank at most 4, or part of a very explicit list of nilpotent groups of length 2. We give some examples of the more extreme cases in this result. This talk is based on joint work with J. Moraga and Z. Liu.**Christian Lehn (Bochum):**Singular varieties with trivial canonical class

Abstract:

We will present recent advances in the field of singular varieties with trivial canonical class obtained in joint work with Bakker and Guenancia building on work by many others. This includes the decomposition theorem which says that such a variety is up to a finite cover isomorphic to a product of a torus, irreducible Calabi-Yau (ICY) and irreducible symplectic varieties (ISV). The proof uses a reduction argument to the projective case which in turn is possible due to advances in deformation theory and a certain result about limits of Kähler Einstein metrics in locally trivial families.**Johannes Scheffler (Bayreuth):**Auxiliary Monge-Ampère Equations on Orbifolds

Abstract:

During the last years, the technique developped by Guo-Phong-Tong of using auxiliary Monge-Ampère equations on compact Kähler manifolds led to estimates for the Green's function, diameter estimates and a Sobolev type inequality. It is of utmost importance - e.g. for applications to singular spaces - that the constants are uniform even if the Kähler metrics degenerate; in particular, no bounds for the Ricci curvature are needed. At the heart of the arguments is a mean-value inequality by Guo-Phong-Sturm which we could generalize to the singular setting of Kähler orbifolds (cf. arXiv:2404.02812). I will lecture on this technique including a presentation of my own result and a flavor of the arguments.

### SCHEDULE

**10:30 - 11:30** Lehn

**11:45- 12:45** Scheffler

**afterwards** Lunch break

**14:30 - 15:30** Gachet

### VENUE

Talks will take place in

**Seminarraum 2 (Room 204)**in the

**Mathematical Institute**(Weyertal). A campus map can be found here.

# Organisers

Stéphanie Cupit-Foutou

Ruhr-Universität Bochum

stephanie [dot] cupit [at] ruhr-uni-bochum [dot] de

Daniel Greb

Universität Duisburg-Essen

daniel [dot] greb [at] uni-due [dot] de

Ursula Ludwig

WWU Münster

ursula [dot] ludwig [at] uni-muenster [dot] de

George Marinescu

Universität zu Köln

gmarines [at] math [dot] uni-koeln [dot] de

Jean Ruppenthal

Bergische Universität Wuppertal

jean [dot] ruppenthal [at] math [dot] uni-wuppertal [dot]de

# Past Meetings

**26.4.2013, Bochum:** Tim Kirschner, Christian Miebach, Henrik Seppänen

**28.6.2013, Wuppertal:** Rafael Andrist, Immanuel Stampfli, Matei Toma

**22.11.2013, Bochum:** Sébastien Boucksom, Egmont Porten, Sönke Rollenske

**24.1.2014, Wuppertal:** Clemens Jörder, Helge Ruddat, Jörg Winkelmann

**16.5.2014, Bochum:** Alberto Abbondandolo, Judith Brinkschulte, Julius Ross

**20.6.2014, Wuppertal:** Julie Déserti, Slawomir Dinew, Slawomir Rams

**24.10.2014, Bochum:** Henri Guenancia, Shulim Kaliman, Adriano Tomassini

**15.12.2014, Wuppertal:** Richard Lärkäng, Christian Miebach, Marco Spinaci

**7.5.2015, Essen:** Brent Doran, Erwan Rousseau, Emanuel Scheidegger

**15.6.2015, Bochum:** Roya Beheshti, Daniel Greb, Hossein Raufi

**27.11.2015, Wuppertal:** Francesco Bei, Kai Cieliebak, Tyson Ritter

**1.2.2016, Essen:** Ursula Ludwig, George Marinescu, Wenhao Ou

**25.4.2016, Wuppertal:** Gian Maria Dall’Ara, Christian Lehn, Luca Tasin

**26.6.2016, Cologne:** Chin-Yu Hsiao, Stefan Nemirovski, Nikhil Savale

**25.11.2016, Bochum:** Ana-Maria Brecan, Antonio di Scala, Dan Popovici

**27.1.2017, Essen**: Tim Kirschner, Viêt Anh Nguyên, Stefan Schreieder

**21.4.2017, Wuppertal**: Vicente Cortés, Philipp Naumann, Markus Reineke

**7.7.2017, Cologne**: Roger Bielawski, Dan Coman, Martin Schwald

**3.11.2017, Bochum**: Junyan Cao, Sönke Rollenske, Robert Szöke

**1.2.2018, Essen**: Gilberto Bini, Ruadhaí Dervan, Hendrik Herrmann

**27.4.2018, Wuppertal**: Hugues Auvray, Bernd Stratmann, Michael Lennox Wong

**6.7.2018, Cologne**: Turgay Bayraktar, Jarek Buczynski, Andrew Dancer

**23.11.2018, Bochum**: Ben Anthes, Kevin Fritsch, Ariyan Javanpeykar

**18.1.2019, Essen**: André Belotto, Andreas Höring, Valdemar Tsanov

**12.4.2019, Wuppertal**: Ya Deng, Christian Miebach, Duc Viet Vu

**5.7.2019, Cologne**: Tien-Cuong Dinh, Xiaonan Ma, Nessim Sibony

**21.11.2019, Bochum**: Patrick Graf, Ulrike Rieß, Jonas Stelzig

**16.1.2020, Essen**: Anda Degeratu, Takeo Ohsawa, Mihai Paun

**14.5.2020, Wuppertal (via ZOOM)**: Lynn Heller, Simone Marchesi, Jan Swoboda

**16.7.2020, Cologne (via ZOOM)**: Shin-ichi Matsumura, Sönke Rollenske, Lars Martin Sektnan

**17.11.2020, Bochum (via ZOOM)**: Rafael Andrist, Nicholas Buchdahl, Eleonora di Nezza

**29.1.2021, Essen (via ZOOM)**: Robert Berman, Simone Diverio, Ilaria Mondello

**7.5.2021, Wuppertal (via ZOOM)**: Siarhei Finski, Laszlo Lempert, Katharina Neusser

**18.6.2021, Cologne (via ZOOM)**: Gordon Heier, Louis Ioos, Ursula Ludwig

**26.11.2021, Bochum**: Nikhil Savale, Martin Schwald, Jörg Winkelmann

**11.03.2022, Essen**: Narasimha Chary Bonala, Matteo Costantini, Josias Reppekus

**27.05.2022, Münster**: Markus Banagl, Francesco Bei, Nicolina Istrati

**20.06.2022, Essen**: Workshop organised by JS organisers

**25.11.2022, Wuppertal**: Masanori Adachi, Laurentiu Maxim, Sara Torelli

**20.1.2023, Cologne**: Fabrizio Bianchi, Tobias Harz, Susanna Zimmermann

**28.4.2023, Bochum**: Hans-Joachim Hein, Silvia Sabatini, Richard Wentworth; 10 year celebration

**7.7.2023, Essen**: Ravjot Kohli, Thomas Kurbach, Niklas Müller

**27.10.2023, Münster**: Stefan Nemirovski, Shu Shen, Carolina Tamborini

**19.2.2024, Wuppertal**: Bo Berndtsson, Ana Botero, Jörg Winkelmann