# Joint Seminar - 2013-2023

# 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

At the next meeting, we will **CELEBRATE** that the seminar has been running continuously for **10 YEARS** now !

### DATE AND PLACE

The next meeting will take place on **Friday, April 28th, 2023** at **Ruhr-Universität Bochum** (on-site).

### TALKS

**Hans-Joachim Hein (Münster) :**A gluing construction for surfaces with hyperbolic cusps

Abstract:

We will describe an example of a degeneration of sextics in P^3 with only ordinary triple point singularities on its central fiber. Then we will show how the unique negative Kähler-Einstein metrics on the smooth fibers, which exist by the Aubin-Yau theorem, disintegrate into three distinct geometric pieces on approach to the central fiber: (1) Kobayashi's complete Kähler-Einstein metric on the complement of the triple points, (2) long thin neck regions, and (3) Tian-Yau's complete Ricci-flat Kähler metrics in small neighborhoods of the vanishing cycles. All of the necessary background will be explained in the talk. Joint work with Xin Fu and Xumin Jiang.**Silvia Sabatini (Cologne):**Topological properties of (tall) monotone complexity one spaces

Abstract:

In symplectic geometry it is often the case that compact symplectic manifolds with large group symmetries admit indeed a Kähler structure. For instance, if the manifold is of dimension 2n and it is acted on effectively by a compact torus of dimension n in a Hamiltonian way (namely, there exists a moment map which describes the action), then it is well-known that there exists an invariant Kähler structure. These spaces are called symplectic toric manifolds or also complexity-zero spaces, where the complexity is given by n minus the dimension of the torus. In this talk I will explain how there is some evidence that a similar statement holds true when the complexity is one and the manifold is monotone (the latter being the symplectic analog of the Fano condition in algebraic geometry), namely, that every monotone complexity-one space is simply connected and has Todd genus one, properties which are also enjoyed by Fano varieties. These results are largely inspired by the Fine-Panov conjecture and are in collaboration with Daniele Sepe. Moreover, in ongoing work with Isabelle Charton and Daniele Sepe, we completely classify monotone complexity one space that are “tall” (no reduced space is a point), proving as a byproduct that the torus action extends to a full toric action and that each of these spaces admits a Kähler structure.**Richard Wentworth (Maryland / MPI Bonn):**A Donaldson-Uhlenbeck-Yau theorem for normal projective varieties

Abstract:

The correspondence between polystable reflexive sheaves on compact Kaehler manifolds and the existence of suitably singular Hermitian-Einstein metrics can be extended to normal projective varieties that are smooth in codimension two. A particular application is a characterization of those sheaves which saturate the Bogomolov-Gieseker inequality. This talk will present some of the key details of this result, which is joint work with Xuemiao Chen.

### SCHEDULE

**11:00 - 12:00** Sabatini

**afterwards** Lunch break

**14:00 - 15:00** Hein

**afterwards** Coffee break

**16:00 - 17:00** Wentworth

### VENUE

The talks will take place in Room IA 01/473 at the Ruhr-Universität Bochum. A campus map indicating the location of the Buliding 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