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