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, run by the algebraic and complex geometry research groups in Bochum, Essen, Cologne, Münster, and Wuppertal since 2013. 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"

Next Meeting

DATE AND PLACE

The next meeting will take place on Friday, December 6th, 2024 at Universität Duisburg-Essen.

TALKS

• Michele Ancona (Nice): Metric and spectral aspects of random plane curves
  
  Abstract:
  A (complex) plane curve is the zero locus in $\mathbb{CP}^2$ of a homogeneous complex polynomial in three variables. Any plane curve is endowed with a Riemannian metric induced by the ambient Fubini-Study metric of the complex projective plane. We give probabilistic lower bounds on some metric and spectral quantities (such as the systole or the spectral gap) of the plane curves when these are chosen randomly in the Fubini-Study ensemble. This is a joint work with Damien Gayet.



• Siarhei Finski (École Polytechnique): Holomorphic Morse Inequalities, Harder-Narasimhan Filtrations and Yang-Mills Functionals
  
  Abstract:
  Holomorphic Morse Inequalities provide upper bounds on the dimension of the cohomology of high tensor powers of a holomorphic line bundle in terms of the volumes of the index sets of closed (1, 1)-forms in the bundle's first Chern class. Motivated by the search for the converse to the Andreotti-Grauert theorem, Demailly conjectured in 2010 that these bounds are sharp in the sense that for any holomorphic line bundle one can cook up a closed (1, 1)-form in its first Chern class so that the volumes of its index sets approximate accurately the dimension of the cohomology groups. We establish this conjecture in a fibered setting by making a relation between the volumes of the index sets with Yang-Mills functionals and the so-called Wess-Zumino-Witten equation studied previously in the context of Mabuchi geometry. The study of Harder-Narasimhan Filtrations of direct image sheaves plays a crucial role in our approach.



• Alice Garbagnati (Milano): Singular symplectic surfaces
  
  Abstract:
  There are several possible generalizations of the definition of irreducible holomorphic symplectic manifold to the singular context (primitive symplectic variety, irreducible symplectic orbifold, irreducible symplectic variety). We review these definitions and we consider them in the lowest dimensional case, i.e. the case of the surfaces. We classify the surfaces which satisfy these definitions, showing that all of them are contractions of rational curves on K3 surfaces, but that not all the possible contractions of rational curves on K3 surfaces satisfy all these definitions. Then we consider the Hilbert scheme of points of the singular surfaces considered, and we show that in some specific cases they are irreducible symplectic orbifolds. The talk is based on a joint work with M. Penegini and A. Perego.

SCHEDULE

10:30 - 11:30 Garbagnati

11:45- 12:45 Ancona

afterwards Lunch break

14:30 - 15:30 Finski

VENUE

Talks will take place in the WSC, 5th floor meeting room. A map how to reach the building can be found here. Please enter the building by the foyer at Thea-Leymann-Straße, then take the elevator to the 5th floor.

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

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

26.4.2024, Cologne: Cécile Gachet, Christian Lehn, Johannes Scheffler

12.7.2024, Bochum: Stéphanie Cupit-Foutou, Bingxiao Liu, Jörg Schürmann